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�Father of Modern Philosophy

�one of the key figures in the Scientific Revolution of the 17th Century, and is sometimes considered the first of the modern school of mathematics.

�He was a soldier. But, after a series of dreams or visions, and after meeting the Dutch philosopher and scientist Isaac Beeckman, who sparked his interest in mathematics and the New Physics, he concluded that his real path in life was the pursuit of true wisdom and science.

�In 1637, he published his ground-breaking philosophical and mathematical treatise "Discours de la méthode" (the “Discourse on Method”), and one of its appendices in particular, "La Géométrie", is now considered a landmark in the history of mathematics.
�Following on from early movements towards the use of symbolic expressions in mathematics by Diophantus, Al-Khwarizmi and François Viète, "La Géométrie" introduced what has become known as the standard algebraic notation, using lowercase a, b and c for known quantities and x, y and z for unknown quantities. It was perhaps the first book to look like a modern mathematics textbook, full of a's and b's, x ²'s, etc.

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THE ERA OF DESCARTES, FERMAT, NEWTON AND LEIBNIZ 

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THE ERA OF DESCARTES, FERMAT, NEWTON AND LEIBNIZ 

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1.Started in 17th century, also known as the beginning of Scientific Revolution period.

2.Galileo: observed the moons of Jupiter in orbit about that planet, using a telescope based on a toy imported from Holland.

3.Tycho Brahe: gathered an enormous quantity of mathematical data describing the positions of the planets in the sky.

4.Johannes Kepler: succeeded in formulating mathematical laws of planetary motion.

5.The analytic geometry developed by René Descartes (1596–1650) allowed those orbits to be plotted on a graph, in Cartesian coordinates.
6.Isaac Newton: discovered the laws of physics explaining Kepler's Laws, and brought together the concepts now known as calculus.

7.Gottfried Wilhelm Leibniz, who is arguably one of the most important mathematicians of the 17th century: developed calculus and much of the calculus notation still in use today.

8.In addition to the application of mathematics to the studies of the heavens, applied mathematics began to expand into new areas, with the correspondence of Pierre de Fermat and Blaise Pascal. Pascal and Fermat set the groundwork for the investigations of probability theory and the corresponding rules of combinatorics in their discussions over a game of gambling.

9. In some sense, this foreshadowed the development of utility theory in the 18th–19th century.

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* Frenchman of the 17th Century

BIOGRAPHY / BACKGROUND HISTORY
* invented modern number theory virtually single-handedly, despite being a small-town amateur mathematician

CONTRIBUTION: TWO SQUARE THEOREM
CONTRIBUTION: FERMAT'S LAST THEOREM

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Click the + button at the bottom right of this page for writing your group's post. PLEASE, A POST PER GROUP FOR EACH SCHOLAR.

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GROUP 8

AIDA AZRINIE BINTI ALI (D20151070905)

SITI SAHARAH BINTI SA'IM (D20151070901)

NUR SYAHIRAH BINTI HASHIM (D20151071569)

NUR ADDINIE NASUHA BINTI RAOP (D20151070898)

BLAISE PASCAL

Ø A French mathematician, inventor, writer, physicist and religious scholar

Ø Blaise Pascal was born on June 19, 1623 in Clermont Ferrand.

Ø Blaise Pascal died at age 39 on August 19, 1662.

Ø He mastered Euclid’s Elements at the age of 12.

Ø He invented syringe andcreated the hydraulic press, an instrument based upon Pascal’s law.

Contribution to Mathematics

He made many great influence on mathematics such as digital calculator, Pascal’s triangle and Pascal’s theorems.

Ø He invented the first digital calculator and name it ‘Pascaline’

Ø At age 16, he wrote and presented a paper on the subject of basic theorems of projective geometry. These theorems known as Pascal‘s theorem.

Pascal’s Triangle

Ø Pascal’s Triangle is a convenient tabular presentation of binomial coefficients, where each number is the sum of two numbers directly above.

Ø Pascal’s triangle can be used in Algebra and in Probability.

Ø Pascal did contribute an elegant proof by defining the numbers by recursion, and he also discovered many useful and interesting patterns among the rows, columns and diagonals of the array of numbers(Luke Mastin, 2010).

Theory of Probability

Ø Developed with collaboration with Pierre de Fermat, the theory was initially applied to gambling before finding application in several other fields as well.

Ø Pascal and Fermat considered two intrasigent problems such as Gambler’s Ruin and Problem of Points.

REFERENCE

http://www.famousmathematicians.net/blaise-pascal/

https://www.thefamouspeople.com/profiles/blaise-pascal-131.php

http://www.storyofmathematics.com/17th_pascal.html

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GROUP 8 

AIDA AZRINIE BINTI ALI (D20151070905) 

SITI SAHARAH BINTI SA’IM (D20151070901) 

NUR SYAHIRAH BINTI HASHIM (D20151071569) 

NUR ADDINIE NASUHA BINTI RAOP (D20151070898) 

 

RENE DESCARTES 


 
Biography/History 

· Was born on March 31, 1596  in Touraine, France and died on February 11, 1650 in Stockholm, Sweden. 
. He was a French mathematician, scientist, and philosopher. 
· Has been called as the father of modern philosophy due to the formulation of the first modern version of mind-body dualism and promoted the development of a new science grounded in observation and experiment. 

Contributions 

· His contribution lies chiefly in geometry. 
· Development of analytic geometry which is applying algebra into geometry. 
· His major contribution lies in bringing forth coordinate system that also bears his name 
· Developed the coordinate system as a “device to locate points on a plane” named Cartesian Coordinate system. 

 
·         Construct a system of knowledge based upon rationalization and logical deduction by negating the principle of perception. 
·         His famous dictum : “Cogito, ergo sum” which means “I think, therefore I am”. 

 

 

References : 

http://www.kcvs.ca/martin/math/math499/projects/descartes/Descartes%20contributions.pdf 

https://www.britannica.com/biography/Rene-Descartes 

https://famous-mathematicians.com/rene-descartes/ 



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Contributions by Descartes, Fermat, Pascal, Newton and Leibniz in Mathematics.

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Contributions by Descartes, Fermat, Pascal, Newton and Leibniz in Mathematics.
GROUP 4: 

Izzah Athirah Binti Samsul Kamar                             D20151070899

Hajar Ummi Umairah Binti Mohamad Nazali             D20151070914

Sofia Dini Binti Muhamad Din                                     D20151070944

Nurul Safikah Binti Saat                                              D20151070938

 
Rene Descartes

Biography/History: 

Date of Birth: 31 March 1596

Birth of Place: La Haye en Touraine, France

Death: February 11, 1650

Death of Place: Stockholm, Sweden

Occupation: Philosopher, mathematician, and scientist

René Descartes was a. Rene Descardes was born in La Haye in 1596. Dubbed the father of modern western philosophy, much of subsequent Western philosophy is a response to his writings, which are studied closely to this day. A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces.

Contribution: In mathematics, his contribution lies chiefly in geometry that’s why today he is known as father of analytical geometry. His main achievement was to bridge the gulf between algebra and geometry. Thus he is widely acclaimed as first mathematician who laid the foundation of modern geometry that resulted in development of analysis and calculus. With regard to algebra, he explained in detail that how algebraic equations can be expressed and explained through use of geometrical shapes.


Pierre de Fermat

Biography/History:

Date of Birth: 17 August 1601

Birth of Place: Beaumont de Lomagne, France

Death: January 12, 1665

Death of Place: Castres, France

Occupation: Mathematician

Best Known Work: Fermat’s Last Theorem

 

Contribution: 

Fermat’s favorite area of math was the development of modern number theories which led to Fermat’s Last Theorem. Fermat’s last theorem states: xn + yn = zn has no non-zero integer solutions for x, y, and z when n> 2. Afterwards Fermat wrote: “I have discovered a truly remarkable proof which this margin is too small to contain.” In 1993 Andrew J. Wiles provided the first proof. Fermat is considered to be one of the “Fathers of Analytic Geometry” along with Rene Descaretes. One of the founders of the probability theory along with Blaise Pascal. Provided a law on light travel and wrote a few papers about calculus.


Isaac Newton


Biography/History: 

Date of Birth: 4 January 1643

Birth of Place: Woolsthrope, Lincolnshire, England.

Death: 20 March 1727

Death of Place: England

Occupation: Mathematician and Physicist

Best of Work: 'Principia' and Newton’s Laws of Motion

 

Contribution: 

1)      Laws of motion: these laws are put into use every day. A forensic scientist would use the laws of motion to gather evidence at an accident scene. A rocket scientist uses these laws to figure out how much thrust is necessary to send a space shuttle into orbit. You might not even realize it, but you use the laws to some extent when you open a jar of peanut butter.
2)      Colour theory (refraction and defraction)
3)      Reflecting telescope: A reflecting telescope is an optical telescope which uses a combination of curved or plane mirrors to reflect light and form an image,rather than lenses to refract or bend light to form an image. It is generally used for astronomical purposes. 
4)      Calculus: Without Calculus, most advances in science and engineering that occurred in the 12th century and are part of everyday life, such as space travel, television, computers, weather prediction, advances in medical imaging, cell phones, internet, would not have happened.

 

Gottfried Wilhelm Leibniz

Biography/History: 

Date of Birth: 1 July 1646

Birth of Place: Leipzig, Germany

Death: 14 November 1716

Death of Place: Hanover, Germany

Occupation: Mathematician and Philosopher.

Best of Work: De Arte Combinatoria (“On the Art of Combination”).

 

Contribution:

1)      He was the first to describe a Pinwheel Calculator in 1685 and invented the Leibniz Wheel, used in the Arithmometer, the first mass-produced mechanical calculator. 
2)      He refined the Binary Number System. which is at the foundation of virtually all Digital Computers.
3)       Leibniz's calculus ratiocinator, which resembles symbolic logic, can be viewed as a way   of making calculations feasible.
4)      Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix.
5)      Leibniz's discoveries of Boolean algebra and of symbolic logic, also relevant to mathematics.
6)      Leibniz thought symbols were important for human understanding. His notation for the infinitesimal calculus is an example of his skill in this regard.
7)      The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x..."

 

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GROUP 8

List of Members:

1)      Aida Azrinie Binti Ali (D20151070905)

2)      Nur Addinie Nasuha Binti Raop (D20151070898)

3)      Nur Syahirah Binti Hashim (D20151071569)

4)      Siti Saharah Binti Sa’im (D20151070901)

Leibniz

a) Biography

Name: Gottfried Wilhelm Leibniz

Born: Gottfried Wilhelm Leibniz

Father’s name: Friedrich Leibniz (a professor of moral philosophy at Leipzig. Friedrich Leibniz)

Mother’s name: Catharina Schmuck (the daughter of a lawyer and Friedrich Leibniz's third wife)

Education: Leibniz entered the Nicolai School in Leipzig. He was taught Latin at school, Leibniz had taught himself far more advanced Latin and some Greek by the age of 12. In 1661, at the age of fourteen, Leibniz entered the University of Leipzig. It may sound today as if this were a truly exceptionally early age for anyone to enter university, but it is fair to say that by the standards of the time he was quite young but there would be others of a similar age. He studied philosophy, which was well taught at the University of Leipzig, and mathematics which was very poorly taught.

Died: 14 November 1716 in Hannover, Hanover (now Germany)

b) Contribution to Mathematics

i) Calculus

Leibniz re-discovered a method of arranging linear equations into an array, now called a matrix, which could then be manipulated to find a solution. A similar method had been pioneered by Chinese mathematicians almost two millennia earlier, but had long fallen into disuse. Leibniz paved the way for later work on matrices and linear algebra by Carl Friedrich Gauss. He also introduced notions of self-similarity and the principle of continuity which foreshadowed an area of mathematics which would come to be called topology.

ii) Binary System

In 1670s, Leibniz worked on the invention of a practical calculating machine, which used the binary system and was capable of multiplying, dividing and even extracting roots, a great improvement on Pascal’s rudimentary adding machine and a true forerunner of the computer. He is usually credited with the early development of the binary number system (base 2 counting, using only the digits 0 and 1), although he himself was aware of similar ideas dating back to the I Ching of Ancient China. Because of the ability of binary to be represented by the two phases "on" and "off", it would later become the foundation of virtually all modern computer systems, and Leibniz's documentation was essential in the development process.

References:

http://www.storyofmathematics.com/17th_leibniz.html

https://plato.stanford.edu/entries/leibniz/

http://www-history.mcs.st-andrews.ac.uk/Biographies/Leibniz.html

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GROUP 8

List of Members:

1)      Aida Azrinie Binti Ali (D20151070905)

2)      Nur Addinie Nasuha Binti Raop (D20151070898)

3)      Nur Syahirah Binti Hashim (D20151071569)

4)      Siti Saharah Binti Sa’im (D20151070901)

PIERRE DE FERMAT

a) Biography

Name: Pierre de Fermat

Born: Beaumont-de-Lomagne, in Southern France in late 1607 or early 1608

Father’s name: Dominique Fermat (successful and wealthy businessman who deal with agricultural products like wheat, wine, cattle and animal hides)

Mother’s name: Claire de Long (came from aristocratic family and died when Pierre 7 years old)

Education: In 1623: Studied civil law at the University of Orleans and graduated in 1626. Later, he moved to the city of Bordeaux where an attorney in the high court. At the same time, he also started doing some high level mathematics.

Family Goals: In June 1631, Fermat (23 years old) married his cousin Louise de Long (15 years old). Both of them had eight children, whereby five of whom survived until adulthood.

b) Contribution to Mathematics

i) Number Theory

Fermat was the inventor of modern number theory. For instance, he was discovered numbers of the form:

The above numbers are called Fermat numbers and when the Fermat number is prime was called as Fermat prime. It was only known when it had been proven by Fermat primes which only for the cases when n=0, 1, 2, 3 and 4. Those numbers are important to the study of prime numbers and Mersenne numbers which both of them are stated in number theory. The figure below showed the example of number theory that Fermat contributed:

ii) Field of Optics

Fermat also made great advancements in the field of optics. According to his research in this area, Fermat was stated that ‘the path between two points taken by a ray of light leaves the optical length stationary under variations in a family of nearby paths’. It was meaning that the ray of lights always prefers the path that has other paths nearby along which the ray would take very nearly the exact same amount to traverse. He also was introduce the laws of refraction and reflection. The figure below shows how Fermat’s principle work:

iii) Fermat’s Little Theorem and Fermat’s Last Theorem

-The Fermat’s Little Theorem in mathematical notation states that if is a prime number, then for any integer a, where p does not divide a

If we have two numbers a and p, where p is a prime number and not a factor of a, then a multiplied by itself p - 1 times and then divided by p will always have a remainder of 1

-A lesson on Pierre de Fermat wouldn't be complete without mention of Fermat's Last Theorem, which states that x n + y n = z nhas no whole integer solutions for n > 2.

References:

https://study.com/academy/lesson/pierre-de-fermat-contributions-to-math-accomplishments.html

https://www.famousscientists.org/pierre-de-fermat/

http://www.storyofmathematics.com/17th_fermat.html

# data[].attributes.body
| MOHAMAD HASIF IQBAL BIN MOHD HATTA | D20151070907
| DINIE RUZAINI BINTI MOH ZAINUDIN | D20151070897
| NUREEN MARINI BINTI MUHAMMAD SUKRI | D20151071230
| ALIAH FATIN BINTI ABU SETAMAN | D20151071246

RENE DESCARTES

Biography/ History.

NAME                                     : RENE DESCARTES

BORN                                     : 31 MARCH 1596

PLACE OF BIRTH                : LA HAYE, TOURAINE, FRANCE

OCCUPATION                      : FRENCH MATHEMATICIAN, SCIENTIST, PHILOSOPHER.

DIED                                       : FEBUARY 11, 1650( AGED 53)

PLACE OF DEATH               : STOCKHLOM, SWEDEN

CONTRIBUTION:

Ø  His contribution lies chiefly in geometry that what we call today as father of analytical geometry.

Ø  His main achievement was to bridge the gulf between algebra and geometry. He explained in detail that how algebraic equation can be expressed and explained through use of geometrical shapes.

Ø  His major contribution lies in bringing forth coordinate system that also bears his name.

Ø  He “invented the convention of representing unknowns in equation by x, y, z”.

Ø  Lastly, he invented rule of signs to establish the positive and negative roots of polynomials.

OTHER DISTRIBUTIONS:

Ø  In his treatise “Discourses on Methods”, he called into question scholastic beliefs and put forward a deductive method implies inferring through generalization.

Ø  His famous dictum is “ Cogito, ergo sum or I Think, therefore I am”.

Ø  Also advanced his views on motion of objects in his treatise “Principles of Philosophy”. His ideas influenced later philosophers like Hobbes, Pascal, Locke and Kant.

References:

Ø  https://famous-mathematicians.com/rene-descartes/

Ø  https://www.britannica.com/biography/Rene-Descartes

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MOHAMAD HASIF IQBAL BIN MOHD HATTA

DINIE RUZAINI BINTI MOH ZAINUDIN

NUREEN MARINI BINTI MUHAMMAD SUKRI

ALIAH FATIN BINTI ABU SETAMAN

Contribution by Fermet in Mathematics

Pierre de Fermat

Pierre de Fermat was a French lawyer that was born around 1601-1607 in Beaumont de Lomagne, and died January 12, 1665, in Castres. We say his birth was around 1601-1607 because details of his early life are fairly sketchy, and it may be that he had an older brother, also named Pierre, that died young. Because of this, some say that Fermat's assumed birthday of August 17, 1601, is actually his brother's birthday, and Fermat was born sometime after that.

Despite his early life being a bit of a mystery, we do know that in his twenties, he attended the University of Orléans where he earned his degree in civil law. At this point, you may be wondering why we are talking about a lawyer in a math lesson, but this is what makes Fermat so fascinating.

You see, Fermat was a lawyer by trade and only studied math as a hobby. This may lead you to believe that his contributions to mathematics are few, but that is definitely not the case! Fermat was, and still is, one of the most well-known and brilliant mathematicians out there.

He never published any of his work, and rarely provided evidence of his claimed proofs for his many conjectures. Although he never published his works, he was in frequent contact with many other mathematicians through correspondence.

Contributions to Mathematics

Fermat made contributions in many areas of mathematics, such as probability theory, analytic geometry, optics, and infinitesimal calculus. He was the inventor of modern number theory, and this was where a lot of his work was concentrated. For instance, Fermat discovered numbers of the form

These numbers are called Fermat numbers, and when a Fermat number is prime, it is called a Fermat prime. The only known and proven Fermat primes are for the cases when n = 0, 1, 2, 3, and 4. These numbers are extremely important to the study of prime numbers and Mersenne numbers, both of which are strongly studied in number theory.

Fermat Numbers

Fermat Primes

Another area that Fermat made great advancements in is in the field of optics. Fermat's research in this area led to what is known as Fermat's principle, which states that 'the path between two points taken by a ray of light leaves the optical length stationary under variations in a family of nearby paths.' In other words, a ray of light always prefers the path that has other paths nearby along which the ray would take very nearly the exact same amount of time to traverse. From this principle, he deduced the laws of refraction and reflection.

Fermat's Little Theorem and Fermat's Last Theorem

Of all of Fermat's mathematical contributions and accomplishments, he is best known for two of his theorems, and those are his Little Theorem and his Last Theorem.

Let's start with Fermat's Little Theorem. In mathematical notation, this theorem states that if p is a prime number, then for any integer a, where p does not divide a,

In words, this says that if we have two numbers a and p, where p is a prime number and not a factor of a, then a multiplied by itself p - 1 times and then divided by p will always have a remainder of 1.

The Little Theorem isn't so little in all it has helped to create today. As an example, if you've ever used your credit card to complete an online transaction, you can thank Fermat and his Little Theorem for that transaction being secure. You see, the code for keeping our online credit card transactions secure highly revolves around this theorem.

A lesson on Pierre de Fermat wouldn't be complete without mention of Fermat's Last Theorem, which states that x n + y n = z n has no whole integer solutions for n > 2.

References

Study.com (2018). Pierre de Fermat: Contributions to Math & Accomplishments. Retrieved on May 14, 2018 from https://study.com/academy/lesson/pierre-de-fermat-contributions-to-math-accomplishments.html

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MOHAMAD HASIF IQBAL BIN MOHD HATTA
DINIE RUZAINI BINTI MOH ZAINUDIN
NUREEN MARINI BINTI MUHAMMAD SUKRI
ALIAH FATIN BINTI ABU SETAMAN

BIOGRAPHY / BACKGROUND HISTORY

Name: Blaise Pascal

Birth: June 19, 1623 in Clermont- Ferrand, France

Death: August 19, 1662

Field of study: Philosopher, Mathematician, Theologian, Physicist, Scientist

Blaise Pascal as known as The Frenchman Blaise Pascal was a child prodigy and pursued many different avenues of intellectual endeavour throughout his life. Was the third of four children and only son to Etienne and Antoinette Pascal.

CONTRIBUTIONS

1)      Pascal has contributed Pascal’s Theorem to the emerging field of Projective Geometry.

2)      Blaise Pascal invented the world’s first fully functional mechanical calculator

3)      Blaise Pascal did important work concerning atmospheric pressure and vacuum

4)      Pascal rediscovered that atmospheric pressure decreases with height

5)      He discovered the influential Pascal’s Law in hydrostatics

6)      The SI unit of pressure is named pascal after him due to his contributions to hydrostatics

7)      Pascal was one of the pioneers of the theory of probability

8)      He popularized the Pascal’s triangle in the western world

9)      He wrote the influential work Provincial letters

10)  His work Pensees is considered a landmark in French prose

REFFERENCES

https://www.biography.com/people/blaise-pascal-9434176

https://famous-mathematicians.com/blaise-pascal/

https://learnodo-newtonic.com/blaise-pascal-contribution

# data[].attributes.body
AMIRA BINTI ZUNIKASMA – D20151070923

AIN RASHIDAH BINTI BIYAMIN – D20151070946

MUSLIHA BINTI MUSTAPA – D20151070900

NURUL AZIELA AISHAH BINTI MOHD BAHARUDDIN – D20151070941

1. Rene Descartes

-          French mathematician and philosopher

-          Born in 1596

-          Also known as father of analytical geometry

Contributions:

-          In geometry, resulted in development of analysis and calculus.

-          In algebra, he explained detailed on how algebraic equations can be expressed and explained through use of geometrical shapes.

-          His major contribution is the Cartesian coordinate system tended to explain the algebraic equations through geometrical shapes.

https://famous-mathematicians.com/rene-descartes/

2. Sir Isaac Newton

-          English physicist and mathematician

-          Born in 1643

Contributions:

-          Developed the principles of modern physics, including the laws of motion

-          In 1687, he published Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)

https://www.biography.com/people/isaac-newton-9422656

3. Frenchman Blaise Pascal

-          A prominent 17th century scientist, philosopher and mathematician.

-          Born on June 19, 1623

Contributions:

-          Wrote a significant treatise on the subject of projective geometry, known as Pascal's Theorem.

-          Built a functional calculating machine, able to perform additions and subtractions, to help his father with his tax calculations

http://www.storyofmathematics.com/17th_pascal.html

4. Gottfried Willhelm Leibniz

-          German philosopher, mathematician, scientist and polymath of the Age of Reason

-          Born on 1 July 1646

Contributions:

-          Discovery of infinitesimal calculus

-          Introduced several notations used to this day (e.g. the elongated S for the integral sign, and the d used for differentials) and, in the autumn of 1676, he discovered the familiar d(xn) = nxn-1dx.

-          He had perfected his binary system of arithmetic (base 2)

https://www.philosophybasics.com/philosophers_leibniz.html

5. Pierre de Fermat

-          Pierre de Fermat was a French lawyer that was born around 1601-1607 in Beaumont de Lomagne, and died January 12, 1665, in Castres. We say his birth was around 1601-1607 because details of his early life are fairly sketchy, and it may be that he had an older brother, also named Pierre, that died young. Because of this, some say that Fermat's assumed birthday of August 17, 1601, is actually his brother's birthday, and Fermat was born sometime after that.

Contributions:

-          Fermat made contributions in many areas of mathematics, such as probability theory, analytic geometry, optics, and infinitesimal calculus.

-          He was the inventor of modern number theory, and this was where a lot of his work was concentrated. For instance, Fermat discovered numbers of the form F n = 2² n + 1

-          He deduced the laws of refraction and reflection.

-          He is best known for two of his theorems, and those are his Little Theorem – a p⁻¹ = 1(mod p) and his Last Theorem –  x n + y n = z n

https://study.com/academy/lesson/pierre-de-fermat-contributions-to-math-accomplishments.html

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Siti Sarah Binti Samsuddin (D20151070930)
Nur Bahirah Binti Badarudin (D20151070937)
Siti Umirah binti Mopid (D20151070926)
Farah Fahilah Binti Ishak (D20151070935)

Blaise Pascal’s Biography

Ø  Born in Clermont, France, in 1623

Ø  in Paris, Pascal was home-schooled by his father who did not trust the local schools

Ø  his father forbidding Pascal from studying mathematics and geometry

Ø  As an amateur mathematician himself, Pascal's father feared an interest in math would cause his son to forego learning other topics.

Ø  before long Pascal was teaching himself geometry.

Ø  After discovering this, Pascal's father relented, teaching his son Euclid and allowing the young Pascal to accompany him to meetings of the local mathematical society

Ø  There Pascal met and conversed with many of the leading mathematicians of the period, including Marin Mersenne and Pierre Gassendi.

Blaise Pascal’s Contributions

Ø  In 1640, he published the Essay on Conic Sections, which made important advances in the transcription of objects onto two-dimensional paper.

Ø  In 1642, he created a rudimentary calculator to aid his father in tax calculations.

Ø  In mathematics, you might recognize his name in Pascal's triangle.

Ø  The numbers that form Pascal's triangle are binomial coefficients. Each number is the sum of the two numbers above it

Ø  Pascal laid the foundation for probability theory

Rene Descartes’s Biography

Ø  René Descartes, Latinized: Renatus Cartesius; adjectival form: "Cartesian”

Ø  Born 31st March 1596

Ø  a French philosopher, mathematician, and scientist. Dubbed the father of modern  Western philosophy, much of subsequent Western philosophy is a response to his writings, which are studied closely to this day.

Ø  A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces.

Ø  He is generally considered one of the most notable intellectual representatives of the Dutch Golden Age.

Rene Descartes’s Contributions

Ø  Cartesian Method and Cartesian Coordinate System

Ø  Descartes' Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system (see below) was named after him.

Ø  He is credited as the father of analytical geometry, the bridge between algebra and geometry, used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the scientific revolution.

Ø  His best known philosophical statement is "Cogito ergo sum" (French: Je pense, donc je suis; I think, therefore I am), found in part IV of Discours de la méthode (1637; written in French but with inclusion of "Cogito ergo sum") and §7 of part I of Principles of Philosophy (1644; written in Latin).

Pierre de Fermat ’s Biography

·         French lawyer that was born around 1601-1607 in Beaumont de Lomagne

·         Died January 12, 1665, in Castres.

·         We say his birth was around 1601-1607 because details of his early life are fairly sketchy, and it may be that he had an older brother, also named Pierre, that died young. Because of this, some say that Fermat's assumed birthday of August 17, 1601, is actually his brother's birthday, and Fermat was born sometime after that.

·         attended the University of Orléans where he earned his degree in civil la.

Pierre de Fermat ’s Contributions

·         Fermat made contributions in many areas of mathematics, such as probability theory, analytic geometry, optics, and infinitesimal calculus.

·         He was the inventor of modern number theory, and this was where a lot of his work was concentrated. For instance, Fermat discovered numbers of the form

F n = 2² n + 1

·         These numbers are called Fermat numbers, and when a Fermat number is prime, it is called a Fermat prime.

·         The only known and proven Fermat primes are for the cases when n = 0, 1, 2, 3, and 4. These numbers are extremely important to the study of prime numbers and Mersenne numbers, both of which are strongly studied in number theory.

·         Another great area made by Fermat is advancements in the field of optics. Fermat's research in this area led to what is known as Fermat's principle, which states that 'the path between two points taken by a ray of light leaves the optical length stationary under variations in a family of nearby paths.

·          In other words, a ray of light always prefers the path that has other paths nearby along which the ray would take very nearly the exact same amount of time to traverse. From this principle, he deduced the laws of refraction and reflection.

|

Gottfried Leibniz biography

·         Gottfried Wilhelm von Leibniz, a German mathematician and philosopher, was born July 1, 1646 in Leipzig, Germany.

·         At age 15, he enrolled at the University of Leipzig, where his father used to teach, and earned both a bachelor's and master's degree in philosophy

·

Gottfried Leibniz contributions

·         Gottfried Leibniz discovered infinitesimal calculus, a distinction he shared with Sir Isaac Newton

·         Infinitesimal calculus is the branch of mathematics that is concerned with differentiation, integrations, and limits of functions

·         Leibniz also developed the law of continuity and transcendental law of homogeneity, cutting-edge theories that were not published or used in mathematics until the 20th century.

·         Gottfried Leibniz's major contribution to mathematics was his discovery of the binary numeral system, or the base-2 system

Sir Isaac Newton’s Biography

·         Born 4 January 1643 in Lincolnshire, England

·         Came from a poor family, allowed to attend school at King’s College for free because of his academic ability and bible knowledge

·         Attended Trinity College with intention of becoming an England Minister, graduated in 1666, bible knowledge impressed teachers again

Sir Isaac Newton’s contribution

·         Developed calculus, revolutionary form of mathematics, allowed for the calculation of the area inside a shape with curved sides, and to calculate the rate of change of physical quantities

·         Newton and Leibniz accused of stealing ideas on calculus from each other, later established that both came up with it at the same time

·         Used prisms to show that light was made up of colours of the rainbow, disproved ancient Greek ideas on light

·         Telescopes in his time broke light into unwanted colours, causing an obscure view of objects, solved problem by being first to construct a telescope with a curved mirror rather than lenses

·         In 1672, he became a member of the royal society (group of scientist who believed in experimental method)

·         Laws of motion

https://schoolworkhelper.net/sir-isaac-newton-biography-contributions/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

https://www.britannica.com/biography/Pierre-de-Fermat

# data[].attributes.body
 
iii) Fermat’s Little Theorem and Fermat’s Last Theorem 


-The Fermat’s Little Theorem in mathematical notation states that if is a prime number, then for any integer a, where p does not divide a 
                      

If we have two numbers a and p, where p is a prime number and not a factor of a, then a multiplied by itself p - 1 times and then divided by p will always have a remainder of 1 

-A lesson on Pierre de Fermat wouldn't be complete without mention of Fermat's Last Theorem, which states that xn + yn = znhas no whole integer solutions for n > 2. 


 
 

References: 

https://study.com/academy/lesson/pierre-de-fermat-contributions-to-math-accomplishments.html 

https://www.famousscientists.org/pierre-de-fermat/ 

http://www.storyofmathematics.com/17th_fermat.html 

 

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# data[].attributes.headline
Contributions by Descartes, Fermat, Pascal, Newton and Leibniz in Mathematics.

# data[].attributes.subject
Contributions by Descartes, Fermat, Pascal, Newton and Leibniz in Mathematics.

# data[].attributes.body
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Rene Descartes

Biography/History:

Date of Birth: 31 March 1596

Birth of Place: La Haye en Touraine, France

Death: February 11, 1650

Death of Place: Stockholm, Sweden

Occupation: Philosopher, mathematician, and scientist

René Descartes was a. Rene Descardes was born in La Haye in 1596. Dubbed the father of modern western philosophy, much of subsequent Western philosophy is a response to his writings, which are studied closely to this day. A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces.

Contribution: In mathematics, his contribution lies chiefly in geometry that’s why today he is known as father of analytical geometry. His main achievement was to bridge the gulf between algebra and geometry. Thus he is widely acclaimed as first mathematician who laid the foundation of modern geometry that resulted in development of analysis and calculus. With regard to algebra, he explained in detail that how algebraic equations can be expressed and explained through use of geometrical shapes.

References:
1) https://www.biography.com/people/ren-descartes-37613
2) https://www.slideshare.net/kamalnafis/ren-descartes-48472676

Pierre de Fermat

Biography/History:

Date of Birth: 17 August 1601

Birth of Place: Beaumont de Lomagne, France

Death: January 12, 1665

Death of Place: Castres, France

Occupation: Mathematician

Best Known Work: Fermat’s Last Theorem

Contribution:

Fermat’s favorite area of math was the development of modern number theories which led to Fermat’s Last Theorem. Fermat’s last theorem states: xn + yn = zn has no non-zero integer solutions for x, y, and z when n> 2. Afterwards Fermat wrote: “I have discovered a truly remarkable proof which this margin is too small to contain.” In 1993 Andrew J. Wiles provided the first proof. Fermat is considered to be one of the “Fathers of Analytic Geometry” along with Rene Descaretes. One of the founders of the probability theory along with Blaise Pascal. Provided a law on light travel and wrote a few papers about calculus.

References:
1) https://www.slideshare.net/aharning/pierre-de-fermat
2) https://www.slideshare.net/sbrierton/pierre-de-fermat-8471140

Isaac Newton

Biography/History:

Date of Birth: 4 January 1643

Birth of Place: Woolsthrope, Lincolnshire, England.

Death: 20 March 1727

Death of Place: England

Occupation: Mathematician and Physicist

Best of Work: 'Principia' and Newton’s Laws of Motion

Contribution:

1)      Laws of motion: these laws are put into use every day. A forensic scientist would use the laws of motion to gather evidence at an accident scene. A rocket scientist uses these laws to figure out how much thrust is necessary to send a space shuttle into orbit. You might not even realize it, but you use the laws to some extent when you open a jar of peanut butter.

2)      Colour theory (refraction and defraction)

3)      Reflecting telescope: A reflecting telescope is an optical telescope which uses a combination of curved or plane mirrors to reflect light and form an image,rather than lenses to refract or bend light to form an image. It is generally used for astronomical purposes.

4)      Calculus: Without Calculus, most advances in science and engineering that occurred in the 12th century and are part of everyday life, such as space travel, television, computers, weather prediction, advances in medical imaging, cell phones, internet, would not have happened.

References:
1) https://www.slideshare.net/lschmidt1170/newton-presentation
2) https://www.slideshare.net/ryedevaught/isaac-newton-8825558
3) https://www.slideshare.net/denissegutierrezm/isaac-newton-history

Gottfried Wilhelm Leibniz

Biography/History:

Date of Birth: 1 July 1646

Birth of Place: Leipzig, Germany

Death: 14 November 1716

Death of Place: Hanover, Germany

Occupation: Mathematician and Philosopher.

Best of Work: De Arte Combinatoria (“On the Art of Combination”).

Contribution:

1)      He was the first to describe a Pinwheel Calculator in 1685 and invented the Leibniz Wheel, used in the Arithmometer, the first mass-produced mechanical calculator.

2)      He refined the Binary Number System. which is at the foundation of virtually all Digital Computers.

3)       Leibniz's calculus ratiocinator, which resembles symbolic logic, can be viewed as a way   of making calculations feasible.

4)      Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix.

5)      Leibniz's discoveries of Boolean algebra and of symbolic logic, also relevant to mathematics.

6)      Leibniz thought symbols were important for human understanding. His notation for the infinitesimal calculus is an example of his skill in this regard.

7)      The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x..."

References:
1) https://www.slideshare.net/shivekkhurana/gottfried-wilhelm-leibniz-28847575
2) https://www.slideshare.net/sbrierton/gottfried-leibniz-8472549
3) https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz

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RENÉ DESCARTES

BIOGRAPHY/HISTORY

·         René Descartes is often credited with being the “Father of Modern Philosophy”

·         He studied classics, logic and traditional Aristotelian philosophy at the Jesuit college of La Flèche in Anjou.

·         He also learnt mathematics and he cultivate the study of geometry in Paris.

·         Rene Descartes, French mathematician and philosopher was born in 1596.

·         In mathematics, his contribution lies chiefly in geometry that’s why today he is known as father of analytical geometry.

·         His main achievement was to bridge the gulf between algebra and geometry.

·         He is widely acclaimed as first mathematician who laid the foundation of modern geometry that resulted in development of analysis and calculus.

·         With regard to algebra, he explained in detail that how algebric equations can be expressed and explained through use of geometrical shapes.

·         In 1637, he published his ground-breaking philosophical and mathematical treatise "Discours de la méthode" (the “Discourse on Method”), and one of its appendices in particular, "La Géométrie".

CONTRIBUTION

La Géométrie

·         In La Géométrie Descartes developed his analytic geometry as an example of how his method could arrive at certain knowledge.

·         "La Géométrie" introduced what has become known as the standard algebraic notation, using lowercase a, b and c for known quantities and x, y and z for unknown quantities.

·         In "La Géométrie" ,Descartes first proposed that each point in two dimensions can be described by two numbers on a plane, one giving the point’s horizontal location and the other the vertical location, which have come to be known as Cartesian coordinates.

·         He used perpendicular lines (or axes), crossing at a point called the origin, to measure the horizontal (x) and vertical (y) locations, both positive and negative, thus effectively dividing the plane up into four quadrants.

ADDITIONAL INFO

Descartes’s rule of signs

·         In algebra, rule for determining the maximum number of positive real number solutions (roots) of a polynomial equation in one variable based on the number of times that the signs of its real number coefficients change when the terms are arranged in the canonical order (from highest power to lowest power)

For example, the polynomial

changes sign three times, so it has at most three positive real solutions. Substituting −x for x gives the maximum number of negative solutions (two).

The rule of signs was given, without proof, by the French philosopher and mathematician René Descartes in La Géométrie (1637). The English physicist and mathematician Sir Isaac Newton restated the formula in 1707, though no proof of his has been discovered; some mathematicians speculate that he considered its proof too trivial to bother recording. The earliest known proof was by the French mathematician Jean-Paul de Gua de Malves in 1740. The German mathematician Carl Friedrich Gauss made the first real advance in 1828 when he showed that, in cases where there are fewer than the maximum number of positive roots, the deficit is always by an even number. Thus, in the example given above, the polynomial could have three positive roots or one positive root, but it could not have two positive roots.

REFERENCE

http://www.purplemath.com/modules/drofsign.htm

https://mathed.byu.edu/~williams/Classes/300W2012/PDFs/PPTs/Descartes%20Fermat%20Analytic%20Geometry.pdf

http://www.storyofmathematics.com/17th_descartes.html

https://prezi.com/qubkqclnucru/the-mathematical-contributions-of-rene-descartes/

GOTTFRIED LEIBNIZ

BIOGRAPHY.

Gottfried Leibniz (1646-1716)

Real name : Gottfried Wilhelm (von) Leibniz

Born on : July 1, 1646  toward the end of Thirty Year’s War

Born in : Leipzig, Holy Roman Empire

Subject of study : Mathematics, Law, Modern Logic and Analytic Philosophy.

LEIBNIZ CONTRIBUTION IN MATHEMATICS.

·         Leibniz developed a very similar theory of calculus as Newton, apparently completely independently.

·         Leibniz states a theorem for differentiating a product for any "curves".

·         Leibniz first introduced the modern symbols for integration and differentiation.

·         Within the short period of about two months he had developed a complete theory of differential calculus and integral calculus (see the section on Newton for a brief description and explanation of the development of calculus).

·         Leibniz believed there are categories for simple terms, or concepts, which could then be arranged systematically to form propositions. Propositions, or complex terms, should then be categorized to form truths, which then could be further arranged to form deductive arguments.

·         Leibniz published his Dissertation De Arte Combinatoria.

·         Leibniz re-discovered a method of arranging linear equations into an array, now called a matrix, which could then be manipulated to find a solution.

·          Leibniz paved the way for later work on matrices and linear algebra by Carl Friedrich Gauss.

·         He also introduced notions of self-similarity and the principle of continuity which foreshadowed an area of mathematics which would come to be called topology.

·         He discovered a way to find the moment of any curve, by building on Pascal's method of finding the moment of a circle's quadrant through the use of a "characteristic triangle".

·         Leibniz believed he had found the "arithmetical quadrature" of the circle through what is the equivalent of   1 -1/3 +1/5 -1/7 +... = p/4

·          He was recognized for introducing Transcendental Law of Homogeneity and the Law of Continuity.

·         He is usually credited with the early development of the binary number system (base 2 counting, using only the digits 0 and 1), although he himself was aware of similar ideas dating back to the I Ching of Ancient China.

Binary Number System

ADDITIONAL INFORMATION.

·         It was also through the influence of Pascal's works that Leibniz discovered his transmutation theorem, for which he gave a detailed proof in 1675 .

·         Through this breakthrough, Leibniz claimed he had found a method to determine the quadratures of virtually all curves.

·         Leibniz is also often considered the most important logician between Aristotle in Ancient Greece and George Boole and Augustus De Morgan in the 19th Century.

REFERENCES.

http://www.storyofmathematics.com/17th_leibniz.html

http://scienceworld.wolfram.com/biography/Leibniz.html

http://sites.math.rutgers.edu/courses/436/Honors02/leibniz.html

http://www.famousmathematicians.net/gottfried-leibniz/

CONTRIBUTION BY FERMAT IN MATHEMATICS

BIOGRAPHY

NAME : Pierre de Fermat is a French

BORN : Born around 1601-1607 in Beaumont de Lomagne

DIED : Died on January 12, 1665 in Castres

CONTRIBUTIONS : Probability Theory, Analytic Geometry, Optics, And Infinitesimal Calculus.

FERMAT CONTRIBUTION IN MATHEMATICS.

Fermat died at a young age but he still has a contribution in mathematics. Fermat was a lawyer in mathematics and Fermat contributions in mathematics making Fermat a very interesting person. Fermat's contribution in mathematics has also made him a famous and brilliant overseas. Fermat did not release any of his works in mathematics-related books but the evidence of Fermat contributions in the field of mathematics was through his correspondence that often met with many mathematicians. Fermat who the first has found the shape number in . The Fermat findings in the form of numbers have been known as Fermat number where Fermat uses number prime only and makes Fermat prime. The only known and proven Fermat primes are for the cases when n = 0, 1, 2, 3, and 4. These numbers are extremely important to the study of prime numbers and Mersenne numbers, both of which are strongly studied in number theory.

In addition, the contribution of Fermat in mathematics is where Fermat has shown that any prime number when divided by number 4 will give the balance 1. It can also be written in the form of 4n + 1. Fermat has proved the use of the Two Square Theorem also known as Little Theorem which is always used to prove the prime number.

The Fermat contribution in the probability is to find the fundamental theories for the probability that Fermat is associated with pascal which finds the probability theory. Thus, Fermat and pascal have become the founders for the existence of probability theory used today.

REFERENCES

https://study.com/academy/lesson/pierre-de-fermat-contributions-to-math-accomplishments.html

http://www.storyofmathematics.com/17th_fermat.html

http://famous-mathematicians.org/pierre-de-fermat/

FRENCHMAN BLAISE PASCAL

BIOGRAPHY

Frenchman Blaise Pascal was the one that laid the foundation for the modern  and then formulated what came to be known as Pascal’s principle of pressure and many more.

CONTRIBUTION

1.      Described a convenient tabular presentation for binomial coefficients, now called Pascal's triangle where each number is the sum of the two numbers directly above it.

The table of binomial coefficients known as Pascal’s Triangle

2.      Made the conceptual leap to use the Triangle to help solve problems in probability theory.

Fermat and Pascal’s solution to the Problem of Points

3.      Invented the world’s first fully functional mechanical calculator.

Blaise Pascal constructed a mechanical calculator that can performs addition and subtraction directly. However, by using this mechanical calculator, multiplication and division can be solved through repeated addition or subtraction. The functional mechanical calculator known as Pascal’s calculator or the Pascaline, was especially successful in the design of its carry mechanism, which adds 1 to 9 on one dial, and when it changes from 9 to 0, carries 1 to the next dial.

4.      Discovered the influential Pascal’s Law in hydrostatics

Pascal’s Law is one of the most important discoveries in hydrostatics which uses hydraulic pressure to multiply force. Instead of as the underlying principle of the hydraulic press. It states that pressure applied to a confined liquid is transmitted undiminished through the liquid in all directions regardless of the area to which the pressure is applied.  Syringe was also invented by Pascal as an application of his principle.

REFERENCES

https://www.britannica.com/biography/Blaise-Pascal

http://www.storyofmathematics.com/17th_pascal.html

https://learnodo-newtonic.com/blaise-pascal-contribution

Isaac Newton

BIOGRAPHY

Best known for his work on gravity, but he worked on and discovered many other scientific wonders during his lifetime (1642-1727). He make huge advancements in mathematics and created theorems that we still use heavily to this day.

CONTRIBUTION

1.      Find way to find the 🤬 of a tangent line to the curve at any point in the calculus.

Newton’s work in calculus intitially started as a way to find the 🤬 at any point on a curve whose 🤬 was constantly varying (the 🤬 of a tangent line to the curve at any point). He calculated the derivative in order to find the 🤬. He called this the “method of fluxions” rather than differentiation.

2.      Create the First Fundamental Theorem of Calculus

Newton’s Fundamental Theorem of Calculus states that differentiation and integration are inverse operations, so that, if a function is first integrated and then differentiated (or vice versa), the original function is retrieved.

The integral of a curve can be thought of as the formula for calculating the area bounded by the curve and the x axis between two defined boundaries. For example, on a graph of velocity against time, the area “under the curve” would represent the distance travelled.

REFERENCES

https://askabiologist.asu.edu/sir-isaac-newton

https://3010tangents.wordpress.com/2015/05/05/isaac-newton-and-his-contributions-to-mathematics/

http://www.storyofmathematics.com/17th_newton.html

# data[].attributes.body
known as general topology and lastlym he proposed the basis for the modern branch of mathematics known as symbolic logic.

 

Additional info: 

 

He never married and is known to complain about money at times, his sister’s stepson inherited what he left behind after his death. Leibniz was fond of documenting all this mathematical pursuits and is known to have backdating and tweaking his journal too which fuels the debate centered on ‘Calculus and Newton’.

 

References: 

 

https://famous-mathematicians.com/gottfried-leibniz/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

 
 

 

Add comment

# data[].attributes.body
known as general topology and lastlym he proposed the basis for the modern branch of mathematics known as symbolic logic.

 

Additional info: 

 

He never married and is known to complain about money at times, his sister’s stepson inherited what he left behind after his death. Leibniz was fond of documenting all this mathematical pursuits and is known to have backdating and tweaking his journal too which fuels the debate centered on ‘Calculus and Newton’.

 

References: 

 

https://famous-mathematicians.com/gottfried-leibniz/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

 
 

 

Add comment
 
Anonymous
1m
 known as general topology and lastlym he proposed the basis for the modern branch of mathematics known as symbolic logic.

 

Additional info: 

 

He never married and is known to complain about money at times, his sister’s stepson inherited what he left behind after his death. Leibniz was fond of documenting all this mathematical pursuits and is known to have backdating and tweaking his journal too which fuels the debate centered on ‘Calculus and Newton’.

 

References: 

 

https://famous-mathematicians.com/gottfried-leibniz/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

 
 

 

Add comment
 

Add comment

# data[].attributes.body
known as general topology and lastlym he proposed the basis for the modern branch of mathematics known as symbolic logic.

 

Additional info: 

 

He never married and is known to complain about money at times, his sister’s stepson inherited what he left behind after his death. Leibniz was fond of documenting all this mathematical pursuits and is known to have backdating and tweaking his journal too which fuels the debate centered on ‘Calculus and Newton’.

 

References: 

 

https://famous-mathematicians.com/gottfried-leibniz/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

 
 

 

Add comment
known as general topology

Anonymous
1m
 known as general topology and lastlym he proposed the basis for the modern branch of mathematics known as symbolic logic.

 

Additional info: 

 

He never married and is known to complain about money at times, his sister’s stepson inherited what he left behind after his death. Leibniz was fond of documenting all this mathematical pursuits and is known to have backdating and tweaking his journal too which fuels the debate centered on ‘Calculus and Newton’.

 

References: 

 

https://famous-mathematicians.com/gottfried-leibniz/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

 
 

 

Add comment
 

Add comment
 
Anonymous
1m
 known as general topology and lastlym he proposed the basis for the modern branch of mathematics known as symbolic logic.

 

Additional info: 

 

He never married and is known to complain about money at times, his sister’s stepson inherited what he left behind after his death. Leibniz was fond of documenting all this mathematical pursuits and is known to have backdating and tweaking his journal too which fuels the debate centered on ‘Calculus and Newton’.

 

References: 

 

https://famous-mathematicians.com/gottfried-leibniz/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

 
 

 

Add comment
 
Anonymous
1m
 known as general topology and lastlym he proposed the basis for the modern branch of mathematics known as symbolic logic.

 

Additional info: 

 

He never married and is known to complain about money at times, his sister’s stepson inherited what he left behind after his death. Leibniz was fond of documenting all this mathematical pursuits and is known to have backdating and tweaking his journal too which fuels the debate centered on ‘Calculus and Newton’.

 

References: 

 

https://famous-mathematicians.com/gottfried-leibniz/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

 
 

 

Add comment
 

Add comment
 

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ISAAC NEWTON
Biography / History:

born on January 4, 1643, in Woolsthorpe, Lincolnshire, England. Using the "old" Julien calendar, Newton's birth date is sometimes displayed as December 25, 1642.

Isaac Newton was a physicist and mathematician who developed the principles of modern physics.

In 1687, he published his most acclaimed work, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)

In 1705, he was knighted by Queen Anne of England, making him Sir Isaac Newton.

Newton was enrolled at the King's School in Grantham, a town in Lincolnshire.

By the time he reached 80 years of age, Newton was experiencing digestion problems and had to drastically change his diet and mobility. In March 1727, Newton experienced severe pain in his abdomen and blacked out, never to regain consciousness. He died the next day, on March 31, 1727, at the age of 84.

Contributions:

Newton made discoveries in optics, motion and mathematics.

Newton's first major public scientific achievement was designing and constructing a reflecting telescope in 1668.

References:
https://en.wikipedia.org/wiki/Isaac_Newton#Early_life
https://www.biography.com/people/isaac-newton-9422656
https://www.britannica.com/biography/Isaac-Newton#ref12254

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AIDA AZRINIE BINTI ALI (D20151070905)

SITI SAHARAH BINTI SA’IM (D20151070901)

NUR SYAHIRAH BINTI HASHIM (D20151071569)

NUR ADDINIE NASUHA BINTI RAOP (D20151070898)

RENE DESCARTES

Biography/History

· Was born on March 31, 1596  in Touraine, France and died on February 11, 1650 in Stockholm, Sweden.

. He was a French mathematician, scientist, and philosopher.

· Has been called as the father of modern philosophy due to the formulation of the first modern version of mind-body dualism and promoted the development of a new science grounded in observation and experiment.

Contributions

· His contribution lies chiefly in geometry.

· Development of analytic geometry which is applying algebra into geometry.

· His major contribution lies in bringing forth coordinate system that also bears his name

· Developed the coordinate system as a “device to locate points on a plane” named Cartesian Coordinate system.

·         Construct a system of knowledge based upon rationalization and logical deduction by negating the principle of perception.

·         His famous dictum : “Cogito, ergo sum” which means “I think, therefore I am”.

References :

http://www.kcvs.ca/martin/math/math499/projects/descartes/Descartes%20contributions.pdf

https://www.britannica.com/biography/Rene-Descartes

https://famous-mathematicians.com/rene-descartes/

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| CHIMAOGACHI BINTI LOWRANCE | D20151070891
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| NUR SYUHADAH BINTI AZIMIDON | D20161074109

René Descartes

Biography / History:

Name                    : René Descartes

Occupation         : Academic, Philosopher, Mathematician, Scientist

Birth date            : March 31, 1596

Death date         : February 11, 1650

Education            : Jesuit College of Henri IV, University if Poitiers

Place of birth     : La Haye, Touraine, France

Place of death   : Stockholm, Sweden

Contributions:

·         In mathematics, his contribution lies chiefly in geometry that’s why today he is known as father of analytical geometry.

·         He also sought to find out the systematic meaning of knowledge by application of mathematical techniques.

·         Descartes also tended to apply geometric method to physics and also explained it by deductive method that results can be inferred by perceptions of geometric properties of body.

·         His major contribution lies in bringing forth coordinate system that also bears his name. This Cartesian coordinate system tended to explain the algebraic equations through geometrical shapes.

·         he also invented rule of signs to establish the positive and negative roots of polynomial.

Additional info:

·         Descartes is considered by many to be the father of modern philosophy, because his ideas departed widely from current understanding in the early 17th century, which was more feeling-based. While elements of his philosophy weren’t completely new, his approach to them was.

·         In his treatise “Discourses on Methods”, he called into question scholastic beliefs and put forward a deductive method that implies inferring through generalization rather than sensation. As his famous dictum is “Cogito, ergo sum” or “I think, therefore I am”.

References:

https://famous-mathematicians.com/rene-descartes/

https://www.biography.com/people/ren-descartes-37613

Pierre de Fermat

Biography / History:

Name                                    : Pierre de Fermat

Birth date                            : August 17, 1601 Beaumont-de-Lomagne, France

Death date                         : January 12, 1665 Castres, France

Notable works                  : Introduction to Loci

Subject of study               : Analytic geometry, differentiation, Fermat’s last theorem, Fermat   theorem and prime

Contributions:

·         The analytic geometry. A contemporary of René Descartes, he independently came up with a three-dimensional geometry, but did not publish his work, and the field became known as Cartesian geometry.

·         The number theory. His brilliant research entitled him to rank as the founder of the modern number theory.

·         He stated the Fermat’s Last Theorem (1637) as well as “Fermat’s little theorem” (1640), and developed the inductive “infinite descent method”, which was the first general proof of Diophantine questions.

·         Mathematical analysis. He discovered an original method for determining maxima, minima, and tangents to various curves that was equivalent to differential calculus. He obtained a technique for finding the centres of gravity of various plane and solid figures, which led to his further work in quadrature.

·         The theory of probability. In 1654, Blaise Pascal wrote a letter asking about Fermat’s views on probability. Their series of correspondences became the foundation of probability theory.

Additional info:

Major works: “Ad Locos Planos et Solidos Isagoge” (Introduction to Plane and Solid Loci) (1636, publ,. 1679), “The method of finding of the maximum and minimum values“Methodus and disquirendam maximam et minima” (publ,. 1679), “De tangentibus linearum curvarum”. Issued in the book “The different mathematical works” (“Varia opera mathematica”, Tolosae, 1679)

References:

https://www.britannica.com/biography/Pierre-de-Fermat

https://geniusrevive.com/en/pierre-de-fermat-one-of-the-greatest-mathematicians-of-all-times/

Blaise Pascal

Biography / History:

Name                                    : Blaise Pascal

Born                                      : June 19, 1623 Clermont-Ferrand, France

Died                                      : August 19, 1662 Paris, France

Notable works                  : “Essai pour les coniques”. Les Provinciales”, “Pensees”, “The Physical  Treatises of Pascal”, “Traite du triangle arithmetique”

Subjects of study: probability, conic section, Jansenism, grace, Pascal’s triangle

Contributions:

Pascal had a great influence on mathematics. ‘Pascal’s triangle’ (1953) and ‘Pascal’s theorems’ are two examples of the many influences that Pascal made to this field. Pascal was inspired by his friend who had a big interest in gambling and introduced the concept of probability and the idea of expected value was presented.

One of the major contributions of Pascal includes his textbook written for a school ‘Petites-Ecoles de Port-Royal’. It was ‘De l’Esprit géométrique’ which means ‘Of the Geometrical Spirit’. This work of his was however published a century after his death. He worked around the idea in the ‘De l’Esprit géométrique’ on the theory of definition.

Looking deeply into geometric axiomatic method he also wrote ‘De L’Art De Persuader’ (The Art of Persuasion). It was Pascal’s work on ‘binomial coefficients’ that guided Newton to discover the binomial theorem.

References:
https://www.britannica.com/biography/Blaise-Pascal
https://famous-mathematicians.com/blaise-pascal/

Isaac Newton
Biography/History:

Name: Isaac Newton
Born: January 4, 1643
Death: March 31, 1727
Occupation: Physicist and mathematician

Contributions:

Developed a new theory of light, discovered and quantified gravitation, and pioneered a revolutionary new approach to mathematics: infinitesimal calculus.

His theory of calculus built on earlier work by his fellow Englishmen John Wallis and Isaac Barrow, as well as on work of such Continental mathematicians as Rene Descrates, Pieree de Fermat, Bonaventura Cavalieri, Johann van Waveren Hudde and Gilles Personne de Roberval.

Unlike the static geometry of the Greeks calculus allowed mathematicians and engineers to make sense of the motion and dynamic change in the changing world around us, such as the orbits of planets, the motion of fluids, and etc.

References:
https://www.biography.com/people/isaac-newton-9422656
http://www.storyofmathematics.com/17th_newton.html

Gottfried Leibniz

Biography/History:

NAME
Gottfried Leibniz
BORN

July 1, 1646

DIED

November 14, 1716 (aged 70)

NOTABLE WORKS

“De Arte Combinatoria”

“De Principio Individui”

“Hypothesis Physica Nova”

“Monadologia”

“Nova Methodus pro Maximis et Minimis”

“On the Ultimate Origin of Things”

“Principes de la nature et de la grâce fondés en raison”

“Reflections on Knowledge, Truth, and Ideas”

“Système nouveau”

“Theodicy”

Contributions:

Leibniz made many contributions to the study of differential equations, discovering the method of separation of variables

reduction of homogeneous equations to separable ones,

and the procedure for solving first order linear equations.

He used the idea of the determinant

References:
http://scienceworld.wolfram.com/biography/Leibniz.html
https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz

# data[].attributes.body
AIDA AZRINIE BINTI ALI (D20151070905)

SITI SAHARAH BINTI SA’IM (D20151070901)

NUR SYAHIRAH BINTI HASHIM (D20151071569)

NUR ADDINIE NASUHA BINTI RAOP (D20151070898)

ISAAC NEWTON

Biography/History

·  Was born on January 4, 1643 in Lincolnshire, England and died on March 31, 1727 in London.

·  Was an English physicist and mathematician, who was the culminating figure of the scientific revolution of the 17th century.

·  Went to The King’s School, Grantham from the time he was twelve until he was seventeen

Contributions

· work in calculus intitially started as a way to find the 🤬 at any point on a curve whose 🤬 was constantly varying

· create the First Fundamental Theorem of Calculus

· discovery of the generalised binomial theorem

· contributed to the theory of finite differences

· developed a method for finding better approximation to the zeroes or roots of a function, and was the first to use infinite power series

· developed theories in optics and gravitation

· observed that prisms refract different colors at different angles, which led him to conclude that color is a property intrinsic to light

References :

https://3010tangents.wordpress.com/2015/05/05/isaac-newton-and-his-contributions-to-mathematics/

https://www.britannica.com/biography/Isaac-Newton

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GROUP 2

List of members :
Siti Sarah Binti Samsuddin (D20151070930)
Nur Bahirah Binti Badarudin (D20151070937)
Siti Umirah binti Mopid (D20151070926)
Farah Fahilah Binti Ishak (D20151070935)

Blaise Pascal’s Biography

Ø  Born in Clermont, France, in 1623

Ø  in Paris, Pascal was home-schooled by his father who did not trust the local schools

Ø  his father forbidding Pascal from studying mathematics and geometry

Ø  As an amateur mathematician himself, Pascal's father feared an interest in math would cause his son to forego learning other topics.

Ø  before long Pascal was teaching himself geometry.

Ø  After discovering this, Pascal's father relented, teaching his son Euclid and allowing the young Pascal to accompany him to meetings of the local mathematical society

Ø  There Pascal met and conversed with many of the leading mathematicians of the period, including Marin Mersenne and Pierre Gassendi.

Blaise Pascal’s Contributions

Ø  In 1640, he published the Essay on Conic Sections, which made important advances in the transcription of objects onto two-dimensional paper.

Ø  In 1642, he created a rudimentary calculator to aid his father in tax calculations.

Ø  In mathematics, you might recognize his name in Pascal's triangle.

Ø  The numbers that form Pascal's triangle are binomial coefficients. Each number is the sum of the two numbers above it

Ø  Pascal laid the foundation for probability theory

Rene Descartes’s Biography

Ø  René Descartes, Latinized: Renatus Cartesius; adjectival form: "Cartesian”

Ø  Born 31st March 1596

Ø  a French philosopher, mathematician, and scientist. Dubbed the father of modern  Western philosophy, much of subsequent Western philosophy is a response to his writings, which are studied closely to this day.

Ø  A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces.

Ø  He is generally considered one of the most notable intellectual representatives of the Dutch Golden Age.

Rene Descartes’s Contributions

Ø  Cartesian Method and Cartesian Coordinate System

Ø  Descartes' Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system (see below) was named after him.

Ø  He is credited as the father of analytical geometry, the bridge between algebra and geometry, used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the scientific revolution.

Ø  His best known philosophical statement is "Cogito ergo sum" (French: Je pense, donc je suis; I think, therefore I am), found in part IV of Discours de la méthode (1637; written in French but with inclusion of "Cogito ergo sum") and §7 of part I of Principles of Philosophy (1644; written in Latin).

Pierre de Fermat ’s Biography

Ø  French lawyer that was born around 1601-1607 in Beaumont de Lomagne

Ø  Died January 12, 1665, in Castres.

Ø  We say his birth was around 1601-1607 because details of his early life are fairly sketchy, and it may be that he had an older brother, also named Pierre, that died young. Because of this, some say that Fermat's assumed birthday of August 17, 1601, is actually his brother's birthday, and Fermat was born sometime after that.

Ø  attended the University of Orléans where he earned his degree in civil la.

Pierre de Fermat ’s Contributions

Ø  Fermat made contributions in many areas of mathematics, such as probability theory, analytic geometry, optics, and infinitesimal calculus.

Ø  He was the inventor of modern number theory, and this was where a lot of his work was concentrated. For instance, Fermat discovered numbers of the form :

Ø  F n = 2² n + 1

Ø  These numbers are called Fermat numbers, and when a Fermat number is prime, it is called a Fermat prime.

Ø  The only known and proven Fermat primes are for the cases when n = 0, 1, 2, 3, and 4. These numbers are extremely important to the study of prime numbers and Mersenne numbers, both of which are strongly studied in number theory.

Ø  Another great area made by Fermat is advancements in the field of optics. Fermat's research in this area led to what is known as Fermat's principle, which states that 'the path between two points taken by a ray of light leaves the optical length stationary under variations in a family of nearby paths.

Ø   In other words, a ray of light always prefers the path that has other paths nearby along which the ray would take very nearly the exact same amount of time to traverse. From this principle, he deduced the laws of refraction and reflection.

|

Gottfried Leibniz biography

Ø  Gottfried Wilhelm von Leibniz, a German mathematician and philosopher, was born July 1, 1646 in Leipzig, Germany.

Ø  At age 15, he enrolled at the University of Leipzig, where his father used to teach, and earned both a bachelor's and master's degree in philosophy

Gottfried Leibniz contributions

Ø  Gottfried Leibniz discovered infinitesimal calculus, a distinction he shared with Sir Isaac Newton

Ø  Infinitesimal calculus is the branch of mathematics that is concerned with differentiation, integrations, and limits of functions

Ø  Leibniz also developed the law of continuity and transcendental law of homogeneity, cutting-edge theories that were not published or used in mathematics until the 20th century.

Ø  Gottfried Leibniz's major contribution to mathematics was his discovery of the binary numeral system, or the base-2 system

Sir Isaac Newton’s Biography

Ø  Born 4 January 1643 in Lincolnshire, England

Ø  Came from a poor family, allowed to attend school at King’s College for free because of his academic ability and bible knowledge

Ø  Attended Trinity College with intention of becoming an England Minister, graduated in 1666, bible knowledge impressed teachers again

Sir Isaac Newton’s contribution

Ø  Developed calculus, revolutionary form of mathematics, allowed for the calculation of the area inside a shape with curved sides, and to calculate the rate of change of physical quantities

Ø  Newton and Leibniz accused of stealing ideas on calculus from each other, later established that both came up with it at the same time

Ø  Used prisms to show that light was made up of colours of the rainbow, disproved ancient Greek ideas on light

Ø  Telescopes in his time broke light into unwanted colours, causing an obscure view of objects, solved problem by being first to construct a telescope with a curved mirror rather than lenses

Ø  In 1672, he became a member of the royal society (group of scientist who believed in experimental method)

Ø  Laws of motion

References :

https://schoolworkhelper.net/sir-isaac-newton-biography-contributions/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

https://www.britannica.com/biography/Pierre-de-Fermat

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MOHAMAD HASIF IQBAL BIN MOHD HATTA
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DINIE RUZAINI BINTI MOH ZAINUDIN
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NUREEN MARINI BINTI MUHAMMAD SUKRI
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Biography / History:

Sir Isaac Newton, he was an English mathematician, astronomer, theologian, author and physicist who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. He was born on January 4, 1643 in Woolsthorpe Manor, United Kingdom and died on March 31, 1727 in Kensington, London, United Kingdom. He published Philosophiae Naturalis Principia Mathematica (Mathematical Principles Of Natural Philosophy) in 1687 which has been called the single most influential book on physics. The name Sir Isaac Newton was knighted by Queen Anne of England in 1705.

Contributions: In mathematics, he is the founder of Calculus. He contribute in differentiation, integration, fluxions and inverfluxion.  His theory of calculus built on earlier work by his fellow Englishmen John Wallis and Isaac Barrow, as well as on work of such Continental mathematicians as Rene Descartes, Pierre de Fermat, Bonaventura Cavalieri, Johann van Waveren Hudde and Gilles Personne de Roberval. Unlike the static geometry of the Greeks, calculus allowed mathematicians and engineers to make sense of the motion and dynamic change in the changing world around us, such as the orbits of planets, the motion of fluids, etc.

First problem he face is although it was easy enough to represent and calculate the average of the curve, the of a curve was constantly varying and there was no method to give the exact at any one individual point on the curve.

Newton and his contemporary Gottfried Leibniz calculated a derivative function f ‘(x) which gives the at any point of a function f(x). This process of calculating the or derivative of a curve or function is called differential calculus or differentiation (or, in Newton’s terminology, the “method of fluxions”. He called the instantaneous rate of change at a particular point on a curve the "fluxion", and the changing values of x and y the "fluents"). For instance, the derivative of a straight line of the type f(x) = 6x is just 6; the derivative of a squared function f(x) = x ² is 2x; the derivative of cubic function f(x) = 6x ³ is 18x 2.

Additional info: Philosophiae Naturalis Principia Mathematica (Mathematical Principles Of Natural Philosophy) was recognized as the greatest scientific book ever written. In it, he presented his theories of motion, gravity and mechanics, explained the eccentric orbits of comets, the tides and their variations, the precession of the Earth's axis and the motion of the Moon. This book was divided into an introduction and three books. Book 1 states the foundation of the science of mathematics, Book 2 states about inaugurates the theory of fluids and lastly book 3 shows the laws of gravitation at work in the universe.

Referrences:

http://www.storyofmathematics.com/17th_newton.html

https://www.biography.com/people/isaac-newton-9422656

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Group 6

MOHAMAD HASIF IQBAL BIN MOHD HATTA
D20151070907
DINIE RUZAINI BINTI MOH ZAINUDIN
D20151070897

NUREEN MARINI BINTI MUHAMMAD SUKRI
D20151071230
ALIAH FATIN BINTI ABU SETAMAN
D20151071246

Biography / History:

Gottfried Wilhelm Leibniz was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy, having developed differential and integral calculus independently of Sir Isaac Newton.

BORN: On July 1, 1646 in Leipzig, Germany.

DIED: On November 14, 1716 in Hanover, Germany.

NATIONALITY: Roman

EDUCATION: Leipzig University, University of Altdorf, University of Jena.

Contributions:

Gottfried Leibniz's major contribution to mathematics was his discovery of the binary numeral system, or the base-2 system, which we find today in computers and related devices. The binary numeral system is a way of writing numbers using only two digits: 0 and 1.

Besides, he independently developed differential and integral calculus the same time as Isaac Newton, devising a superior notation (dx and ∫) that is still used today. He also proposed the basis for the branch of mathematics now known as general topology and lastlym he proposed the basis for the modern branch of mathematics known as symbolic logic.

Additional info:

He never married and is known to complain about money at times, his sister’s stepson inherited what he left behind after his death. Leibniz was fond of documenting all this mathematical pursuits and is known to have backdating and tweaking his journal too which fuels the debate centered on ‘Calculus and Newton’.

References:

https://famous-mathematicians.com/gottfried-leibniz/

https://study.com/academy/lesson/gottfried-leibniz-biography-contributions-to-math.html

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References : 

https://3010tangents.wordpress.com/2015/05/05/isaac-newton-and-his-contributions-to-mathematics/ 

https://www.britannica.com/biography/Isaac-Newton 

 

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https://3010tangents.wordpress.com/2015/05/05/isaac-newton-and-his-contributions-to-mathematics/ 

https://www.britannica.com/biography/Isaac-Newton 

 

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https://www.britannica.com/biography/Isaac-Newton 

 

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