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Click on the name of the person to go to their page. See also the side bar for other links.

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Take a look at this math time line to see if your dates match.

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Not content merely to point out the mathematical references, Mr. Singh uses them as a starting point for lively discussions of mathematical topics, anecdotes and history. Even someone with no mathematical background will enjoy his accounts of the nature of infinity and the meaning of the number e, the life of the tragic genius Srinivasa Ramanujan and the obsessions of Bill James, the oracle of baseball statistics.

Perhaps the most surprising revelation is the composition of "The Simpsons" creative team, which over the years has included J. Stewart Burns, who has a master's degree in math from Harvard; David X. Cohen (master's in computer science, University of California, Berkeley); and Ken Keeler (Ph.D. in applied math, Harvard). Most astonishing is Jeff Westbrook (Ph.D., computer science, Princeton), who was an associate professor at Yale before he joined the team.

It is understandable that a group with such credentials would enjoy sprinkling the show with tidbits from their previous line of work. As Mr. Cohen explains, "It cancels out those days when I've been writing those bodily function jokes."

This might explain the prevalence of mathematics in the show, but it also cries out for an explanation: Why would so many talented mathematicians forsake academia to write outrageous stories and gags for an animated TV show? After all, the contrast between the elegant abstractions of higher mathematics and the foibles of the imbecilic Homer Simpson could hardly be greater.

But perhaps the similarities are closer than it appears. Think of it this way: To write an episode of "The Simpsons," one begins with a known set of characters - Homer, Bart, Lisa, Marge - and confronts them with a problem. The rest of the episode follows the characters through a complicated series of moves until the problem is resolved.

And while the show certainly allows for a wide range of improbable turns (Homer disappears into the third dimension, Lisa is rescued from an angry mob by Stephen Hawking), not everything is allowable: The characters must remain true to their personalities and the stories must follow their own inner logic, for a story free of the constraints of personality, logic and motivation is no story at all.

Now think of proving a geometric theorem: Once again, one has a certain set of elements - points, lines, triangles, circles - and is confronted with a problem. What is the sum of the angles of a triangle? What is the area of a polygon? The proof then consists of a series of moves that leads to a resolution of the problem.

Just as in a story, there are constraints. All geometric objects must remain true to their unique characteristics, and each step in the proof must follow the strict rules of logical deduction. A proof that breaks these conditions is no proof at all.

In their basic structure, then, mathematical reasoning and storytelling might not be so different after all. In a series like "The Simpsons," the similarities are particularly strong. In the end, it turns out that the improbable world of Springfield is in some ways not that different from the equally surprising world of higher mathematics.

This seems to me to go a long way in explaining why so many mathematicians found a welcome home on "The Simpsons" writing team, and why they have left such a strong imprint on the show. It also points to the deeper implication of Mr. Singh's highly entertaining book: that every mathematical theory or theorem, however difficult and inaccessible it may seem, always has a story to tell.

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the simpsons and their mathematical secrets (book)

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simpsons and their mathematical secrets  the (book)

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Investigating 'The Simpsons and Their Mathematical Secrets'

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Not content merely to point out the mathematical references, Mr. Singh uses them as a starting point for lively discussions of mathematical topics, anecdotes and history. Even someone with no mathematical background will enjoy his accounts of the nature of infinity and the meaning of the number e, the life of the tragic genius Srinivasa Ramanujan and the obsessions of Bill James, the oracle of baseball statistics.

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As the pickings grow sparser and modern proofs sprawl in size and complexity, it becomes that much harder, and more artificial, to separate out a single discoverer. But that is what society with its accolades and heroes demands. The geometry of the universe almost guarantees that a movie treatment heralding Dr. Perelman is already in the works: "Good Will Hunting" set in St. Petersburg, where he lives, unemployed, with his mother, or a Russian rendition of "Proof."

To hear him tell it, he is above such trivialities. What matters are the ideas, not the brains in which they alight. Posted without fear of thievery on the Internet beginning in 2002, his proof, consisting of three dense papers, gives glimpses of a world of pure thought that few will ever know.

Who needs prizes when you are free to wander across a plane so lofty that a soda straw and a teacup blur into the same topological abstraction, and there is nothing that a million dollars can buy? Until his death in 1996, the Hungarian number theorist Paul Erdos was content to live out of a suitcase, traveling from the home of one colleague to another, seeking theorems so sparse and true that they came, he said, "straight from The Book," a platonic text where he envisioned all mathematics was prewritten.

Down here in the sublunar realm, things are messier. Truths that can be grasped in a caffeinated flash become rarer all the time. If Poincaré's conjecture belonged to that category it would have been proved long ago, probably by Henri Poincaré.

It has taken nearly four years for Dr. Perelman's colleagues to unpack the implications of his 68-page exposition, which is so oblique that it doesn't actually mention the conjecture. The Clay Institute Web site carries links to three papers by others - 992 pages in total - either explicating the proof or trying to absorb it as a detail of their own.

Those intent on parceling out credit may have as hard a time with the intellectual forensics: Who got what from whom? Dr. Perelman's papers are almost as studded with names as with numbers. "The Hamilton-Tian conjecture," "Kähler manifolds," "the Bishop-Gromov relative volume comparison theorem," "the Gaussian logarithmic Sobolev inequality, due to L. Gross" - all have left their fingerprints on The Book. Spread among everyone who contributed, the Clay Prize might not go very far.

A purist would say that no one person deserves to stake a claim on a theorem. That seemed to be what Dr. Perelman, who has said he disapproves of politics in mathematics, was implying.

"If anybody is interested in my way of solving the problem, it's all there - let them go and read about it," he told The Telegraph. "I have published all my calculations. This is what I can offer the public."

He sounded a little like J. D. Salinger, hiding away in his New Hampshire hermitage, fending off a pesky reporter: "Read the book again. It's all there."

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As the pickings grow sparser and modern proofs sprawl in size and complexity, it becomes that much harder, and more artificial, to separate out a single discoverer. But that is what society with its accolades and heroes demands.

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Type "Fibonacci". Look at the pictures. You can use Tag Galaxy to see related pictures

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You need a newer Version of the Adobe Flash Player to view the Tag Galaxy Website. Get it here!

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You may scroll to the right using the bar at the bottom and you may scroll up or down using the scroll bar to the right.

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View these pictures for examples of Fibonacci's Golden Ratio

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by Keiren 1.9k Views

The fibonacci spiral appears not only in the perfect nautilus shell...

...but in events and objects viewed from afar.

An energy system in the shape of a fibonacci moves with limited losses. Hurricane Irene.

What is the Fibonacci Sequence?

The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is a recursive sequence, generated by adding the two previous numbers in the sequence.: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...

Here is a good video explanation from SciShow. He points out that plant sections, petals, and rows of seeds almost always count up to a Fibonacci number.

If you were to draw a line starting in the right bottom corner of a golden rectangle within the first square, and then touch each succeeding multiple square's outside corners, you would create a fibonacci spiral.

How Common Is The Fibonacci Sequence in Nature?

The fibonacci appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner. Here, a microscopic view of the ovary of an Anglerfish. Nikon's It's a Small World Competition.

Spirals are the most common galaxy shape. Galaxies group together in superclusters and superclusters group together in walls. These walls or filaments of numerous superclusters, gravitationally-bound and separated by large areas of void, are the largest known structures in the universe.

The Milky Way's dust obstructs us from seeing the depth of these filaments or sheets, so we do not yet know the exact shape of these walls. More information can be found at www.spacetelescope.org.

Cancer cell division. This composite confocal micrograph uses time-lapse microscopy to show a cancer cell (HeLa) undergoing cell division (mitosis). The DNA is shown in red, and the cell membrane is shown in cyan. The round cell in the centre has a diameter of 20 microns.

This is part 1 of three-part video series from "recreational mathematician" Vi Hart, explaining the mathematics behind the Fibonacci Sequence. Part 1 shows how you can draw the sequence and shows how it actually on pinecones and pineapples.

18 Amazing Examples of the Fibonacci Sequence in Nature

1) Chicken Egg

Fibonacci as starting point of life.

2) Romanesque Broccoli

Romanesque broccoli is a striking example of the fibonacci. Each nub is a Fibonacci spiral of its own.

3) Aloe Plant

Spiral aloe. Numerous cactus display the Fibonacci spiral. You can see how each set of leaves spiral outward.

4) Buena Mulata Pepper

This pepper has grown into a Fibonacci Spiral.

5) Sunflower

Sunflower. www.thestrong.org. The Fibonacci spiral is a little more subtle in this photo, but you can still see the spiral in the unopened disk florets.

6) Rock Daisy

Marlborough Rock Daisy by Sid Mosdell. Again, the spiral is visible in the disk florets of the flower.

7) Pinecone

All pinecones display a fibonacci sequence. The umbo on pinecones increase in size as you move outward, displaying a Fibonacci spiral.

8) Panther Chameleon

The tail of these creatures naturally curls into a Fibonacci spiral.

9) American Giant Millipede

American giant millipede. The fibonacci is thought to be the design of least resistance.

10) Monarch Caterpillar

A monarch caterpillar about to form a chrysalis.

11) Pangolin

Fibonacci and armor = very safe. The Pangolin is able to protect its soft underbelly by forming a Fibonacci spiral.

12) Double Fibonacci

This flower exhibits two Fibonacci spirals. You can faintly see how the spirals form from the center of the opened disk florets.

13) Koru

Fibonacci in spores. A fiddlehead or koru.

14) Snails And Fingerprints

Snails and fingerprints. Images are from www.123rf.com, and originally "artcatalyst.blogspot.com/2011/04/fibonacci-sequence-mathematics-nature.html" (respectively). Both have a distinct Fibonacci spiral.

15) Famous Art

Fibonacci in "The Great Wave Off Kanagawa." It seems even famous art can't escape the Fibonacci sequence.

16) Falling Water

Water falls into the shapes of a Fibonacci during numerous events. Another example would be a vortex.

17) Population

One blogger has applied the Fibonacci sequence to population density and land mass. In Africa the majority of highly populated cities fall on or close to where the spiral predicts.

18) Shell Fossil

A Shell Fossil with the Fibonacci sequence. You can see as the shell grew, a Fibonacci spiral was formed.

Who was Fibonacci?

The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci. Though Fibonacci first introduced the sequence to the western world in 1202, it had been noted by Indian mathematicians as early as the sixth century.

The Fibonacci defines how the density of branches increases up a tree trunk, the arrangement of leaves on a stem, and how a pine cone's scales are arranged. Yet you will not see the Fibonacci everywhere, as nature has many different methods and shades of survival.

Hang Fibonacci In Your Home

These prints from Art.com can be printed at any size you like-they'll frame them for you or you can print directly to canvas. We've had really good luck with their prints; shipping is fast and the prints are good quality. These start at around $25 each.

This is "The Great Wave," by Katsushika Hokusai. A stunning example of the Fibonacci spiral in art.

Fibonacci Spiral by Seymour. If you like a more simplistic look, this drawing of the Fibonacci spiral may be more your style.

Nautilus Shell by Babar760. A natural depiction of the Fibonacci spiral, great for someone who enjoys math and nature.

Some stock traders are using the Fibonacci sequence as an attempt to "crack" the stock market, by selling or buying when certain sequences appear on stock charts. Not recommended!

There's also a Fibonacci betting system. The idea here is to start with an even money bet, like red/black in roulette. You keep moving up the Fibonacci sequence every time you lose a bet on the idea that, eventually, you'll win and recoup your money. Also not recommended!

The Best Books about Fibonacci and the Fibonacci Sequence

The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Mario Livio

Growing Patterns: Fibonacci Numbers in Nature by Sarah and Richard Campbell

The Golden Section: Nature's Greatest Secret by Scott Olsen

The Fabulous Fibonacci Numbers by Alfred Posamentier and Ingmar Lehmann

Blockhead: The Life of Fibonacci by Joseph D'Agnese and John O'Brien (children's book, named a Mathical Honor Book April 2015)

Fascinating! A must watch!
Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series.

Check out this Custom Fibonacci Spiral Generator - chromatism.net

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by Keiren 1.9k Views The fibonacci spiral appears not only in the perfect nautilus shell... ...but in events and objects viewed from afar. An energy system in the shape of a fibonacci moves with limited losses. Hurricane Irene. The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected.

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http://www.nytimes.com/2012/03/27/science/emmy-noether-the-most-significant-mathematician-youve-never-heard-of.html?pagewanted=all&_r=0

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Pascal's triangle - Copy and paste this link to see how it was useful. Then watch the video below.

http://milan.milanovic.org/math/english/division/division.html

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Go to this site to create your own. Briefly describe what you do to create sierpinski's triangle. Then watch the video below.

http://www.shodor.org/interactivate/activities/SierpinskiTriangle/

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Charles' Law and Boyle's Law - direct and inverse variation.

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One of the major contributions Archimedes made to mathematics was his method for approximating the value of pi. It had long been recognized that the ratio of the circumference of a circle to its diameter was constant, and a number of approximations had been given up to that point in time by the Babylonians, Egyptians, and even the Chinese. There are some authors who claim that a biblical passage1also implies an approximate value of 3 (and in fact there is an interesting story2 associated with that).
At any rate, the method used by Archimedes differs from earlier approximations in a fundamental way. Earlier schemes for approximating pi simply gave an approximate value, usually based on comparing the area or perimeter of a certain polygon with that of a circle. Archimedes' method is new in that it is an iterative process, whereby one can get as accurate an approximation as desired by repeating the process, using the previous estimate of pi to obtain a new one. This is a new feature of Greek mathematics, although it has an ancient tradition among the Chinese in their methods for approximating square roots.

Archimedes' method, as he did it originally, skips over a lot of computational steps, and is not fully explained, so authors of history of math books have often presented slight variations on his method to make it easier to follow. Here we will try to stick to the original as much as possible, following essentially Heath's translation3.

The Approximation of Pi

The method of Archimedes involves approximating pi by the perimeters of polygons inscribed and circumscribed about a given circle. Rather than trying to measure the polygons one at a time, Archimedes uses a theorem of Euclid to develop a numerical procedure for calculating the perimeter of a circumscribing polygon of2n sides, once the perimeter of the polygon ofn sides is known. Then, beginning with a circumscribing hexagon, he uses his formula to calculate the perimeters of circumscribing polygons of 12, 24, 48, and finally 96 sides. He then repeats the process using inscribing polygons (after developing the corresponding formula). The truly unique aspect of Archimedes' procedure is that he has eliminated the geometry and reduced it to a completely arithmetical procedure, something that probably would have horrified Plato but was actually common practice in Eastern cultures, particularly among the Chinese scholars.

The Key Theorem

The key result used by Archimedes is Proposition 3 of Book VI of Euclid'sElements. The full statement of the theorem is as follows:

If an angle of a triangle be bisected and the straight line cutting the angle cut the base also, the segments of the base will have the same ratio as the remaining sides of the triangle; and, if the segments of the base have the same ratio as the remaining sides of the triangle, the straight line joined from the vertex to the point of section will bisect the angle of the triangle.4

We will just prove one direction of this theorem here, namely that the angle bisector cuts the opposite side in the ratio claimed. More precisely, in the diagram shown, ifAD bisects angle BAC, then BD : CD = BA : AC.

Our proof differs from the original somewhat: the proof (and diagram) given here makes it more clear how Archimedes will use the theorem in his approximation scheme. For Euclid's original, complete proof, along with avery neat interactive diagram, seeDavid Joyce's Elements Web site.

Archimedes' Method

Here we outline the method used by Archimedes to approximate pi. The specific statement of Archimedes is Proposition 3 of his treatiseMeasurement of a Circle:
The ratio of the circumference of any circle to its diameter is less than 3¹/₇ but greater than 3¹⁰/₇₁.
The proof we give below essentially follows that of Archimedes, as set out in Heath's translation 5. Much of the text skips over steps in the proof; rather than adding intermediate steps as Heath does6, we are putting those in pop-up windows. Look for buttons like this: . Clicking on these will bring up pop-up windows showing intermediate steps that Archimedes has left out of this text (HTGT stands for How'd They Get That?).
Proof:
[Note: throughout this proof, Archimedes uses several rational approximations to various square roots. Nowhere does he say how he got those approximations--they are simply stated without any explanation--so how he came up with some of these is anybody's guess.]

I. Let AB be the diameter of any circle, O its center, AC the tangent at A; and let the angle AOC be one-third of a right angle.

Then
(1) OA : AC > 265 : 153

and

(2) OC : AC = 306 : 153.

First, draw OD bisecting the angle AOC and meeting AC in D.
Now

CO : OA = CD : DA

so that

(CO + OA) : CA = OA : AD

Therefore

(3) OA : AD > 571 : 153.

Hence

OD ² : AD ² > 349450 : 23409

so that

Secondly, let OE bisect the angle AOD, meeting AD in E.
Therefore

Thus

(6) OE : EA > 1172¹/₈ : 153.

Thirdly, let OF bisect the angle AOE and meet AE in F.
We thus obtain the result that

Thus

Fourthly, let OG bisect the angle AOF, meeting AF in G.
We have then

Now the angle AOC, which is one-third of a right angle, has been bisected four times, and it follows that angle AOG = 1/48 (a right angle).
Make the angle AOH on the other side of OA equal to the angle AOG, and let GA produced meet OH in H.
Then angle GOH = 1/24 (a right angle).
Thus GH is one side of a regular polygon of 96 sides circumscribed to the given circle.
And, since

while

AB = 2 OA, GH = 2 AG,

it follows that

AB : (perimeter of a polygon of 96 sides) > 4673 ¹/₂ : 14688

But

Therefore the circumference of the circle (being less than the perimeter of the polygon) is a fortiori less than 3 1/7 times the diameter AB.

II. Next let AB be the diameter of a circle, and let AC, meeting the circle in C, make the angle CAB equal to one-third of a right angle. Join BC.

Then

AC : BC < 1351 : 780.

First, let AD bisect the angle BAC and meet BC in d and the circle in D. Join BD.
Then

angle BAD = angle dAC = angle dBD

and the angles at D, C are both right angles. It follows that the triangles ADB, BDd are similar.
Therefore

AD : BD = BD : Dd = AB : Bd
= (AB + AC) : (Bd + Cd)
= (AB + AC) : BC

or (BA + AC) : BC = AD : DB.

Therefore

(1) AD : DB < 2911 : 780.

Thus

(2)

Secondly, let AE bisect the angle BAD, meeting the circle in E; and let BE be joined. Then we prove, in the same way as before, that

Therefore

Thirdly, let AF bisect the angle BAE, meeting the circle in F.
Thus,

(5) AF : FB < 3661 ⁹/₁₁ x ¹¹/₄₀ : 240 x¹¹/₄₀
= 1007 : 66.

Therefore,

Fourthly, let the angle BAF be bisected by AG meeting the circle in G.
Then

, by (5) and (6).

Therefore

Therefore BG is a side of a regular inscribed polygon of 96 sides.

It follows from (7) that

(perimeter of polygon) : AB > 6336 : 2017 ¹/₄.

And .

Much more then is the circumference to the diameter

< 3 ¹/₇ but > 3 ¹⁰/₇₁.

Copyright ©1997. All rights reserved. Created 10 June 1997; last updated 3 August 1997.
[Table of Contents] [FGCU Home Page] [DR. L's Home page]

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One of the major contributions Archimedes made to mathematics was his method for approximating the value of pi. It had long been recognized that the ratio of the circumference of a circle to its diameter was constant, and a number of approximations had been given up to that point in time by the Babylonians, Egyptians, and even the Chinese.

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His work with fractals has assisted doctors in better cancer detection methods allowing them to prescribe better treatments. Check out this video

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Doodling in Math- Spirals, Fibonacci, and Being a Plant [1 of 3].mp4.crdownload

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Watch this Ted Talk - One discovery leads to another

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SafeShare.tv - Arthur Benjamin: The magic of Fibonacci ...

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SafeShare.tv removes unwanted distractions from YouTube and Vimeo videos and reduces ads, so you can focus on the content. Perfect for schools and businesses!

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A special relationship between the sides lengths of all right triangles. Copy and paste the link to see how it is useful in everyday life.

http://www.ask.com/question/how-is-the-pythagorean-theorem-used-today

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Helps to determine if a number is prime. Scroll down and use this to determine prime numbers up to 100. Use snipping tool to take a picture and attach it to your assignment.

http://nlvm.usu.edu/en/nav/frames_asid_158_g_3_t_1.html?open=instructions&from=grade_g_3.html

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Sieve of Eratosthenes: an ancient way of getting the prime numbers. Eratosthenes (276-194 B.C.) was the third librarian of the famous library in Alexandria and an outstanding scholar all around

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Meet Daniel Tammet who has mastered pi to 20,000 places. Archimedes is given credit for approximating pi. Check it out at the top right.

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3.14 Pi Day March 14 Math genius Worlds greatest math prodigy Mathematics savant Maths Daniel Tammet.mp4.crdownload

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Do you know Newton's 3 Laws? Check out this video (in blue) OR the one below.

http://science360.gov/obj/video/642db496-d506-432e-85b4-4e38f75d9142/newtons-three-laws-motion

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Newton's 3 (three) Laws of Motion.mp4.crdownload

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Your assignment.

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Most Influential Mathematician - Activity http://padlet.com/kristal_norman/w76znf711vie  I. Reference - Preview research sites to get an overview of some of the most influential mathematicians of our time. . II. Move through the Padlet board.  There are videos, interactives, and informational sli...

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A mathematician is an expert in the field of mathematics; a person who is highly skilled and knowledgeable. It is a science that deals with numbers and their interrelations, combinations and operations, data, measurements, quantity, structure, space and generalizations. The science is extensively used in the fields of finance, engineering, industries, robotics, astronomy, business, information technology, and various other fields. Mathematicians analyze data, study patterns and develop mathematical models that not only help to further human knowledge, but are also utilized for solving problems in various fields. These scientists work in the fields of pure and applied mathematics. In the pure form of this science, the researchers work through abstract problems with the sole motive of furthering human knowledge and contributing to theory formation. On the other hand, professionals working in the applied form formulate mathematical models for problem solving in real-world situations. But these two fields are overlapping-what starts out as a theoretical study may spawn some practical applications, while applied study of maths may sometimes contribute to its theoretical base. They need to be highly analytical and technologically savvy with excellent reasoning skills. Browse this section to explore about the life and works of various famous mathematicians from all over the world.

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A mathematician is an expert in the field of mathematics; a person who is highly skilled and knowledgeable. It is a science that deals with numbers and their interrelations, combinations and operations, data, measurements, quantity, structure, space and generalizations. The science is extensively used in the fields of finance, engineering, industries, robotics, astronomy, business, information technology, and various other fields.

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Often called the language of the universe, mathematics is fundamental to our understanding of the world and, as such, is vitally important in a modern society such as ours. Everywhere you look it is likely mathematics has made an impact, from the faucet in your kitchen to the satellite that beams your television programs to your home. As such, great mathematicians are undoubtedly going to rise above the rest and have their name embedded within history. This list documents some such people. I have rated them based on contributions and how they effected mathematics at the time, as well as their lasting effect. I also suggest one looks deeper into the lives of these men, as they are truly fascinating people and their discoveries are astonishing - too much to include here. As always, such lists are highly subjective, and as such please include your own additions in the comments!

Greek Mathematician Pythagoras is considered by some to be one of the first great mathematicians. Living around 570 to 495 BC, in modern day Greece, he is known to have founded the Pythagorean cult, who were noted by Aristotle to be one of the first groups to actively study and advance mathematics. He is also commonly credited with the Pythagorean Theorem within trigonometry. However, some sources doubt that is was him who constructed the proof (Some attribute it to his students, or Baudhayana, who lived some 300 years earlier in India). Nonetheless, the effect of such, as with large portions of fundamental mathematics, is commonly felt today, with the theorem playing a large part in modern measurements and technological equipment, as well as being the base of a large portion of other areas and theorems in mathematics. But, unlike most ancient theories, it played a bearing on the development of geometry, as well as opening the door to the study of mathematics as a worthwhile endeavor. Thus, he could be called the founding father of modern mathematics.

The only currently living mathematician on this list, Andrew Wiles is most well known for his proof of Fermat's Last Theorem: That no positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n greater then 2. (If n=2 it is the Pythagoras Formula). Although the contributions to math are not, perhaps, as grand as other on this list, he did 'invent' large portions of new mathematics for his proof of the theorem. Besides, his dedication is often admired by most, as he quite literally shut himself away for 7 years to formulate a solution. When it was found that the solution contained an error, he returned to solitude for a further year before the solution was accepted. To put in perspective how ground breaking and new the math was, it had been said that you could count the number of mathematicians in the world on one hand who, at the time, could understand and validate his proof. Nonetheless, the effects of such are likely to only increase as time passes (and more and more people can understand it).

I have placed these two together as they are both often given the honor of being the 'inventor' of modern infinitesimal calculus, and as such have both made monolithic contributions to the field. To start, Leibniz is often given the credit for introducing modern standard notation, notably the integral sign. He made large contributions to the field of Topology. Whereas all round genius Isaac Newton has, because of the grand scientific epic Principia, generally become the primary man hailed by most to be the actual inventor of calculus. Nonetheless, what can be said is that both men made considerable vast contributions in their own manner.

Blgollo, also known as Leonardo Fibonacci, is perhaps one of the middle ages greatest mathematicians. Living from 1170 to 1250, he is best known for introducing the infamous Fibonacci Series to the western world. Although known to Indian mathematicians since approximately 200 BC, it was, nonetheless, a truly insightful sequence, appearing in biological systems frequently. In addition, from this Fibonacci also contributed greatly to the introduction of the Arabic numbering system. Something he is often forgotten for.

Haven spent a large portion of his childhood within North Africa he learned the Arabic numbering system, and upon realizing it was far simpler and more efficient then the bulky Roman numerals, decided to travel the Arab world learning from the leading mathematicians of the day. Upon returning to Italy in 1202, he published his Liber Abaci, whereupon the Arabic numbers were introduced and applied to many world situations to further advocate their use. As a result of his work the system was gradually adopted and today he is considered a major player in the development of modern mathematics.

Computer Scientist and Cryptanalyst Alan Turing is regarded my many, if not most, to be one of the greatest minds of the 20th Century. Having worked in the Government Code and Cypher School in Britain during the second world war, he made significant discoveries and created ground breaking methods of code breaking that would eventually aid in cracking the German Enigma Encryptions. Undoubtedly affecting the outcome of the war, or at least the time-scale.

After the end of the war he invested his time in computing. Having come up with idea of a computing style machine before the war, he is considered one of the first true computer scientists. Furthermore, he wrote a range of brilliant papers on the subject of computing that are still relevant today, notably on Artificial Intelligence, on which he developed the Turing test which is still used to evaluate a computers 'intelligence'. Remarkably, he began in 1948 working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in existence. He would play the 'part' of the machine in testing such programs.

French Philosopher, Physicist and Mathematician Rene Descartes is best known for his 'Cogito Ergo Sum' philosophy. Despite this, the Frenchman, who lived 1596 to 1650, made ground breaking contributions to mathematics. Alongside Newton and Leibniz, Descartes helped provide the foundations of modern calculus (which Newton and Leibniz later built upon), which in itself had great bearing on the modern day field. Alongside this, and perhaps more familiar to the reader, is his development of Cartesian Geometry, known to most as the standard graph (Square grid lines, x and y axis, etc.) and its use of algebra to describe the various locations on such. Before this most geometers used plain paper (or another material or surface) to preform their art. Previously, such distances had to be measured literally, or scaled. With the introduction of Cartesian Geometry this changed dramatically, points could now be expressed as points on a graph, and as such, graphs could be drawn to any scale, also these points did not necessarily have to be numbers. The final contribution to the field was his introduction of superscripts within algebra to express powers. And thus, like many others in this list, contributed to the development of modern mathematical notation.

Living around 300BC, he is considered the Father of Geometry and his magnum opus: Elements, is one the greatest mathematical works in history, with its being in use in education up until the 20th century. Unfortunately, very little is known about his life, and what exists was written long after his presumed death. Nonetheless, Euclid is credited with the instruction of the rigorous, logical proof for theorems and conjectures. Such a framework is still used to this day, and thus, arguably, he has had the greatest influence of all mathematicians on this list. Alongside his Elements were five other surviving works, thought to have been written by him, all generally on the topic of Geometry or Number theory. There are also another five works that have, sadly, been lost throughout history.

Bernhard Riemann, born to a poor family in 1826, would rise to become one of the worlds prominent mathematicians in the 19th Century. The list of contributions to geometry are large, and he has a wide range of theorems bearing his name. To name just a few: Riemannian Geometry, Riemannian Surfaces and the Riemann Integral. However, he is perhaps most famous (or infamous) for his legendarily difficult Riemann Hypothesis; an extremely complex problem on the matter of the distributions of prime numbers. Largely ignored for the first 50 years following its appearance, due to few other mathematicians actually understanding his work at the time, it has quickly risen to become one of the greatest open questions in modern science, baffling and confounding even the greatest mathematicians. Although progress has been made, its has been incredibly slow. However, a prize of $1 million has been offered from the Clay Maths Institute for a proof, and one would almost undoubtedly receive a Fields medal if under 40 (The Nobel prize of mathematics). The fallout from such a proof is hypothesized to be large: Major encryption systems are thought to be breakable with such a proof, and all that rely on them would collapse. As well as this, a proof of the hypothesis is expected to use 'new mathematics'. It would seem that, even in death, Riemann's work may still pave the way for new contributions to the field, just as he did in life.

Child prodigy Gauss, the 'Prince of Mathematics', made his first major discovery whilst still a teenager, and wrote the incredible Disquisitiones Arithmeticae, his magnum opus, by the time he was 21. Many know Gauss for his outstanding mental ability - quoted to have added the numbers 1 to 100 within seconds whilst attending primary school (with the aid of a clever trick). The local Duke, recognizing his talent, sent him to Collegium Carolinum before he left for Gottingen (at the time it was the most prestigious mathematical university in the world, with many of the best attending). After graduating in 1798 (at the age of 22), he began to make several important contributions in major areas of mathematics, most notably number theory (especially on Prime numbers). He went on to prove the fundamental theorem of algebra, and introduced the Gaussian gravitational constant in physics, as well as much more - all this before he was 24! Needless to say, he continued his work up until his death at the age of 77, and had made major advances in the field which have echoed down through time.

If Gauss is the Prince, Euler is the King. Living from 1707 to 1783, he is regarded as the greatest mathematician to have ever walked this planet. It is said that all mathematical formulas are named after the next person after Euler to discover them. In his day he was ground breaking and on par with Einstein in genius. His primary (if that's possible) contribution to the field is with the introduction of mathematical notation including the concept of a function (and how it is written as f(x)), shorthand trigonometric functions, the 'e' for the base of the natural logarithm (The Euler Constant), the Greek letter Sigma for summation and the letter '/i' for imaginary units, as well as the symbol pi for the ratio of a circles circumference to its diameter. All of which play a huge bearing on modern mathematics, from the every day to the incredibly complex.

As well as this, he also solved the Seven Bridges of Koenigsberg problem in graph theory, found the Euler Characteristic for connecting the number of vertices, edges and faces of an object, and (dis)proved many well known theories, too many to list. Furthermore, he continued to develop calculus, topology, number theory, analysis and graph theory as well as much, much more - and ultimately he paved the way for modern mathematics and all its revelations. It is probably no coincidence that industry and technological developments rapidly increased around this time.

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Top 10 Greatest Mathematicians - Listverse

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Often called the language of the universe, mathematics is fundamental to our understanding of the world and as such is vitally important in a modern society such as our. Everywhere you look it is likely mathematics has played a part, from the facet in your kitchen to the satellite that beams your television programs to your home.