Significant Figure 2: In the early 9th century, the Persian mathematician Muhammad ibn Musa al-Khwarizmi discovered the Hindu number system, which utilized nine symbols for numbers and a small circle to represent zero. Intrigued, Al-Khwarizmi recognized the potential of the place value system, where a number's position determined its value. This breakthrough led to the adoption of the Hindu-Arabic numeral system, which revolutionized mathematical calculations and paved the way for various technological advancements. Al-Khwarizmi's work laid the foundation for modern arithmetic and algebra, enabling developments ranging from the Industrial Revolution to contemporary technologies like cars, computers, space travel, and robotics.

Diverse Culture 1: The ancient Egyptians expressed numbers with different symbols for each place like the ones, tens, hundreds and so on within hieroglyphic writing. However, to complete arithmetic operations, this type of writing was not efficient, so they used hieratic writing instead. For multiplication, scribes used successive doubling then used addition to add the corresponding multiples. Division was the reverse process. Fraction operations are also evident in the hieratic writings.

Diverse Culture 2: The Babylonians made significant contributions to number theory through their development of a base 60 number system. They were the first to use place value notation, allowing for the representation of large numbers with more accuracy. Further, Babylonian mathematicians created mathematical tables, including tables for multiplication, division, and square roots, which aided with complex calculations. Their mathematical achievements extended to astronomy, where they used numerical methods to track celestial movements and predict astronomical events. A Babylonian tablet dating back to approximately 1700 BC also displays an extensive list of Pythagorean triples.

Significant Figure 2: Brahmagupta, an Indian mathematician and astronomer, is an immensely influential mathematician who aided in developing the rules for computing with zero.In the Brahmasphutasiddhanta , his 25 chapter work, he defined zero as the result of subtracting a number from itself. He also provides arithmetic rules in terms of fortunes (positive numbers) and debts (negative numbers). He goes on to provide formulas for cyclic quadrilaterals, rules for summing various series, solving quadratic indeterminate equations, and more, in addition to his work in astronomy.

Significant Figure 2: Zu Gengzhi, a Chinese mathematician, (approximately 450-520) is most famous for working with Liu Hui to finish what is now inappropriately named Cavalieri's principle to provide the formula for the volume of a sphere. Zu Gengzhi's statement of Cavalieri's principle, before Cavalieri, is as follows: "If blocks are piled up to form volumes,
And corresponding areas are equal,
Then the volumes cannot be unequal." This follows from Liu Hui's assumption. With their combined statements, Zu Gengzhi developed the formula for the volume of a sphere: πd³/6

Diverse Culture 2: Another culture to contribute to geometry was Egyptian culture. They are credited with using practical geometry in the surveying the land after the flooding of the Nile every year, building the pyramids, and storing resources such as food and water. This is pre-Euclidean geometry.

Significant Figure 2: John Graunt, an English demographer, made a significant contribution to the field of statistics. Graunt wanted to predict mortality rates. He wrote the paper, "Natural and Political Observations Made upon the Bills of Mortality" . He was the first to coin the term "excess deaths" in epidemiology. He also provided the first accurate male:female ratios based on his data. He also noticed the "urban penalty", that being that those living in urban areas die faster than those living in rural areas. He is regarded as the father of demography, epidemiology, and vital statistics.

Significant Figure 2: Sir Isaac Newton, an English mathematician, developed Calculus independently of Gottfried Wilhelm von Leibniz. When developing calculus, Newton considered the variables to be changing with the time. Newton also used x' and y' as quantities to represent finite velocities to compute tangent. Newton thought of calculus in more geometrical terms. While Leibniz was very conscious of notation, Newton was not. Instead, Newton used different notations by the day, which is why we instead use and accredit today's calculus notation to Leibniz. Both Leibniz and Newton used infinitesimals, which bothered later mathematicians when criticizing and tweaking the foundations of calculus.

Significant Figure 2: One cannot speak about discrete mathematics without discussing the Hungarian mathematician, Paul Erdos. Paul Erdos was a legendary mathematician who made significant contributions to discrete mathematics. He pioneered the study of combinatorics, with a focus on problems that involved discrete structures and finite objects. Erdos introduced the concept of Ramsey theory, which explores the order in random structures. I hated this in my undergraduate years. He also played an important role in developing the probabilistic method, a powerful tool for solving combinatorial problems. He was known for his collaboration with other mathematicians. This lead to the creation of the Erdos number, which measured collaborative distance. His work continues to inspire mathematicians working in the realm of discrete mathematics.