Rene Descartes: "He pioneered the idea of representing algebraic forms and equations using geometric lines and curves on a coordinate plane. His basic ideas are still taught in high-school mathematics today, with students learning how to graph an equation like y = 3x + 5 as a line, or an equation like y = x2 - 4 as a parabola."
Blaise Pascal: "Pascal's Triangle provides a remarkably elegant way to calculate binomial coefficients, a set of numbers that are important in algebra and elsewhere. He also developed one of the first mechanical calculators in the world, a distant and primitive relative of modern computers."
Isaac Newton: "With his invention of calculus (an achievement shared with our next entry), mathematics was able for the first time to systematically describe how things change across space and time. Newton developed calculus in the context of developing his theories of physics."
Gottfried Wilhelm Leibniz: "He had a strong belief in rationalism, with a focus on formal symbolism that would later come to fruition in the late 19th and early 20th centuries with the development of modern logic and set theory. Leibniz also had a hand in the improvement of mechanical calculators like the one developed by Pascal."
Thomas Bayes: "Thomas Bayes provided one of the most important tools used in probability theory and statistics. It allows us to figure out how likely something is based on the evidence we have at hand. Finding the probability of an event when we have a good understanding of the underlying mechanism tends to be pretty straightforward. Some basic calculations can give you the probability of drawing a full house in a hand of poker, or getting five heads in a row when flipping a coin five times, or of holding a winning lottery ticket."
Leonhard Euler: "Euler also furthered the theory of power series: a way of representing complicated functions using infinitely long sums of much simpler terms. His work on the power series representations of trigonometric and exponential functions led to, as a special case of a more general and extremely important formula, his famous equation eiπ +1 = 0."
