I saw a thread like this some time ago, but thought I'd start another just for fun. List your top 5 favorite mathematicians. These don't necessarily have to be who you feel are the "best", but just the five that you have the most respect for or interest in. Here's my five: 1. Gauss 2. Euler 3. Newton 4. Archimedes 5. Riemann [Edit] If anyone would like to discuss works or ideas by someone in your list, feel free.
1. Gauss 2. Euler 3. Liebnitz 4. Riemann 5. Poincaré Teachers of mathematics: 5. A certain professor. 6. Spivak 7. Courant The numbers are not ordinal with respect to status.
Blaise Pascal, 1623-1662, was one of the most famous child protégés that ever lived. (At 12 he discovered many geometry theorems on his own, being forbidden to study the subject. At 16 he wrote a book on conic sections.) He not only discovered Pascal's Principal in Physics, but the cycloid, and was known for his writings in Philosophy such as "The Wager," which commented on the afterlife and existence of God. Kummer was the one who introduced unique factorization into algebraic numbers and advanced Fermat's last Theorem. Gauss: The Prince of Mathematicians; he first computed the movements of the asteroid Ceres, and discovered the Bell curve, as is shown on a 10 Mark German note. Archimedes completed an infinite series, found the value of pi to two decimals, discovered a way to integrate the parabola using an infinite series of triangles**. Oh yes! He also trisected the angle by way of a paper strip. Fermat, 1601-1665, a complete amateur in mathematics and a jurist by trade, was unbelievably ahead of his time in Number Theory. He not only knew that every integer is the sum of four squares, but also that evey integer is the sum of three triangle numbers, of five pentangle, etc. He completed a whopper in one fell swoop*. He and Pascal introduced the theory of probability through a series of personal correspondence. He is know in Physics for the fact that light from one medium to another travels the path of least time. *Note: A theorem also known as Bachet's conjecture which was stated but not proven by Diophantus. It states that every positive integer can be written as the sum of at most four squares. Although the theorem was proved by Fermat using infinite descent, the proof was suppressed. Euler was unable to prove the theorem. The first published proof was given by Lagrange in 1770 (more than 100 years after Fermat died) and made use of the Euler four-square identity. http://mathworld.wolfram.com/LagrangesFour-SquareTheorem.html **In Archimedes day, of course, there was no Cartesian coordinate system. His method of computing the area of a parabola was to find a series of triangles,doubling in number and decreasing in size, with a fixed ratio of A= area of largest then: A/8, A/64....etc. This was suitable to the use of plane geometry. The modern method using rectangles and of general use for continuous functions was, of course, unknown to him. So that it is probably not proper to speak of him as a discoverer of the Calculus, as a few have suggested; but he did have an understand of the limit process of converging infinite sums.
-- fourier (shouldn't have to list this guy, know what i mean?) -- norb wiener -- edwin hewitt -- gh hardy topologists -- tietze -- urysohn -- tychonoff -- hilbert for his quotation: "physics is much too hard for physicists" -- galois for the following quotations, anticipating the abstract method by many decades. imho it's his most important & revolutionary contribution, more important than his theory of equations: 1) "Go to the roots of the calculations! Group the operations. Classify them according to their complexities rather than their appearances! This, I believe is the mission of future mathematicians. This is the road on which I am embarking in this work" 2) "Since the beginning of the century, computational procedures have become so complicated that any progress by those means has become impossible, without the elegance which modern mathematicians have brought to bear on their research, and by means of which the spirit comprehends quickly and in one step a great many computations. It is clear that elegance, so vaunted and so aptly named, can have no other purpose." edit: maybe galois theory can be considered as a spectacular application of his abstract method, since he wasn't interested in the roots of an equation in themselves. rather, he considered an equation solved if he only showed that the roots were algebraic over the field of coefficients. he wasn't interested in the roots themselves since that is/was too much fuss to compute them. he never intended to find a specific procedure that would explicitly give the roots of any particular equation.