Greatest Mathematicians

Mathematicians

1. Aristotle of Stagira (384-322 BC) Macedonia 

 Aristotle is considered the greatest scientist of the ancient world, and the most influential philosopher and logician ever; he ranks #13 on Michael Hart's list of the Most Influential Persons in History. (His science was a standard curriculum for almost 2000 years, unfortunate since many of his ideas were quite mistaken.) His writings on definitions, axioms and proofs may have influenced Euclid. He was also the first mathematician to write on the subject of infinity. His writings include geometric theorems, some with proofs different from Euclid's or missing from Euclid altogether; one of these (which is seen only in Aristotle's work prior to Apollonius) is that a circle is the locus of points whose distances from two given points are in constant ratio. Even if, as is widely agreed, Aristotle's geometric theorems were not his own work, his status as the most influential logician and philosopher makes him a candidate for the List. 

2. Nicole  Oresme (ca 1322-1382) France

 Oresme was of lowly birth but excelled at school (where he was taught by the famous Jean Buridan), became a young professor, and soon personal chaplain to King Charles V. The King commissioned him to translate the works of Aristotle into French (with Oresme thus playing key roles in the development of both French science and French language), and rewarded him by making him a Bishop. He wrote several books; was a renowned philosopher, natural scientist (challenging several of Aristotle's ideas, and postulating that the Earth moved), and important economist (anticipating Gresham's Law). Oresme used a graphical diagram to demonstrate the Merton College Theorem (a discovery related to Galileo's Law of Falling Bodies made by Thomas Bradwardine, et al); it is said this was the first abstract graph. (Some believe that this effort inspired Déscartes' coordinate geometry.) Oresme was also first to use fractional exponents; first to write of general curvature; and, most famously, first to prove the divergence of the harmonic series. His work was largely ignored, so may have had little historic importance, but with several discoveries ahead of his time, Oresme deserves recognition. 

3. Simon  Stevin (1549-1620) Flanders, Holland 

 Stevin was one of the greatest practical scientists of the Late Middle Ages. He worked with Holland's dykes and windmills; as a military engineer he developed fortifications and systems of flooding; he invented a carriage with sails that travelled faster than with horses and used it to entertain his patron, the Prince of Orange. He discovered several laws of mechanics including those for energy conservation, hydrostatic pressure, the equal rate of falling bodies attributed to Galileo, and the influence of the moon on tides. He was first to write on the concept of unstable equilibrium. He invented improved accounting methods, and the equal-temperament music scale. He also did work in descriptive geometry, trigonometry, optics, geography, and astronomy. In mathematics, Stevin is best known for the notion of real numbers (previously integers, rationals and irrationals were treated separately) and for introducing decimal fractions to Europe. His theorems include the Intermediate Value Theorem attributed to Cauchy. He also invented basic notation like the symbol √; Stevin's historical importance may warrant a place on the List despite that he may have proved no difficult theorems of pure mathematics. 

4.Takakazu  Seki (Kowa) (ca 1637-1708) Japan 

 Seki Takakazu (aka Shinsuke) was a self-taught prodigy who developed a new notation for algebra, and made several discoveries before Western mathematicians did; these include determinants, the Newton-Raphson method, Newton's interpolation formula, Bernoulli numbers, discriminants, methods of calculus, and probably much that has been forgotten (Japanese schools practiced secrecy). He calculated π to ten decimal places using Aitkin's method (rediscovered in the 20th century). He also worked with magic squares. He is remembered as a brilliant genius and very influential teacher. 

5. Johann  Bernoulli (1667-1748) Switzerland

 Johann Bernoulli learned from his older brother and Leibniz, and went on to become principle teacher to Leonhard Euler. He developed exponential calculus; together with his brother Jacob, he founded the calculus of variations. Johann solved the catenary before Jacob did; this led to a famous rivalry in the Bernoulli family. (No joint papers were written; instead the Bernoullis, especially Johann, began claiming each others' work.) Although his older brother may have demonstrated greater breadth, Johann had no less skill than Jacob, contributed more to calculus, discovered L'Hôpital's Rule before L'Hôpital did, and made important contributions in physics, e.g. about vibrations, elastic bodies, optics, tides, and ship sails.