I have been asked to write something which addresses the issue that there are no mathematicians who are household words. This means that there are no famous role models for kids to emulate. At first I was planning to do a series of detailed several page descriptions of the lives of a few specific mathematicians. However, after considering what would have intrigued me as a kid, this will only contain a some of the exciting parts about some great mathematicians and historical events.
Many sources try to make mathematicians and mathematics sound far removed from the world, but this is not at all the case. There are politically active mathematicians, mathematicians who steal others' ideas, and even murder over theorems. There is passion and excitement, as in any history when the people involved really care about it. I am sorry for the lack of women in this description, but there really are not yet that many famous women mathematicians. Emmy Noether, Sophie Germain, and Sonya Kovalevsky are the only three that I can think of offhand.
Born in around 532 B.C., the ancient Greek Pythagorus was the founder of a school of mathematicians and is credited with the discovery of the relationship between the lengths of the sides of a right triangle (although it is not clear Pythagorus actually deserves credit for this theorem). Pythagorus was also important politically; he founded the religious sect of the Pythagoreans, who became a major political force in Southern Italy, even gaining the rule of some of the cities. The major beliefs of the Pythagoreans included the transmigration of souls, that everything depended on whole numbers, and the sinfulness of eating beans. Other laws included not touching a white cock and not looking in a mirror beside a light.[Russell, Bertrand, "A History of Western Philosophy," Simon and Schuster, NY, 1945.] So great was the importance of whole numbers that the discovery that the square root of two is irrational remained a religious secret. It is said that when the Pythagorean Hippasus disclosed the secret, other members of the sect drowned him in the sea.[Eves, Howard, "An Introduction to the History of Mathematics," third edition, Holt, Rinehart and Winston, NY, 1964.]
In the sixteenth century, mathematicians wanted to find a formulas like the quadratic formula for factoring third and fourth degree polynomials. The answers were first published by Cardan (1501-76), though it was not his work. He found out the secret of how to solve the cubic from Tartaglia (1500-57), who probably also did not discover it. Cardan's publication came after he promised Tartaglia that he would never reveal the secret. According to Boyer, it is probably Scipione del Ferro (1465-1526) who actually discovered the formula. He kept it a secret, revealing it to one student before he died.[Boyer, Carl, "A History of Mathematics," John Wiley & Sons, NY, 1968.]
After the discovery of formulas to factor third and fourth degree polynomials, it is natural to wonder about five and beyond. In fact, it is impossible to write down a general formula to factor polynomials of any degree greater than four. It was Galois (1812-1832) who proved this result in the course of developing a branch of mathematics now called Galois theory. Through a series of unfortunate circumstances, Galois repeatedly was denied entrance to the Ecole Polytechnique, the most pretigious university in France, as well as never getting his work recognized in his lifetime, although two papers were published in 1830. This same year, Galois became a revolutionary, fighting for France to be a republic. Through this political activity (or perhaps over a woman), he was challenged to a duel. It was in this dual that he died at the age of twenty. According to legend, knowing that he would die, he wrote down many of his ideas in a letter to a friend the night before the duel. The letter and other partial manuscripts were finally published in the Journal de Mathematiques in 1846.[Boyer]
I will not write much about Newton (1642-1727), but there are a few interesting things to mention. Newton was the first to discover calculus, but because he did not publish for more than ten years, Leibniz independently arrived at the same discovery and published first. The result was a terrible fight between the two, making the last part of Newton's life unhappy. In 1696, he was appointed Warden of the Mint and promoted to Master of the Mint in 1699.[Eves] He took the job seriously, saving the country money by introducing the idea of coin milling. This meant that people were no longer able to clip silver off the edges of the coins.[Barrow, John, "The World Within the World," Oxford University Press, 1990.]
Credited with the invention of modern analysis, Euler (1707-83) is probably the most prolific mathematician ever. Spending the last seventeen years of his life blind did not slow down his productivity. He just dictated to his children. Aside from the mathematical content of his work, Euler standardized mathematical notation. He is responsible for the use of the letter e for exponential functions, the capital sigma for summation, i for the square root of minus one, and even for the use of the letter pi for the ratio of the circumference to diameter of the circle! [Boyer] Thus it is that we can write one of the most fundamental equations of modern mathematics, voted the most beautiful theorem by readers of the Mathematical Intelligencer.[Wells, David, "Are These the Most Beautiful?" Mathematical Intelligencer, Vol 12, No 3, 1990.] Namely:
That mathematicians participate in the world is not something of the past. The contemporary mathematician Steve Smale, who is very important in many areas including Dynamical Systems, had to appear in front of the House Un-American Activities Committee and was active in the Free Speech Movement in Berkeley. He caused quite a bit of contraversy when he spoke against the U.S. and Soviet involvement in Vietnam in Moscow, 1966. The University of California denied him summer support; he then has his NSF proposal returned for political reasons.[Smale, Steve, "The Story of the Higher Dimensional Poincare Conjecture (What Actually Happened on the Beaches of Rio)," Mathematical Intelligencer, Vol 12, No 2, 1990.]
Perhaps the most telling comment regarding the importance of mathematics comes from the algebraic geometer Alexandre Grothendieck, when he was teaching math in Vietnam in 1967. He says: "In general, I can attest that both the political leaders and the senior academic people are convinced that scientific research--including theoretical research having no immediate practical applications--is not a luxury, and that it it necessary ... starting now, without waiting for a better future."[Koblitz, Neal, "Recollections of Mathematics in a Country Under Siege," Mathematical Intelligencer, Vol 12, No 3, 1990.]
I would like to thank Scott Carlson for sharing his knowledge and books with me for this article.