The Four Greatest Mathematicians

"History of Mathematics" was my final course in the master's program. I took it because I thought it would be fun, informative, and perhaps easy. The textbook we used was not the dreadnought A History of Mathematics by Victor Katz, but the sloop Journey Through Genius by William Dunham. Both books emphasize the development of mathematics from the perspective of Western civilization, but let's quickly thank the Arabian scholars who preserved the works of the ancient Greeks from annihilation. It was those Greeks who got the ball rolling with demonstrative mathematics around the sixth century B.C. It was the Arabs in the twelveth century who translated and expounded on the Greeks, and brought their works back to Europe.

During the course I learned the top four mathematicians of all time:

• Archimedes (287 - 212 B.C.)
• Newton (1642 - 1727)
• Euler (1707 -1783)
• Gauss (1777 - 1855)

I have taken the liberty of writing a short obituary for each of these towering figures.

Archimedes was a true self-starter who liked to apply math to everyday problems. At an early age he invented a water pump called the Archimedes screw which is still in use today. He exploited the techniques of "method of exhaustion" and double "reductio ad absurdum" to prove many theorems regarding familiar two and three dimensional figures. In order to save his city Syracuse from ruination by the Romans he devised innovative war machines to repel the overwhelming army.

Newton was perhaps the greatest self-learner the world has ever known. In his early twenties he spent two years in rustic isolation during which he: discovered the generalized binomial theorem; invented differential and integral calculus; recognized the universal gravitation as the key mechanism of the solar system; and developed insights into the nature of light by refracting it through a piece of glass called a prism. Having little interest in publishing his world-shattering findings, he turned his attention to alchemy for almost 40 years, but was persuaded to publish something by Edmund Haley. The result was a physics text called Philosophiae Naturalis Principia Mathematica which is considered the greatest contribution to science ever made by one man.

Euler was the most prolific publisher of pure and applied mathematics in history. His mathematical contributions ranged over number theory, calculus of variations, graph theory, complex analysis, and differential equations. He applied math to acoustics, engineering, mechanics, astronomy, and optics. The publication of his complete works was started in 1911, and the end is not yet in sight. Originally planned for 72 volumes, the discovery of new works pushed the project to an estimated 100 volumes. In order to aid his work in number theory he memorized the first 100 prime numbers, their squares, their cubes, all the way to their sixth powers. As a child he memorized the entire Aeneid and could recite it flawlessly late in life.

Gauss was a child prodigy who at the age of 17 invented a technique for inscribing a regular 17 sided polygon within a circle. This was a ruler and compass construction that stunned the math world since no one since classical times thought such a construction was possible. For his Phd. thesis he proved the Fundamental Theorem of Algebra, but being a perfectionist (more about this later) he improved upon the proof three times in subsequent years. His superlative text on number theory established modular arithmetic as the fundamental tool for its study. He tired of pure mathematics and turned his skills to scientific endeavors. In order to predict the position of the asteroid Ceres, he invented the technique of least squares and error theory in general. He mapped the earth's magnetic field, and along with Weber invented an early form of the telegraph. His perfectionist nature made him reluctant to publish until every detail of proof was beyond criticism. One biographer claimed that his unpublished work would have advanced mathematics by 50 years.

The most shocking thing I learned from this course is that all of the math I learned in high school, college, and graduate school only brought me up to around the year 1900. Seems that the twentieth century and beyond is reserved for Phd. students.