Swiss mathematician who was tutored by Johann Bernoulli. He worked at the Petersburg Academy and Berlin Academy of Science. He had a phenomenal memory, and once did a calculation in his head to settle an argument between students whose computations differed in the fiftieth decimal place. Euler lost sight in his right eye in 1735, and in his left eye in 1766. Nevertheless, aided by his phenomenal memory (and having practiced writing on a large slate when his sight was failing him), he continued to publish his results by dictating them. Euler was the most prolific mathematical writer of all times finding time (even with his 13 children) to publish over 800 papers in his lifetime. He won the Paris Academy Prize 12 times. When asked for an explanation why his memoirs flowed so easily in such huge quantities, Euler is reported to have replied that his pencil seemed to surpass him in intelligence. François Arago said of him "He calculated just as men breathe, as eagles sustain themselves in the air" (Beckmann 1971, p. 143; Boyer 1968, p. 482).

Euler systematized mathematics by introducing the symbols e , i , and f(x) for f a function of x. He also made major contributions in optics, mechanics, electricity, and magnetism. He made significant contributions to the study of differential equations. His Introducio in analysin infinitorum (1748) provided the foundations of analysis. He showed that any complex number to a complex power can be written as a complex number, and investigated the beta and gamma functions. He computed the Riemann zeta function to for even numbers.

He also did important work in number theory, proving that that the divergence of the harmonic series implied an infinite number of Primes, factoring the fifth Fermat number (thus disproving Fermat's conjecture), proving Fermat's lesser theorem, and showing that e was irrational. In 1772, he introduced a synodic coordinates (rotating) coordinate system to the study of the three-body problem (especially the Moon ). Had Euler pursued the matter, he would have discovered the constant of motion later found in a different form by Jacobi and known as the Jacobi integral.

Euler also found the solution to the two fixed center of force problem for a third body. Finally, he proved the binomial theorem was valid for any rational exponent. In a testament to Euler's proficiency in all branches of mathematics, the great French mathematician and celestial mechanic Laplace told his students, "Liesez Euler, Liesez Euler, c'est notre maître à tous" ("Read Euler, read Euler, he is our master in everything" (Beckmann 1971, p. 153).

Additional biographies: MacTutor (St. Andrews), Dublin Trinity College, Bonn