🇨🇭Leonhard
Euler

He went blind in his right eye at the age of thirty-one, and he treated this as a minor inconvenience. "Now I will have less distraction," he reportedly said. When total blindness claimed his left eye nearly three decades later, he simply dictated his papers to a secretary and continued producing mathematics at a rate that astonished his contemporaries. Leonhard Euler published 886 separate works in his lifetime and left behind so many unpublished manuscripts that the Saint Petersburg Academy of Sciences, which had employed him for most of his adult life, was still printing them fifty years after his death. No mathematician before or since has produced so much, across so many fields, at such sustained quality. He is the reason every mathematician in the world today writes e for the base of the natural logarithm, i for the square root of negative one, π for the ratio of a circle's circumference to its diameter, Σ for summation, and f(x) for a function of x. He invented the notation. He did not just advance mathematics — he gave it its language.

Euler was born in Basel, Switzerland, on April 15, 1707, the son of a Calvinist pastor who expected him to enter the ministry. His father had studied mathematics under Jacob Bernoulli, and young Leonhard demonstrated such extraordinary ability that Jacob's brother Johann Bernoulli — the finest mathematician in Europe at the time — agreed to tutor him privately on Saturday afternoons. By thirteen, Euler had enrolled at the University of Basel. By sixteen, he had completed his master's degree with a dissertation comparing the natural philosophies of Descartes and Newton. By nineteen, he was submitting papers to the Paris Academy, though the prize went that year to a man twice his age. By twenty, he had been invited to Russia by Peter the Great's Saint Petersburg Academy of Sciences, an institution founded precisely to attract the best European minds. He accepted, packed his bags, and spent the next fourteen years transforming mathematics.

In Saint Petersburg, Euler solved a problem that had defeated the best mathematicians in Europe for nearly a century: the Basel problem, posed by Pietro Mengoli in 1650, which asked for the precise value of the infinite sum 1 + 1/4 + 1/9 + 1/16 + ⋯ — the sum of the reciprocals of the squares of all positive integers. Euler showed, with an argument of stunning cleverness, that this sum equals π²/6. The result was so unexpected — connecting the seemingly unrelated concepts of integers and pi — that it announced to the mathematical world that something genuinely extraordinary had arrived. He followed this with the solution to the Königsberg bridge problem, demonstrating that no walk could cross all seven bridges of the city exactly once, thereby founding the entire field of graph theory and topology. He was twenty-eight years old.

The achievement for which Euler is now most celebrated outside professional mathematics is his identity, derived from his formula e^ix = cos x + i sin x. Setting x = π yields the equation e^iπ + 1 = 0, which combines the five most fundamental constants in mathematics — e, i, π, 1, and 0 — in a single relationship of perfect simplicity. In a 1988 poll, readers of the journal Mathematical Intelligencer voted it the most beautiful theorem in mathematics. Richard Feynman called it "the most remarkable formula in mathematics." Its beauty is not merely aesthetic; it reveals a deep structural unity between exponential growth, circular geometry, and the algebra of imaginary numbers that was entirely unexpected before Euler uncovered it. This formula is to mathematics what a perfect cadence is to music: the resolution of everything into a single, inevitable harmony.

Euler's contributions extended far beyond any single result. He created the study of graph theory. He developed the calculus of variations. He solved the problem of the vibrating string and laid the foundations of acoustics. He created the modern theory of mechanics and fluid dynamics. He wrote textbooks — the Introductio in analysin infinitorum, the Institutiones calculi differentialis, the Institutiones calculi integralis — that defined the standard curriculum in mathematics for more than a century and shaped how every subsequent generation learned the subject. He also worked in number theory, optics, astronomy, naval architecture, and the design of musical instruments. In all of these fields, he made contributions that would have established any lesser mathematician's lasting reputation. For Euler, they were footnotes to a larger career.

On September 17, 1783, Euler spent the afternoon calculating the orbit of the newly discovered planet Uranus and playing with his grandchildren. He drank tea, discussed the recently completed first balloon flight over Paris, and then — mid-sentence, while dictating a calculation — suffered a cerebral hemorrhage. He died within the hour. He was seventy-six years old and had never stopped working. His collected works, published by the Swiss Mathematical Society starting in 1911, run to more than ninety volumes. They are not yet complete. No other mathematician in history leaves a comparable monument. The currency of eighteenth-century mathematics is Euler's notation, Euler's methods, Euler's theorems. Strip Euler from mathematics and you would have to redesign the subject from the ground up.