Every now and then, we encounter the names of great mathematicians, scientists, and engineers of the past. Attached to equations, constants, and even SI units, they remind us of the people who went before us. As you stay in university, you notice that some names just pop up in your course notes and formula sheets again and again, like zombies in a survival game. You can’t get away from them. That’s when you know you’ve encountered a badass genius.
Arguably the greatest mathematician ever, Leonhard Euler (1707-1783) was born in Basel, Switzerland. By the time he was fourteen, he was able to enroll in the University of Basel. The professor of mathematics at the time, Johann Bernoulli, told him he already had too many students, but if Euler really wanted to learn, Bernoulli could give him some books to study by himself. Undeterred, the young Euler hit the books, and once a week would visit Bernoulli’s house to ask him questions. While there, he became best friends with Bernoulli’s son Daniel (who was seven years older than him).
Bernoulli was very impressed with his young pupil, and after a few years, their relationship had almost become reversed, with Euler the teacher. In 1726, Euler wrote his dissertation on the subject of sound wave propagation, and started looking for work. Just a few years earlier, the Empress of Russia had opened a new academy in St. Petersburg and invited young scientists from all over Europe to do research there. Unfortunately, the only job opening in the academy was in medicine, so Euler applied for it – and somehow got the offer. He later found out that Daniel Bernoulli had actually gotten a job at the Academy a few years earlier, and had convinced the Russians that they had to hire Euler even if he didn’t fit the job requirements. Clearly, personal connections were just as valuable in the 18th century as they are in the 21st.
So at the age of twenty, Euler had already gotten a doctorate and had a job in one of the world’s most prestigious research academies. (Side note: What have I been doing with my life?) He spent the remainder of his life going between the St. Petersburg and Berlin Academies (you see, he got so famous the Germans wanted him to work for them too), often collaborating with Daniel Bernoulli on mechanics work. By the time he died in 1783, he had written so many papers about his discoveries that there was a major backlog in the St. Petersburg scientific journal, and it took another forty-eight years after his death before all his work got published.
Euler’s most famous contribution came in mathematics, where he introduced the symbol i for the imaginary numbers and showed that they—which Descartes and Leibniz had written off as useless—actually did stuff. For example, he proved that exponential and trigonometric functions could be linked via what we now call Euler’s formula. He also discovered that the natural log of x was the integral of 1/x , created a formula to calculate perfect numbers, and made contributions to differential equations. His solution method for linear homogeneous ODEs (which are today known as Cauchy-Euler equations) is still taught as the method of undetermined coefficients (and if you end up with imaginary numbers in the exponent, then the aforementioned Euler’s formula can convert it into a trig function).
In solid mechanics, Euler and his pal gave us the Euler-Bernoulli beam equation, which states that the third derivative with respect to length of the beam deflection is proportional to the shear force. Euler additionally derived a formula to calculate the maximum loading on a vertical beam before it buckles.
Euler also published differential equations for continuity and conservation of momentum in inviscid fluids. A century later, Claude-Louis Navier and George Stokes would generalize these equations by adding viscosity terms. But the continuity and momentum equations – along with Bernoulli’s “conservation of energy along a streamline” equation – continue to be foundational for fluid dynamics. Heck, we’ve even developed CFD software specifically to solve these equations.
More than two centuries after his death, Euler has left us a legacy in many different fields. I’m sure I left a lot of his discoveries out, but you get the picture. In fact, in my own field of mechanical engineering, I’m not sure how much we would even be able to study without the contributions of Euler and later generations who built on his work.
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