As a maths enthusiast, there’s one debate that seems to crop up again and again in nerdy conversations—Euler or Gauss? Who deserves the title of the greatest mathematician of all time?
It’s a tough question, and the case for both giants is strong. Euler, with his sheer breadth and prolificacy, seems almost superhuman. The number of concepts, theorems, and formulas named after him is staggering—Euler’s formula, Euler’s totient function, Euler’s constant, and the list goes on. He was like a one-man publishing house, churning out results in analysis, number theory, topology, mechanics, and even music theory. It feels like there isn’t a single branch of mathematics untouched by Euler’s brilliance.
Then there’s Gauss, the so-called "Prince of Mathematicians," whose influence on the subject is almost mythical. His contributions are characterised not just by their depth but by their perfection. Gauss wasn’t just solving problems—he was creating new frameworks for entire fields of mathematics. Number theory, geometry, statistics, electromagnetism—you name it, Gauss elevated it.
But for me, the answer is surprisingly simple. It’s Gauss, and the reason has everything to do with the passage of time.
Why Gauss Wins
Gauss came later. That’s it. That’s the argument.
If Euler and Gauss had been contemporaries—working with the same tools, under the same constraints—I firmly believe Euler would have outshone Gauss. Euler had an almost limitless imagination and a relentless work ethic that allowed him to produce more results than most mathematicians could even dream of. He kept producing groundbreaking work even after going blind, for crying out loud!
But history doesn’t work in hypotheticals. Gauss had the advantage of standing on Euler’s shoulders. By the time Gauss came along, Euler had already paved the way, laying the foundations in fields that Gauss would later refine and expand. This is not to diminish Gauss’s achievements in any way—his contributions were revolutionary. But it’s important to acknowledge that Euler did much of the heavy lifting.
Take, for example, number theory, a field both mathematicians are deeply associated with. Euler’s work on the properties of numbers was groundbreaking, but it was Gauss who synthesised and systematised it into something more cohesive. Gauss’s Disquisitiones Arithmeticae is still considered one of the greatest texts in the history of mathematics, but without Euler’s earlier explorations, would it have even been possible?
The Hypothetical Showdown
Now, let’s imagine an alternate timeline where Euler and Gauss are contemporaries, working side by side. Who would win?
I have no doubt it would be Euler. He had an insatiable appetite for discovery and an uncanny ability to connect ideas across disciplines. Gauss was meticulous and precise, but Euler had a certain creative chaos that allowed him to push the boundaries of what was thought possible.
This isn’t to say that Gauss would have been overshadowed—far from it. Gauss had a genius for depth, for taking an idea and perfecting it to the point of immortality. But in a world where both men were tackling the same problems at the same time, I think Euler’s sheer versatility and volume would have given him the edge.
The Verdict
So, where does this leave us? For me, it’s Gauss—simply because of the historical timeline. Gauss had the advantage of building on Euler’s work, and he used that advantage brilliantly. But if you take away the time gap, if you put them on an equal footing, I think Euler would have taken the crown.
In the end, though, the comparison feels almost unfair. Euler and Gauss were titans of mathematics, each leaving an indelible mark on the field in their own unique way. Perhaps the real answer to the Euler-vs-Gauss debate is that we don’t have to choose. Their combined legacy is a gift to mathematicians everywhere, a reminder of what human curiosity and intellect can achieve.
But for now, if I had to pick one, it’s Gauss—because sometimes history is just as important as talent.
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