Dear 100 Hour Board,
Who is cooler: Sir Isaac Newton, or Leonhard Euler?
Isaac Newton. It seems obvious in the 21st century that we should be able to use math to describe the motion of basically all macroscopic objects, but it was not obvious at all in the 17th century. Decades earlier, Francis Bacon proposed a vision of science in which many phenomena could be described using a few natural laws. In fulfilling that vision, Newton not only discovered calculus and his laws of motion but revolutionized the way Western thinkers thought about the universe and humanity itself. Newton's laws captured the Western imagination and convinced us that the scientific method could help us harness the laws of the universe to control and predict anything.
Does this answer your question?
Euler, obviously. Newton is overrated.
Sure, Newton 'thought up' Calculus, but Leibniz also did that, independently, so how cool is he really? Plus, Newtonian mechanics have been replaced by general relativity. Would we have been able to do that without the foundation of Newtonian mechanics? I guess not. But, we wouldn't have general relativity without Euler either.
His contributions to modern mathematics - and physics - are unmatched, even by Newton. Do you even know how vital Euler's number (e) is? We'd never go to space or figure out radioactivity, economics, demographic studies, microbiology, everything. e is literally so essential we might as well be back in the Stone Age without it.
He also popularized the usage of π to represent 3.14, and dubbed √-1 as 'i'. And that's just basic notation. In complex analysis, he proved e^(iπ)+1=0 which is literally essential to dealing with complex numbers. In number theory, he proved Fermat's little theorem, connected Euler products with the Riemann zeta function and also made contributions to Fermat's sums of squares, Lagrange's four-square theorem and conjectured what would eventually become Gauss's crowning jewel in number theory, quadratic reciprocity. He also has other very significant number-theoretic functions named after him (thanks to his work on them) like the Euler totient function. In graph theory and topology he proved that the seven bridges of Konigsberg problem was unsolvable. He also proved a ton of little things like the centroid and orthocenter and circumvented all being colinear in a triangle, on a line called the Euler line.
Newton may have a handful of laws named after him or whatever, and I will grant, he was a very important physicist.
However, Euler is a far greater mathematician and made a greater number of valuable contributions to modern mathematics, and by extension, physics. Therefore, Euler is cooler, supremely underrated, and people need to know more about him.
Pebble (a huge flippin' nerd)
(A note from Guesthouse - You guys have no idea what kind of rant this question sparked. I had to listen to him talk about this for nearly an hour.)
I have used far more of mathematics either derived or named after Euler. Pebble's answer via Guesthouse just scratches the surface. So, for me personally, Euler is more important.