Carl Friedrich Gauss and Augustin Louis Cauchy

I first heard Gauss's name when I was in Physics II, and I have to say I probably despised him for his Gaussian surfaces (hypothetical/imaginary surfaces enclosing charge distributions), Gauss's Law (which relates thenet flux of an electric field through a closed Gaussian surface to the net charge enclosed by the surface), and the gauss unit for magnetic flux. At the time, I did not understand the math behind any of this, but now that I actually know what it is, it's just incredible.

I'm finding out that not only did Gauss contribute to electromagnetism, but so many other areas. Today I just learned about Gauss' Mean Value Theorem for complex variables, and I got excited enough that I had to look up some stuff about him online. He was a child prodigy who contributed to number theory, differential geometry, optics, and astronomy, to name a few.

Whew!

Another guy that I felt compelled to do a little research on is Cauchy, since every other theorem we've learned in Complex Variables has his name attached to it. It looks like his work dealt mostly with complex analysis, mechanics, and optics. I couldn't find as much information on him right off the bat (the above info on Gauss was from about 2 seconds of Googling, and 7 minutes of reading), but what I've learned of his math so far is "pretty" (to quote my Differential Equations professor. Foo!). Because of the Cauchy-Riemann Equations, the idea of differentiability of a complex function is much stronger than the the idea of differentiability of a real function (for a complex function f, if f is differentiable once, it is infinitely differentiable, but if a real function g is differentiable n times, it may not be differentiable n+1 times). And the Cauchy Integral Theorem! And the Cauchy-Goursat theorem! They seem relatively simple now (to use, derive, prove) because *we* didn't have to come up with them, but how did they do it the first time? It boggles my mind.

I apologize to the 99% of people who will read this and have absolutely no clue what I just said.

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