I was flipping through the number theory book and I noticed a little bio section on C.G. J. Jacobi, the man who gave us the Jacobi symbol, $(\frac{a}{n})$, as defined:

(1)where $\left(\frac{a}{p_1}\right),\left(\frac{a}{p_2}\right),...,\left(\frac{a}{p_r}\right)$ are Legendre symbols.

Now, that's cool and all, but did you know:

- There is a crater on the Moon named after him?
- The phrase "Invert, always invert," is associated with Jacobi because he thought that problems were best addressed backwards?
- He contributed to a great number of mathematical areas, including number theory, vector theory, and partial differential equations.

C.J. Scriba once compared Jacobi to Euler, saying,

"Jacobi and Euler were kindred spirits in the way they created their mathematics. Both were prolific writers and even more prolific calculators; both drew a great deal of insight from immense algorithmical work; both laboured in many fields of mathematics (Euler, in this respect, greatly surpassed Jacobi); and both at any moment could draw from the vast armoury of mathematical methods just those weapons which would promise the best results in the attack of a given problem."

Wikipedia also mentioned that Jacobi was "the most inspiring teacher of his time" and I was wondering if there were any other mathematicians out there who were similarly inspiring and how so. Does anyone out there have a mathematician who inspires them to tackle tough problems and plow through mathematics?

I've always found Paul Erdős to be a huge inspiration because of his undying dedication to mathematics and his treatment of it as a social discipline and one that is always thoroughly interesting. Check out Paul Hoffman's The Man Who Loved Only Numbers for a great read on Erdős.