3
votes
1answer
71 views

Why might one be inclined to think that polynomials of the form $\cos(n\arccos{x})$ would minimize error in Lagrange interpolation?

I was first introduced to Chebyshev polynomials (of the first kind) in the form $T_n(x)=\cos\left(n \operatorname{arccos}(x)\right)$. The usual recurrence relation was then derived from using trig ...
3
votes
0answers
121 views

What makes Beal's conjecture “beautiful” enough to make people offer a million dollar prize? [closed]

What makes Beal's conjecture "beautiful" enough to make people offer a million dollar prize? Is it just a challenge or does it have real applications?
16
votes
2answers
487 views

Motivation for/history of Jacobi's triple product identity

I'm taking a short number theory course this summer. The first topic we covered was Jacobi's triple product identity. I still have no sense of why this is important, how it arises, how it might have ...
7
votes
1answer
472 views

History behind Exact Sequences.

I am very much interested in listening to the history behind the exact sequence. We know that the exact sequence is sequence of objects with morphisms such that image of one morphism equals to the ...
12
votes
6answers
902 views

Motivation of the Gaussian Integral

I read on Wikipedia that Laplace was the first to evaluate $$\int_{-\infty}^\infty e^{-x^2} \, \mathrm dx$$ Does anybody know what he was doing that lead him to that integral? Even better, can ...