"Metrical laws are generally equations of motion and topological laws are generally conservation laws." I'm looking for a good text that can give context to this statement I found floating around the web

This is a re-ask of a deleted question that OP doesn't really wanna undelete but has given me permission to re-ask: https://math.stackexchange.com/questions/2863781/is-this-classic-probability-view-on-fermat-last-theorem-studied-somewhere I was wondering where (or maybe even if) is this or any s...

My question (more of a hypothesis really) is basically this: If a function $f(x)$ is defined such that $f'(x)$ is not constant and never the same for any 2 values of $x$. Then there do not exist positive integers $a,b,c$ and $a\le b\le c$ such that, $$\int_0^{a} f(x)dx = \int_b^{c} f(x)dx\tag1$...

I'm am having trouble coming up with a proof strategy for the following variation of Fermat's Theorem. If the solution is trivial, please forgive me, this is my first encounter with this theorem. I was able to show/understand (with help) the other variations of this theorem that you'd typically s...

Can we reduce Fermat last theorem problem to the case $z=x+1$ where $x^n + y^n = z^n$? Why am I asking that? I found in that case and in case $n=3$ that difference of cubes: $1$,$7$,$19$,$37$ http://oeis.org/A003215 is a combination of diferrence of next sequence: http://oeis.org/A011934

We now that Fermat's last theorem is true so there are not positive integer solutions to $$x^n+y^n=z^n$$ for $n\in\mathbb{N}$ and $n>2$. But what about if $n\in\mathbb{R}$ or $n\in\mathbb{R}^+$?

Can someone please give the original paper by Prof. Wiles of the proof of Fermat's Last Theorem? I cannot find it.

I am studying about topological game, and i found the progression: Point-Open(X)>> Finite-Open(X)>>Compact-Open(X). I understand that a natural way to extend 'be finite' is 'be compact', but looking from a cardinal point of view, the sequence would be 1 (Point) >> n (Finite)>> $\omega$ (Countable...

I know that X, emptyset are omega-open

What are the best consequences of proving this open problem for more than 300 years in 1994 ? What are prerequisites for understanding its proof? After the proof of Andrew Wiles are there any new ways to prove it? If I want to compare it with Trinary Goldbach's Conjecture proven in 2013 . which...