Harald Hanche-Olsen's user avatar
Harald Hanche-Olsen's user avatar
Harald Hanche-Olsen's user avatar
Harald Hanche-Olsen
  • Member for 10 years, 8 months
  • Last seen more than a week ago
1547 votes
86 answers
584k views

Visually stunning math concepts which are easy to explain

  • 821
800 votes
50 answers
126k views

Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)

527 votes
37 answers
71k views

Do complex numbers really exist?

  • 1,605
277 votes
1 answer
25k views

How discontinuous can a derivative be?

179 votes
9 answers
30k views

Self-Contained Proof that $\sum\limits_{n=1}^{\infty} \frac1{n^p}$ Converges for $p > 1$

  • 2,674
130 votes
4 answers
30k views

What is category theory useful for?

  • 103k
117 votes
14 answers
50k views

How can I understand and prove the "sum and difference formulas" in trigonometry?

  • 2,927
96 votes
11 answers
4k views

Problems that become easier in a more general form

  • 9,276
51 votes
5 answers
22k views

How to prove that the sum and product of two algebraic numbers is algebraic? [duplicate]

  • 10.2k
50 votes
3 answers
6k views

Why are smooth manifolds defined to be paracompact?

49 votes
1 answer
5k views

Convergence of $\sum \limits_{n=1}^{\infty}\sin(n^k)/n$

  • 2,541
40 votes
4 answers
3k views

Is Banach-Alaoglu equivalent to AC?

  • 13.8k
37 votes
17 answers
2k views

Examples where it is easier to prove more than less

  • 514
32 votes
3 answers
4k views

Intuitively, why is the Gaussian the Fourier transform of itself?

29 votes
3 answers
8k views

What do compact sets look like in the rationals?

  • 1,410
28 votes
2 answers
4k views

Motivation behind the definition of a Manifold.

  • 423
27 votes
2 answers
3k views

How deal with Gothic letters, like $\mathfrak{ A,B,C,D,a,b,c,d}\dots$, when writing by hand?

  • 271
26 votes
3 answers
4k views

When the trig functions moved from the right triangle to the unit circle?

25 votes
2 answers
1k views

Does Brownian motion visit every point uncountably many times?

25 votes
4 answers
3k views

Infinite Product $\prod\limits_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$

  • 1,972
24 votes
3 answers
3k views

Showing that $\gamma = -\int_0^{\infty} e^{-t} \log t \,dt$, where $\gamma$ is the Euler-Mascheroni constant.

20 votes
7 answers
51k views

Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $

18 votes
5 answers
11k views

The sum: $\sum_{n=1}^\infty (-1)^{n+1}\frac{1}{n}=\ln(2)$ using Riemann Integral and other methods

  • 919
18 votes
1 answer
6k views

About the asymptotic formula of Bessel function

  • 1,055
17 votes
4 answers
3k views

Proofs that involve Tricks

  • 3,225
15 votes
2 answers
2k views

A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$

12 votes
3 answers
714 views

Elementary proof for $\lim\limits_{n \to\infty}\frac{n!e^n}{n^n} = +\infty$

12 votes
2 answers
4k views

How to prove that a bounded linear operator is compact?

11 votes
2 answers
131 views

Students who see ears of another student

  • 2,095
7 votes
1 answer
304 views

$n^3+7$ cannot be a square number.

  • 2,393