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davidlowryduda
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  • Member for 11 years, 2 months
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825 votes
27 answers
194k views

How to study math to really understand it and have a healthy lifestyle with free time? [closed]

  • 10.2k
794 votes
49 answers
124k views

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

508 votes
10 answers
256k views

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

488 votes
10 answers
63k views

Best Sets of Lecture Notes and Articles

  • 48.5k
334 votes
36 answers
30k views

A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language

  • 6,052
302 votes
5 answers
74k views

In Russian roulette, is it best to go first?

  • 2,669
280 votes
63 answers
24k views

Funny identities [closed]

280 votes
27 answers
22k views

Why do mathematicians use single-letter variables?

  • 2,933
276 votes
4 answers
33k views

The Mathematics of Tetris

  • 69.9k
262 votes
32 answers
125k views

Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?

255 votes
40 answers
30k views

Fun but serious mathematics books to gift advanced undergraduates.

224 votes
2 answers
17k views

Proving you *can't* make $2011$ out of $1,2,3,4$: nice twist on the usual

213 votes
10 answers
33k views

How do I sell out with abstract algebra?

212 votes
5 answers
21k views

What do modern-day analysts actually do?

201 votes
32 answers
110k views

Books on Number Theory for Layman

201 votes
34 answers
40k views

List of interesting math videos / documentaries

191 votes
15 answers
33k views

What's the intuition behind Pythagoras' theorem?

190 votes
28 answers
126k views

What is a good complex analysis textbook, barring Ahlfors's?

  • 1,185
178 votes
9 answers
28k views

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

  • 2,654
177 votes
4 answers
11k views

A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$

165 votes
20 answers
28k views

Striking applications of integration by parts

  • 3,091
165 votes
9 answers
40k views

Lesser-known integration tricks

165 votes
7 answers
7k views

Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$

  • 1,785
164 votes
6 answers
27k views

Induction on Real Numbers

  • 1,743
161 votes
33 answers
29k views

Can you provide me historical examples of pure mathematics becoming "useful"?

  • 22.4k
161 votes
4 answers
34k views

Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

152 votes
1 answer
17k views

What's the significance of Tate's thesis?

  • 29.9k
140 votes
32 answers
76k views

Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$

  • 1,753
138 votes
16 answers
10k views

Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$

136 votes
22 answers
80k views

List of interesting math podcasts? [closed]

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