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beep-boop
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379 votes
73 answers
83k views

'Obvious' theorems that are actually false

121 votes
2 answers
8k views

What makes a theorem "fundamental"?

52 votes
16 answers
6k views

Is a proof still valid if only the writer understands it? [closed]

35 votes
5 answers
3k views

"Stick it to the man!" Mathematical discoveries that resulted in persecution.

23 votes
6 answers
13k views

Is $i$ irrational?

21 votes
5 answers
6k views

Is there a(n elementary) function whose derivative we cannot integrate?

21 votes
9 answers
6k views

Is there an interval notation for complex numbers?

19 votes
2 answers
2k views

How to raise a number to a quaternion power

16 votes
2 answers
13k views

Is there a relationship between the cross product and quaternion multiplication?

15 votes
3 answers
9k views

Can asymptotes be curved?

14 votes
7 answers
2k views

How do we know whether certain mathematical theorems are circular?

12 votes
6 answers
4k views

If an inequality is true for all natural numbers, is it necessarily true for all real numbers inbetween?

9 votes
7 answers
933 views

How can $\mathbb Q$ be countable, when there is no "next" rational number?

8 votes
4 answers
2k views

What is the most efficient way to calculate the sine of a rational number?

8 votes
2 answers
1k views

Does it make sense to compare complex numbers in certain circumstances?

7 votes
7 answers
16k views

Intuitively, why does $\int_{-\infty}^{\infty}\sin(x)dx$ diverge? [duplicate]

6 votes
2 answers
938 views

Are there as many real numbers as there are imaginary numbers?

6 votes
4 answers
879 views

Name of this property: even + odd = odd, rational + irrational = irrational [Complementary Subgroup Test]

6 votes
2 answers
2k views

Theorems with one-line proofs [closed]

6 votes
1 answer
402 views

Do there exist equations that cannot be solved in $\mathbb{C}$, but can be solved in $\mathbb{H}$?

6 votes
3 answers
20k views

How to properly construct an $\epsilon-N$ proof

5 votes
3 answers
971 views

Why can mathematicians pick and choose axioms?

5 votes
1 answer
664 views

Why do so few people use the $\equiv$ symbol for identities?

4 votes
3 answers
2k views

Why do we drop the abolute value bars when doing indefinite integration?

4 votes
2 answers
3k views

Determining whether a number is a 'factorial number'

4 votes
5 answers
8k views

'Proof ' that $\ln(x)$ converges

4 votes
1 answer
99 views

Proving that $\lim\limits_{n \to \infty} \frac{E_{n+1}}{E_n}=2^{-2/3}$

4 votes
2 answers
8k views

Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$. [duplicate]

4 votes
2 answers
2k views

Generalising integration by parts for the product of more than two functions

4 votes
3 answers
3k views

Minimum number of attempts to guess a PIN code, given constraints