List questions from fake-proofs

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What are some false proofs for true or false statements where the error in the proof is not obvious?

Published on 13 Oct 2015 - 12:43

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Prove that if 2 divides $x^2-5$ then 4 divides $x^2-5$

Published on 14 Oct 2015 - 1:46

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$2=1$ Paradoxes repository

Published on 26 Mar 2026 - 22:55

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$\lim\limits_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$ prove by polar coordinates.

Published on 23 Mar 2026 - 3:51

100

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Do $L^{2}$ energy estimates implies $H^{k}$ weak solutions?

Published on 10 Mar 2026 - 3:51

86

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Is there a way to prove this wrong?

Published on 21 Oct 2015 - 18:03

245

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What is wrong with the following proof that tries to prove that $2=1$?

Published on 23 Oct 2015 - 12:42

65

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Math: amounts and a proof about amounts

Published on 07 Mar 2026 - 16:34

102

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Strange problem with the imaginary unit

Published on 26 Mar 2026 - 22:55

79

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Flaw in proof involving binomial theorem

Published on 30 Oct 2015 - 14:57

40

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If $f:X\to Y$ is linear and $y^\ast \circ \ f \in X^\ast$ for all $y^\ast \in Y^\ast$, then $f$ is continuous

Published on 31 Oct 2015 - 2:43

103

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What's wrong here?

Published on 27 Mar 2026 - 20:49

126

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A paradox I came up with, proof verification.

Published on 09 Nov 2015 - 18:32

108

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Stumbled on a "proof" to generate primes and I cannot find the wrong step.

Published on 10 Nov 2015 - 15:18

222

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Is $i$ equal to $-i$?

Published on 28 Mar 2026 - 10:17

List Question

What are some false proofs for true or false statements where the error in the proof is not obvious?

Prove that if 2 divides $x^2-5$ then 4 divides $x^2-5$

$2=1$ Paradoxes repository

$\lim\limits_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$ prove by polar coordinates.

Do $L^{2}$ energy estimates implies $H^{k}$ weak solutions?

Is there a way to prove this wrong?

What is wrong with the following proof that tries to prove that $2=1$?

Math: amounts and a proof about amounts

Strange problem with the imaginary unit

Flaw in proof involving binomial theorem

If $f:X\to Y$ is linear and $y^\ast \circ \ f \in X^\ast$ for all $y^\ast \in Y^\ast$, then $f$ is continuous

What's wrong here?

A paradox I came up with, proof verification.

Stumbled on a "proof" to generate primes and I cannot find the wrong step.

Is $i$ equal to $-i$?

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