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### Theorems true but wrong. [closed]

Many theorems have the form : Premise(es) implies Conclusion(s)
Example A of wrongness:
There are many examples in which a theorem is stated without mentioning that part of the premise is not ...

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### Does a referee have to check carefully the proof ?

I have always checked very carefully the papers I was refereeing when I wanted to suggest "accept". Actually I spend almost as much time checking the maths of a paper I referee than checking the maths ...

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### Why is the Gaussian so pervasive in mathematics?

This is a heuristic question that I think was once asked by Serge Lang. The gaussian: $e^{-x^2}$ appears as the fixed point to the Fourier transform, in the punchline to the central limit theorem, as ...

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### Example of a function that behaves like another function

I need a function $f(x)$ with the following properties -
It should be monotonically non-decreasing.
For $x \geq 1$, $x + \frac{1}{x} - f(x) < \epsilon$ where $\epsilon$ is an extremely small ...

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### What is the strategy for “all words valid” scrabble?

The rules for "all words valid" scrabble are exactly the same as ordinary scrabble, except that every single combination of letters is in the dictionary. To make the game deterministic, we will also ...

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### Demonstrating that rigour is important

Any pure mathematician will from time to time discuss, or think about, the question of why we care about proofs, or to put the question in a more precise form, why we seem to be so much happier with ...

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**1**answer

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### Sum of subset of geometric series: a^2^n

The formula for 1 + a + a^2 + .... where 0 < a < 1 is $\frac{1}{1-a}$, but what if you wanted to sum only those where the exponent is a power of 2? That is,
$S = a + a^2 + a^4 + a^8 + \cdots$
...

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### Published results: when to take them for granted?

Two kinds of papers. There are two kinds of papers: self-contained ones, and those relying on published results (which I believe are the vast majority).
Checking the result. Of course, one should ...

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### Proofs by induction [closed]

Background
I'm interested in the issue of "explanatory" mathematical proofs and would like to try to find out what intuitions mathematicians have about induction, because there seems to be some ...

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### Books about polynomials [closed]

Hi,have you a good reference (books) for the study of polynomials with one variable or many variables ? Thanks for your help.
Don't hesitate to correct my English.

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### Most interesting mathematics mistake?

Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincaré's 3d sphere characterization or the search to prove ...