Linked Questions
13 questions linked to/from Computer algebra errors
201
votes
67
answers
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Examples of eventual counterexamples
Define an "eventual counterexample" to be
$P(a) = T $ for $a < n$
$P(n) = F$
$n$ is sufficiently large for $P(a) = T\ \ \forall a \in \mathbb{N}$ to be a 'reasonable' conjecture to ...
107
votes
36
answers
21k
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Interesting examples of vacuous / void entities
I included this footnote in a paper in which I mentioned that the number of partitions of the empty set is 1 (every member of any partition is a non-empty set, and of course every member of the empty ...
111
votes
32
answers
14k
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Special rational numbers that appear as answers to natural questions
Motivation:
Many interesting irrational numbers (or numbers believed to be irrational) appear as answers to natural questions in mathematics. Famous examples are $e$, $\pi$, $\log 2$, $\zeta(3)$ etc. ...
113
votes
25
answers
37k
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Examples of math hoaxes/interesting jokes published on April Fool's day?
What are examples of math hoaxes/interesting jokes published on April Fool's day?
For a start P=NP.
Added 2024-04-01 Anything new in 2024?
20
votes
13
answers
7k
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Longest coinciding pair of integer sequences known
There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by ...
- 9,720
25
votes
8
answers
3k
views
How do we explain the use of a software on a math paper?
Suppose one has written a math/computer science paper that is more focused in the math part of it. I had a very complicated function and needed to find its maximum, so I used Mathematica (Wolfram) to ...
36
votes
8
answers
3k
views
Examples of errors in computational combinatorics results
I would like to collect examples of errors in published numerical results in computational combinatorics: where a result (typically a counting of some objects, or an extremal quantity within some ...
28
votes
3
answers
7k
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Famous examples of "serendipity" in 20th century mathematics
The term "serendipity" is commonly used in the literature to refer to the historical
evidence that very often researchers make unexpected and beneficial discoveries by
chance, while they are ...
11
votes
3
answers
3k
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A two-variable Fourier series and a strange integral
I have recently had occasion to investigate the Fourier series of the function $f(x,y)=\log({2+\cos 2\pi x} +\cos{2\pi y})$. Accordingly, define
$I(m,n)=\int_{0,0}^{1,1}f(x,y)\cos{2\pi mx}\cos{2\pi ...
- 13.1k
13
votes
3
answers
2k
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An elementary number theoretic infinite series
For a positive integer $k$, let $d(k)$ be the number of divisors of $k$. So $d(1)=1$, $d(p)=2$ if $p$ is a prime, $d(6)=4$, and $d(12)=6$.
What are the precise asymptotics of $\sum_{k=1}^n 1/(k d(k))...
- 24.7k
6
votes
6
answers
402
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Physical Disturbances to Computations [closed]
In this paper, page 7 (160 of the Journal), Fig 3, there is a particularly amusing (not to the authors!) caption:
"... On April 1 of year 2 in the $S_0$ experiment, the computer was hit by a cosmic ...
19
votes
1
answer
665
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How can we be sure that results that rely heavily on extensive computations are correct?
Recently a ''bug'' was discovered in one of the most popular mathematics software, Wolfram Mathematica (see links here and here). It concerns the evaluation of the sum
$$
\sum_{k=1}^{n-1} \frac{(-1)^{...
0
votes
0
answers
32
views
Limit/Expansion Problems for Benchmarking
I am interested in collections of ‘interesting’ problems involving limits and/or asymptotic expansions of univariate real-valued functions. The purpose is to test a particular algorithm that I ...
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