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Results tagged with soft-question
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user 103722
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
39
votes
13
answers
4k
views
Examples of "miraculous" proofs [closed]
Concerning the proof that $\zeta(3)$ is irrational, Van der Poorten famously noted that
"Apéry's incredible proof appears to be a mixture of miracles and mysteries".
Indeed, many ideas introduced in …
108
votes
11
answers
12k
views
Examples of notably long or difficult proofs that only improve upon existing results by a sm...
I was recently reading Bui, Conrey and Young's 2011 paper "More than 41% of the zeros of the zeta function are on the critical line", in which they improve the lower bound on the proportion of zeros o …
14
votes
3
answers
4k
views
In a publication, should an `\ldots` always be followed by a period? [closed]
The Latex command \ldots is often used to denote "and so forth". For instance,
$$
\pi \approx 3.1415\ldots
$$
When a sentence ends with an \ldots, one is faced with the conundrum of how to properly …
1
vote
0
answers
189
views
What are some great examples of wordsmanship in published literature? [duplicate]
David L. Goodstein begins his book on statistical mechanics, ''States of Matter'', with the following introduction:
"Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died …
- 1,962
19
votes
1
answer
660
views
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)^{ …
12
votes
3
answers
3k
views
Where to publish new mathematical identities?
Similar questions have been asked before regarding journals that publish:
expository work,
recreational mathematics,
computational results,
new proofs of old theorems,
and even math textbooxs.
How …
4
votes
2
answers
4k
views
$\log(x)$ or $\ln(x)$ to denote the natural logarithm in research papers? [closed]
Since the natural logarithm, i.e. with base $e$, is very commonly used in research papers and that both $\ln(x)$ and $\log(x)$ are used to denote it, it is natural* to ask which of these notations to …
- 1,962
35
votes
5
answers
4k
views
Should computer code be included within publications that present numerical results?
Many research papers include numerical results obtained through computation. Most of the time such computations are performed using software that is used by many mathematicians, i.e., Maple, Mathemati …
7
votes
0
answers
205
views
My research paper involves computing additional terms of an existing OEIS sequence. Should I...
In the course of my research I computed terms of an existing OEIS sequence that are currently unknown. Having prepared my paper for publication, I am now faced with a (small) dilemma:
Do I first con …
- 1,962
29
votes
5
answers
3k
views
Has Apéry's proof of the irrationality of $\zeta(3)$ ever been used to prove the irrationali...
Apéry's proof of the irrationality of $\zeta(3)$ astounded contemporary mathematicians for its wealth of new ideas and techniques in proving the irrationality of a known constant. It is often the case …
- 1,962