Linked Questions

18 votes
8 answers

Conceptual insights and inspirations from experimental and computational mathematics [duplicate]

I am interested in whether experiments on computers can help identifying new ideas or concepts in Mathematics. I am not talking about confirming particular conjectures up to certain numbers (for ...
108 votes
89 answers

Tweetable Mathematics

Update: Please restrict your answers to "tweets" that give more than just the statement of the result, and give also the essence (or a useful hint) of the argument/novelty. I am looking for ...
77 votes
27 answers

What could be some potentially useful mathematical databases?

This is a soft question but it's not meant as a big-list question. I have recently been asked whether I want to provide feedback at the pre-beta stage on a forthcoming website that will provide a ...
149 votes
14 answers

What is an integrable system?

What is an integrable system, and what is the significance of such systems? (Maybe it is easier to explain what a non-integrable system is.) In particular, is there a dichotomy between "...
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54 votes
28 answers

Nontrivial question about Fibonacci numbers?

I'm looking for a nontrivial, but not super difficult question concerning Fibonacci numbers. It should be at a level suitable for an undergraduate course. Here is a (not so good) example of the sort ...
67 votes
11 answers

The use of computers leading to major mathematical advances II

I would like to ask about recent examples, mainly after 2015, where experimentation by computers or other use of computers has led to major mathematical advances. This is a continuation of a question ...
56 votes
14 answers

What advantage humans have over computers in mathematics?

Now that AlphaGo has just beaten Lee Sedol in Go and Deep Blue has beaten Garry Kasparov in chess in 1997, I wonder what advantage humans have over computers in mathematics? More specifically, are ...
35 votes
14 answers

Where have you used computer programming in your career as an (applied/pure) mathematician?

For background: I'm working on a book to help mathematicians learn how to program. However, I need to see some examples from people in the field that have done different kinds of things than I have. ...
16 votes
9 answers

Combinatorial constructions found by computer

In preparation for a talk I am giving to our undergraduate mathematics society, I am trying to collect examples of combinatorial constructions that were found by computer. Thus my question is the ...
21 votes
2 answers

What is the largest Laver table which has been computed?

Richard Laver proved that there is a unique binary operation $*$ on $\{1,\ldots,2^n\}$ which satisfies $$a*1 \equiv a+1 \mod 2^n$$ $$a* (b* c) = (a* b) * (a * c).$$ This is the $n$th Laver table $(A_n,...
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18 votes
3 answers

Results that are easy to prove with a computer, but hard to prove by hand [closed]

Consider the assertion: There is no completely multiplicative function $f:\mathbb{N}\rightarrow \{\pm 1\}$ with $\left|\sum_{n\leq x}f(n)\right|\leq 2$ for all $x\geq 0$. One can write a very short ...