Linked Questions

15
votes
8answers
912 views

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 ...
98
votes
83answers
23k views

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 ...
75
votes
25answers
6k views

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 ...
132
votes
14answers
28k views

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 "integrable" ...
52
votes
27answers
10k views

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 ...
51
votes
12answers
6k views

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 ...
34
votes
14answers
3k views

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. ...
15
votes
9answers
911 views

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
2answers
2k views

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,...
18
votes
3answers
1k views

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 ...