# Open problems and conjectures in Mathematics

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## Main Question or Discussion Point

I know this can be a silly question but it's a curiosity of mine and I have no idea what the answer is, so I'll ask anyway. The question is: How many open problems and conjectures are there in Mathematics currently ? I'm sure nobody knows the exact number but an approximation would be nice. Thanks in advance.

## Answers and Replies

mfb
Mentor
I don't think you can count them. There are a few famous ones, a few less famous ones, but every topic a mathematician works on (or plans to work on in the future) is an open problem - otherwise they wouldn't work on it. The Mathematics Genealogy Project knows about 210,000 mathematicians, most of them still alive, the actual number will be even higher, so going by that we have at least hundreds of thousands of problems someone is investigating.

How do you count open problems? The Collatz conjecture is certainly an open problem. If you replace the 3n+1 rule by 5n+1, is it a different open problem, or is it a variant of the same open problem? If it is different, we can generate infinitely many open problems. Otherwise: How much do we have to vary it until we count it as separate problem?

flamengo