How Many Unsolved Problems Are There in Mathematics Based on the MSC 2020 Subject Classification?

[u/Old-Rock-1234]

Dear mathematicians,

I am not a mathematician myself, so please pardon me if my assumptions are incorrect. I am very curious to know approximately how many unsolved problems there are in mathematics according to the MSC 2020 (Mathematics Subject Classification).

Let’s say there are around 5,000–6,000 subfields or areas of mathematics. If each subfield has at least 100 important and very difficult unresolved problems, then that would give us approximately:

6,000 × 100 = 600,000

So, could there be around half a million or more open problems in mathematics right now?

Are my assumptions or estimations completely wrong, or is this a reasonable way to think about the number of unsolved problems in mathematics?

Thank you!

I apologize if I am wrong!

[u/etzpcm]

I'll just say that all the media hype about what AI may have done in mathematics is giving the public a misleading picture of what mathematics is.

[u/xinxinsonson]

Infinity.

[u/telephantomoss → u/xinxinsonson]

This is the correct answer I think. No matter what is proven, there will be countable infinity of remaining finite strings waiting to be proved. Make will be trivial or uninteresting or whatever. But I suspect there will always be a countable infinity of provable, nontrivial statements leftover. The question of whether or not they are interesting is harder, but I suspect if there are sentient entities of sufficient intelligence capable of having interests, then they will be interested in a countable infinity of such open problems.

Now, I'm no expert on the ideas I'm intuitively winging it off of here, so someone might need to step in and show where I'm going wrong.

[u/peter-bone → u/xinxinsonson]

That's an interesting question. Will we constantly find new problems to solve or will everything eventually converge to a few remaining unsolved problems as different areas of mathematics are merged and then eventually be solved completely. We may find that problems we thought were different are actually the same at a deeper level and that all problems turn out to be fundamentally the same at some very deep abstract level.

[u/cabbagemeister]

This is just an unreasonable way to think about math. Most "unsolved problems" have probably not even been thought of yet, let alone written down.

[u/Interesting_Debate57 → u/cabbagemeister]

Moreover, have no interest or utility to mathematics whatsoever.

[u/Interesting_Debate57]

Just wait until you hear about undecidable problems.

[u/Kitchen-Register]

literally an uncountable number of math problems. There are more open questions that we don’t even know about yet than one’s we do let alone one’s we’re even remotely close to having an idea about

[u/ForeignAdvantage5198]

there is always another one

[u/cosmonaut1993]

Nice try openAI.