In mathematics I'd put forward the conjecture that "for every proven theorem you could ask at least 5 more similar questions which are unproven."
For example it is proven there are infinitely many primes. Are there infinitely primes that differ by 2? By n for any n? Are there infinitely many palindromic primes? Are there infinitely many primes of form n^2 + 1? Is there always a prime between n^2 and (n+1)^2?
If this is true then, assuming there are 200k proven theorems, there would be >1m unproven but readily stated theorems which would mean it wouldn't be too hard to find areas no one is looking into.
For example it is proven there are infinitely many primes. Are there infinitely primes that differ by 2? By n for any n? Are there infinitely many palindromic primes? Are there infinitely many primes of form n^2 + 1? Is there always a prime between n^2 and (n+1)^2?
If this is true then, assuming there are 200k proven theorems, there would be >1m unproven but readily stated theorems which would mean it wouldn't be too hard to find areas no one is looking into.