3 ms·

For example: https://www.quantamagazine.org/amateur-mathematician-finds-smallest-universal-cover-20181115/ https://www.quantamagazine.org/amateur-mathematician-

For example: https://www.quantamagazine.org/amateur-mathematician-finds-smallest-universal-cover-20181115/ https://www.quantamagazine.org/amateur-mathematician-finds-s... No way you'd get research money for this, but an amateur can sit and poke away at it. These are all unsolved: https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m..., and plenty look like they may be solvable without advanced math, just someone dedicated and a unique approach. Particularly the Collatz Conjecture, afaik basically zero progress has been made on it, no "advanced" math topics are known to apply at all. So perhaps a unique angle is all you need. (Or maybe it's false, in which case all you need is a counterexample. Sometimes it happens, see e.g. https://www.ams.org/journals/mcom/1988-51-184/S0025-5718-1988-0930224-9/S0025-5718-1988-0930224-9.pdf https://www.ams.org/journals/mcom/1988-51-184/S0025-5718-198...)

intuitionist 8y ago
For another, more recent counterexample see the Hirsch conjecture: https://en.m.wikipedia.org/wiki/Hirsch_conjecture https://en.m.wikipedia.org/wiki/Hirsch_conjecture
earthicus 8y ago
Here's an old post by terry tao explaining why the collatz conjecture is hard, and giving a heuristic argument that it's unlikely to be solved with purely elementary techniques. The essay is surely worth reading if you want to make an attempt on that problem! https://terrytao.wordpress.com/2011/08/25/the-collatz-conjecture-littlewood-offord-theory-and-powers-of-2-and-3/ https://terrytao.wordpress.com/2011/08/25/the-collatz-conjec...
cjohnson318 8y ago
I don't think that a list of historically unsolved problems in math, and the Collatz Conjecture in particular, count as low-hanging fruit. The fact that they have remained unsolved for so long suggests that they are rather high-hanging.
- daxfohl 8y ago
  Heh, fair enough. Was thinking more things that might not need advanced math to solve. Or at least to understand the problem.

intuitionist 8y ago

For another, more recent counterexample see the Hirsch conjecture: https://en.m.wikipedia.org/wiki/Hirsch_conjecture https://en.m.wikipedia.org/wiki/Hirsch_conjecture

earthicus 8y ago

Here's an old post by terry tao explaining why the collatz conjecture is hard, and giving a heuristic argument that it's unlikely to be solved with purely elementary techniques. The essay is surely worth reading if you want to make an attempt on that problem! https://terrytao.wordpress.com/2011/08/25/the-collatz-conjecture-littlewood-offord-theory-and-powers-of-2-and-3/ https://terrytao.wordpress.com/2011/08/25/the-collatz-conjec...

cjohnson318 8y ago

I don't think that a list of historically unsolved problems in math, and the Collatz Conjecture in particular, count as low-hanging fruit. The fact that they have remained unsolved for so long suggests that they are rather high-hanging.

daxfohl 8y ago
Heh, fair enough. Was thinking more things that might not need advanced math to solve. Or at least to understand the problem.