What is the most perplexing and difficult unsolved math problem?

[ElliotSmith]

TL;DR Summary

What is the most perplexing and difficult unsolved math problem you can think of?

What is the most perplexing and difficult unsolved math problem that you can possibly think of?

 

[fresh_42]

ERH.

 

[mfb]

We generally don't know how difficult a problem is until we solve it. We only set lower bounds on the difficulty. If many leading mathematicians can't solve it after years of work it's probably a hard problem.

The Collatz conjecture is a prominent example of a problem that looks simple but is very hard. You can explain the problem to a 5 year old - but despite many attempts we don't have a solution. Erdős said "Mathematics may not be ready for such problems."

 

[graphking]

ERH.

what is this?

 

[fresh_42]

what is this?

Extended Riemannian Hypothesis.

 

[Office_Shredder]

The ancient greeks wondered about geometric problems like whether it was possible to draw a square with the same area as a given circle, or whether it was possible to trisect an angle. Humanity didn't prove those to be impossible until the 1800s - it took over 2000 years to go from hypothesis to proof! Enormously important new fields of math were invented to solve these seemingly straightforward problems.

The most difficult unsolved math problem that we have right now is whichever one will take 2000 years to solve. We might never actually see something like that again, since the field of mathematics has matured so much, but there are still plenty of examples of questions that are 100+ years old that we still can't answer.

 

[fresh_42]

Here is a nice anecdote about NP=P:
https://www.physicsforums.com/threa...unprovable-unprovability.992095/#post-6376027

 

[Keith_McClary]

https://www.google.com/search?channel=fs&client=ubuntu&q=Open+Problems+in+Mathematics

 

[graphking]

I can't imagine the continuum hypothesis which stated that we couldn't know whether there's a subset of R could have the cardinality exact bigger than N and excatly smaller than R. maybe I would recommend the set theory. it's really weird.

 

[nucl34rgg]

Any problem that is unsolved is unsolved for a reason. It is hard to say it is difficult or easy because it is unsolved! There are some theorems that don't seem too bad, but are actually incredibly hard to prove and others that seemed awful, but ended up having relatively simple proofs. There's no way to really tell. Perhaps the most famous unsolved problem is the Collatz Conjecture because it is so easily stated and yet has eluded all of humanity perhaps since shortly after humans first learned to count.