
Million Dollar Problems (2000) [pdf] - hownottowrite
http://www.math.buffalo.edu/~sww/0papers/million.buck.problems.mi.pdf
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godelmachine
Discussion would be incomplete without -
[https://en.m.wikipedia.org/wiki/List_of_unsolved_problems_in...](https://en.m.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics)

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glaberficken
Would love if someone knowledgeable could point out from this list what are
the most apparently easy or simple problem statements.

i.e. problem statements that someone who has a degree but is not a
mathematician would still be able to appreciate. I'm really interested in
this, but reading through the list it all sounds really "deep" =)

I was wondering what was the most surprising problem to not have been solved
yet.

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hacman
Landau's problems are pretty simple in their statement. I believe that
Goldbach's conjecture is the oldest, dating to 1742. So I wouldn't exactly
call it approachable in the sense of easy to solve, but the statement is quite
simple. The full list of Laundau's problems, from the Wikipedia page (
[https://en.wikipedia.org/wiki/Landau's_problems](https://en.wikipedia.org/wiki/Landau's_problems)
), is:

1\. Goldbach's conjecture: Can every even integer greater than 2 be written as
the sum of two primes?

2\. Twin prime conjecture: Are there infinitely many primes p such that p + 2
is prime?

3\. Legendre's conjecture: Does there always exist at least one prime between
consecutive perfect squares?

4\. Are there infinitely many primes p such that p − 1 is a perfect square? In
other words: Are there infinitely many primes of the form n^2 + 1?

I don't think any of them has a million dollar prize, but tenure at a decent
university seems like a fairly reasonable expectation for solving one of
these.

