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Results tagged with open-problems
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user 4558
If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
36
votes
Open problems with monetary rewards
Paul Erdős was famous for offering money for solutions to math problems. My understanding is that those prizes are still being administered by Ron Graham, even though Erdős passed away several years …
7
votes
Accepted
The shortest path in first passage percolation
It seems that this problem was recently solved by Ahlberg and Hoffman.
https://arxiv.org/abs/1609.02447
- 7,857
5
votes
1
answer
295
views
Updated bounds or references for an old Erdős problem –– coloring the plane with multiple fo...
Define a graph $G_1$ where the vertices of $G_1$ are the points of the plane $\mathbb{R}^2$, and a pair of vertices $p, q$ is connected by an edge if and only if the Euclidean distance $d(p,q) =1$. Th …
- 7,857
33
votes
Open problems in Euclidean geometry?
The Unit Distance Problem asks:
For a set of $n$ points in the plane,
what is the maximal number $g(n)$ of
unit distances realized among the
${n \choose 2}$ pairs?
A properly scaled squar …