Problems worth chasing
Epilogue
Non-trivial problems and the lore behind them.
If every problem were solved tomorrow, who would introduce the next ones worth chasing?
Purpose
Why are we here?
What happens when every open and interesting problem can be solved? Who creates the new ones that drive progress forward?
That is why we are here. Epilogue exists to keep people interested, curious, and passionate about the most compelling problems of our time so that the next Euler (possibly you) can create problems for the following centuries.
Problems
Browse by field
Field
Status
- 1859 → today →
Mathematics · Open · Clay Millennium Prize
The Riemann Hypothesis
Why the zeros of one function may control the rhythm of the primes.
- 1849 → today →
Mathematics · Open
The Twin Prime Conjecture
Primes two steps apart keep appearing. Are there infinitely many of those pairs?
- 1971 → today →
Computer science · Open · Clay Millennium Prize
P versus NP
If a solution is easy to check, must there be an easy way to find it?
- 1822 → today →
Physics · Open · Clay Millennium Prize
Navier-Stokes Regularity
Do the equations of fluid motion always stay smooth, or can a flow tear itself apart?
- 1637 → 1995 →
Mathematics · Solved · 1995
Fermat’s Last Theorem
A margin note promised a proof. Three centuries later, someone finally delivered one.
- 1968 → 2002 →
Physics · Solved · 2001–2002
The Solar Neutrino Problem
The Sun seemed to send too few neutrinos. The missing ones had changed identity.
- 1930s → today →
Mathematics · Open
The Collatz Conjecture
Halve the evens. Triple the odds and add one. Every hailstone we have thrown still falls to 4, 2, 1.
- c. 300 BCE → today →
Mathematics · Open
Odd Perfect Numbers
A perfect number equals the sum of its proper divisors. Every example on record is even, and an odd one is still missing.
- 1906 → 1913 →
Mathematics · Solved · 1906
Markov Chains
Each step can depend on the one before it, and the long-run share can still settle. Markov proved that for his chains, then found the dependence in Pushkin.