Proven, open, impossible: the edges of mathematics
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Truths proven for all time, problems nobody has cracked, and the theorems that prove some things can never be proven or computed.
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Proven, forever
Open, with prizes waiting
Proven impossible
Tools that changed the world
Proven
The Pythagorean Theorem
Proven
The Infinitude of Primes
Proven
The Irrationality of the Square Root of Two
Proven
Fermat's Last Theorem
Proven
The Four Colour Theorem
Proven
Cantor's Diagonal Argument
Hypothesis
The Riemann Hypothesis
Hypothesis
Goldbach's Conjecture
Contested
P versus NP
Proven
Gödel's Incompleteness Theorems
Proven
The Halting Problem
Fact
Calculus
Fact
Zero
Proven
Bayes' Theorem
Theory
Game Theory
Theory
Chaos Theory
Theory
Graph Theory
Fermat wrote that he had a proof but no room in the margin. It took more than 350 years, until Andrew Wiles in the 1990s.
Goldbach's conjecture has been checked by computer for every even number up to 4 billion billion. It is still not proven.
Question
Riemann and P versus NP each carry a one million dollar prize. Which falls first?