With news that a recent proof of the Boolean Pythagorean Triples Theorem is the ‘largest proof ever’, we collect and run-down some of the biggest, baddest, proofiest chunks of monster maths.
You're reading: Posts Tagged: Paul Erdős
Previously unseen footage has been unearthed by The Aperiodical’s crack team of investigative journalists of Kevin Bacon and Paul Erdős writing a paper together, and a still from this is shown above. This has massive consequences for the important topics of Erdős numbers, Bacon numbers and Erdős-Bacon numbers.
Terence Tao has just uploaded a preprint to the arXiv with a claimed proof of the Erdős discrepancy problem.
The big news last year was the quest to find a lower bound for the gap between pairs of large primes, started by Yitang Zhang and carried on chiefly by Terry Tao and the fresh-faced James Maynard.
Now that progress on the twin prime conjecture has slowed down, they’ve both turned their attentions toward the opposite question: what’s the biggest gap between subsequent small primes?
You wait and wait for a movie about a mathematical genius, and then three come at once. I’ve got Turing, I’ve got Ramanujan, I’ve got Erdős.
Boris Konev and Alexei Lisitsa of the University of Liverpool have been looking at sequences of $+1$s and $-1$s, and have shown using an SAT-solver-based proof that every sequence of $1161$ or more elements has a subsequence which sums to at least $2$. This extends the existing long-known result that every such sequence of $12$ or more elements has a subsequence which sums to at least $1$, and constitutes a proof of Erdős’s discrepancy problem for $C \leq 2$.
This is a puzzle I presented at the MathsJam conference. It’s a problem that gave me a headache for a week or so, and I thought others might enjoy it, too. I do know the answer, but I’m not going to give it away — you can tweet me @icecolbeveridge if you want to discuss your theories! (As Colin Wright says: don’t tell people the answer).
You’ve heard of the Monty Hall Problem, right?