Marco Carmosino

They used it to prove that many distinct theorems in complexity theory are actually exactly equivalent.

Marco Carmosino, a complexity theorist at IBM, says he was surprised that they were able to get this much done.

He suspects it'll draw new people into metamathematics.

The story of the reverse mathematics paper began in the summer of 2022.

Chen says at the beginning, they only had two equivalent things, but now they have a big web of stuff.

The team's most striking connection related the same version of the pigeonhole principle to one of the first theorems that students encounter in introductory complexity theory courses.

This classic banger of a theorem, as IBM's Marco Carmosino describes it, sets a lower bound on the amount of time required for a type of theoretical computer called a single-tape Turing machine to determine whether a string of zeros and ones is a palindrome.

So does it read the same forward and backward? Li, Chen, and Oliveira used reverse mathematics to prove that within PV1, this palindrome lower bound theorem is equivalent to the pigeonhole principle.