# Pure maths in crisis?

Proof is the essence of mathematics. Any mathematical result should be derived from first principles using a watertight chain of logical reasoning. Proof is what separates mathematics from other intellectual endeavours, and it’s what makes it so elegant and pure.

It’s a high standard that is diligently applied in undergraduate maths courses — but not in the higher echelons of mathematical research, Kevin Buzzard, Professor of Pure Mathematics at Imperial College, said at a recent seminar talk in Cambridge. There are proofs with holes, proofs with mistakes, and proofs that are only understood by one or two people in the entire world. Something having been published in an academic journal doesn’t always mean it’s true. To know for sure which results to believe you need to be part of an in-crowd with access to experts who make the consensus. “Things are a bit out of control,” Buzzard says.

Buzzard is himself one of those experts. A professional research mathematician since 1998, he worked on some of the maths used in the proof of Fermat’s famous last theorem during his PhD. His unease with the standard of proof in academic maths only crept up on him over recent years, perhaps part of a mathematical mid-life crisis, he says, causing him to re-evaluate how things are done in his chosen line of work.”>:

Proof is the essence of mathematics. Any mathematical result should be derived from first principles using a watertight chain of logical reasoning. Proof is what separates mathematics from other intellectual endeavours, and it’s what makes it so elegant and pure.

It’s a high standard that is diligently applied in undergraduate maths courses — but not in the higher echelons of mathematical research, Kevin Buzzard, Professor of Pure Mathematics at Imperial College, said at a recent seminar talk in Cambridge. There are proofs with holes, proofs with mistakes, and proofs that are only understood by one or two people in the entire world. Something having been published in an academic journal doesn’t always mean it’s true. To know for sure which results to believe you need to be part of an in-crowd with access to experts who make the consensus. “Things are a bit out of control,” Buzzard says.

Buzzard is himself one of those experts. A professional research mathematician since 1998, he worked on some of the maths used in the proof of Fermat’s famous last theorem during his PhD. His unease with the standard of proof in academic maths only crept up on him over recent years, perhaps part of a mathematical mid-life crisis, he says, causing him to re-evaluate how things are done in his chosen line of work.