Check your subscription status, update your details and more. Why do mathematicians keep proving things they already know? What exactly is a mathematical proof?
Columnist Jacob Aron breaks down how mathematicians plot a course to answer open questions, and how finding several solutions to the same problem is an important part of the whole endeavour of maths Many routes can take us through the maths to the same solution Earlier this month, I wrote a story about how OpenAI had inadvertently produced two versions of its proof of the Navier-Stokes problem. You can read the details here, but one thing that has stuck with me is that some non-mathematically minded people I spoke to about the story struggled with the idea that two different proofs of the same problem could both be correct. It got me thinking about how and why mathematicians prove things multiple times – and what happens when it goes wrong.
One thing it’s important to grasp is that proofs are not homework problems. A couple of mathematicians have made this point to me recently: because most people’s experience of maths begins and ends at school, there is a perception that mathematicians are simply working down a big list of problems and writing answers to be ticked off by some sort of cosmic maths teacher. This is not the case – proofs are a way of organising and developing mathematical thinking.
You can think of a proof as a journey, from statement to conclusion – and as with many journeys, there are many routes you can take to get from A to B. This is where we get multiple proofs of the same problem. Receive a weekly dose of discovery in your inbox.
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