Verifiability, access, and allocation in maths

When I was talking about this post with a friend, he asked a thought-provoking question. In the post, I’d argued that I believe it should be appropriate for mathematics to consider a solution to a problem to be illegitimate if mathematicians had arrived at it with help from a machine, device or instrument that wasn’t equitably accessible to all mathematicians. My friend asked if this was like how not all physicists can access the Large Hadron Collider (LHC) and how not all biologists could access biosafety level-4 (BSL-4) labs. By and large today, scientists accept that not every one of them needs to be able to access every instrument to the same degree. Scientific communities also accept work that, as a matter of routine, scientists have produced using scarce, expensive, geographically concentrated or otherwise access-controlled infrastructure. Against this background, let me resolve my position into three components. The first two are access to the instrument that facilitates a…