Here's where you are wrong
> But they might! And you would not notice that the framework had become inconsistent for a while.
As the author stated, the math can be reproduced by reading it: ergo, thee is no barrier to entry except knowledge. The other sciences do not have this luxury - they require access to specialized instruments, participants, funding, and most importantly - time. Math can be checked nearly instantaneously, so the "might" becomes inconsequential my small.
> Math can be checked nearly instantaneously, so the "might" becomes inconsequential my small.
Can it though? Pickovers 2013 edge response comes to mind, can hundreds of pages of a proof based on axioms that require particular expertise to understand be checked instantaneously? I think it would easier to replicate the typical psychology experiment than to check the math in that case.
A few edge case examples do not constitute a crisis. The point is not that 0 cases happen in mathematics, but rather that unreproducible results are not the norm, while in other sciences, it is the norm.
Math cannot be checked instantaneously. Mochizuki's proof for the abc conjecture mentioned in the article was first released in 2012, and despite conferences and lots of time spent trying to figure out what he's saying and whether it's correct there is still no consensus.
Thanks the post. This is the first time I've read an article by a math professor in such an acerbic and relatively handwoven way. Seems like over the years this proof must have generated passionate disagreement.
That’s fundamentally it, there’s a barrier to entry, and it’s knowledge. Other sciences may require specialized instruments and time, but math is also subject to the problems of knowledge not being instantaneously transferable. And I imagine, although I’m not certain how prevalent it is, that many branches of mathematics are also dependent on instrumentation these days, in the form of software.
As the author stated, the math can be reproduced by reading it: ergo, thee is no barrier to entry except knowledge. The other sciences do not have this luxury - they require access to specialized instruments, participants, funding, and most importantly - time. Math can be checked nearly instantaneously, so the "might" becomes inconsequential my small.