[ocfnash]

Note that finite-time singularities for the good old Newtonian n-body problem have been known to exist for quite a while. (See for example [1].)

It's curious to think that a mathematical phenomenon like this can hint at new physics.

[1] Saari, D. and Xia, Z., "Off to Infinity in Finite Time", https://www.ams.org/notices/199505/saari-2.pdf

[xelxebar]

That paper is from 1993. Hard to believe that it took such a long time to find a concrete pathology in a Newtonian system. Now the question is whether these blowups only occur on initial condition sets of zero measure.

John Baez also has a nice, accessible series of articles called "Stuggles with the Continuum" [0]. As a side product, it gives a nice perspective on the development of modern physics as a series of attempts to fix these infinities (only to create more subtle one).

[0]:https://johncarlosbaez.wordpress.com/2016/09/08/struggles-wi...

[TheFiend7]

Honestly I feel as though that's one of the most incredible aspects of theoretical physics I've seen. The fact that often times these underlying physics are danced around and even though they're unknown, we can tell something is not quite right.

I believe this guy even talks about it a bit in this video made by the Royal Institution (which I really enjoy watching), discussing the possibility of different fundamental building blocks of nature. https://www.youtube.com/watch?v=zNVQfWC_evg