Well,

It is interesting that a lot of great mathematicians have believed in truth beyond the sausage factory. Not that the reality isn't a sausage factory but belief in an ideal (truth, beauty) seems to often be what keeps them going.

Kurt Godel proved that the machinery of mathematics couldn't create a complete truth system accessible through proofs (which are ultimately a mechanical process) but he definitely was on the side of ideal-truth when he said "Either mathematics is too big for the human mind, or the human mind is more than a machine."

Edit: And Grigori Perelman was certainly famous for rejecting what he saw as the sausage factory of mathematics.

Brilliant book that. The way he explains how a polished rigorous proof hides the process(compared with frontend and kitchen views of a restaurant) by which a mathematician has arrived at it changed my perception of how mathematics is done.

I notice the same phenomena in programming too. The final piece of code that works doesn't reflect all the failed attempts at solving a problem. This is why I tend to not delete/clear cells at all from my jupyter notebooks. :) It is always informative/fun to refer to them at a later point in time to relive that problem solving experience.

PS: In case you haven't, you should try Proofs and Refutations by Lakatos.

Edit: Fixed name of the book mentioned and added some text.

A big portion of Lakatos’s book is online, https://math.berkeley.edu/~kpmann/Lakatos.pdf

Do you mean "proof and refutations" ?

Ah yes, thanks for correcting me :)

To those like me, not familiar with the term "sausage factory":

"An unpleasant process, especially one that is hidden from public view, that is used to produce a widely consumed product" - Urban Dictionary