[zajio1am]

> My personal favorite is Georg Cantor who was mercilessly attacked by his fellow academics within math and even without for his theories on infinite numbers.

I do not think this is comparable to other examples. Math is not science in the sense that its correctness is not determined by the outside reality, only by its internal consistency.

Different (finite vs infinite) axiomatizations leads to different classes of math structures, so it is only a matter of custom which structures are worthy of studying and how these 'leading' structures are defined.

And there is a point that if one studies countable structures (e.g. arithmetics or graph theory) then using arguments from infinite set theory (e.g. ZFC) is overkill. We do not know whether such theory is consistent and if it is not, then most likely much simpler theories covering the countable structures would still be consistent.

[zajio1am]

> so it is only a matter of custom which structures are worthy of studying

Or in other words, which proof steps are considered valid.