I wonder how analysis made it into mathematics. Now there is just a schism in the doctrine in a lot of places.

I think it is a "does it 'solve' problems I care about?” kind of thing. I think it is the foundation for validating inferences in math. The choice axiom went from, being considered problematic, to being mostly accepted because new problems from it did not hurt old problems.

@jmw150 The book "A Radical Approach to Real Analysis" covers this really well with the summary being "convergence of any kind demands rigorous construction and fourier series are whack"

@cirnog

Can be done rigorously now, wasn't done so for decades. It was tolerated, because such problematic symbolism was used anyway in physics.

I think anyway, such an area had to be pushed for a long time to make it into convention. Philosophy, not being a moneymaker for math, has had less luck.

@jmw150 Tbh I think intuitionism doesn't have a strong case since we still got correct results without the required constructions. Penrose said that strict intuitionism would leave mathematics impoverished and I agree. Interestingly the alignment of the JWST mirrors relies on a theorem that says that for any alignment error there is a unique way to actuate the mirror to correct it (but no construction is given), so intuitionism would have us refusing to make our telescopes work

@cirnog heard about that, I think ( https://m.youtube.com/watch?v=MiGx8xv6xjE at 2:10). they are aligning the mirror though, so what does it mean that there's no construction? just that they wouldn't necessarily find the solution in some cases, but still know there is one? @jmw150