Continuous math is boring to me, but discrete math—starting with probabilities—I can find lots of programming and everyday uses for, so much so that I’m considering going back and finishing a probability and statistics degree.
A word of warning: probability and statistics make heavy use of continuous math. Here Be Integrals.
He worked on both ultrafinitism and nonstandard analysis, bringing new approaches to both. He was discussed around here a couple of years ago for his claim to have proved the existence of a contradiction in Peano Arithmetic, but Terry Tao found the flaw. Unfortunately, he died last year.
In his nonstandard days, he wrote Radically Elementary Probability Theory. This is not simply redoing standard continuous probability theory with nonstandard analysis, but doing discrete probability theory with nonstandard integers. All of the useful things appear, but it all looks very different. Princeton still hosts the PDF: https://web.math.princeton.edu/~nelson/books/rept.pdf
ETA: While ultrafinitism and nonstandard analysis seem almost complete opposites as far as constructivism goes, his approaches to them are actually quite similar to one another.
A word of warning: probability and statistics make heavy use of continuous math. Here Be Integrals.
Unless you take Edward Nelson’s approach.
Sorry, I haven’t heard of him. Could you explain and/or link?
He worked on both ultrafinitism and nonstandard analysis, bringing new approaches to both. He was discussed around here a couple of years ago for his claim to have proved the existence of a contradiction in Peano Arithmetic, but Terry Tao found the flaw. Unfortunately, he died last year.
In his nonstandard days, he wrote Radically Elementary Probability Theory. This is not simply redoing standard continuous probability theory with nonstandard analysis, but doing discrete probability theory with nonstandard integers. All of the useful things appear, but it all looks very different. Princeton still hosts the PDF: https://web.math.princeton.edu/~nelson/books/rept.pdf
ETA: While ultrafinitism and nonstandard analysis seem almost complete opposites as far as constructivism goes, his approaches to them are actually quite similar to one another.