Week 4

A lot of VonNeumann's article was over my head, but I still picked up a few things that I thought were interesting. I learned about set theory in algebra and again this year in Discrete but I never knew there had been controversy about it. The term "intuitionism" confused me, in that the name makes it sound like a less rigorous kind of proof, but the article led me to conclude it was the more rigorous. It's definitely a challenge to learn to write proofs that break down the evidence enough to be unquestionable. It's interesting the way mathematicians settled with a certain rigor of proof, concluding it left their ideas as trustworthy as anything in an empirical science. VonNeumann got a little philosophical on me there with the comment that absolute truth outside of human existence could never be determined, which isn't exactly the kind of thing one usually mentions while proving bijections have inverses. He had an interesting take on the empirical basis of mathematics with Newton and founders, commenting that the empiricism is a thing some mathematicians find hard to accept, but which must be returned to when the practice becomes abstract and baroque (not gonna lie I had to look it up in this context- settled on convulted). Another interesting comment though was how mathematical study is relatively broad compared to other disciplines such as theoretical physics where most energy is focused on a single subject. It was neat to think of the relative freedom that mathematicians have in their research.