Comment by nyc111
2 years ago
Mathematics is built on definitions. There are definitions on the foundations of mathematics. Axioms are definitions that are kept constant by consensus.
Euclid starts with definitions. If you don't like Euclid's definitions you make your own definitions. You create your own geometry etc.
Okay, but where do the definitions come from and what do they refer to?
If you don't care, fine. You simply are only concerned with the utility of this so called "mathematics". But at some point, and with some sophistication, you get bothered about how well it all works and how some surprising connections are made that seem all too natural.
Then you end up writing an essay like Wigner. [1]
I write this to say, no wonder people are bothered about a "foundations". Whether it bothers you or not is immaterial, but you can understand why people get bothered.
[1] https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...