Comment by fooker
1 day ago
This misses a very important point.
It’s not just about out remembering, it’s about breadth.
Mathematicians are all about depth. It’s pretty much impossible to become an expert in more than one narrow field of mathematics.
AI is happily applying techniques and abstractions across these silos.
Euler would like a word. Maybe it's our institutions.
There was no depth to mathematics in Euler's time, he made the depth. He arguably didn't understand analysis on a technical level as well as a modern undergraduate; as I recall, he was confident that all smooth functions are analytic. He had incredible intuition and was able to make great progress by trusting it, but playing around with tools you don't understand stops being effective once a field is past its infancy.