Since my education has not been systematic, I find that there are lots of things in mathematics that I assumed without learning the lengthy proofs. But I keep thinking about them and try to see why they are plausible. The process seems to help but takes time. Sometimes, the final proofs I found are considerably simpler than the original proofs. Here is one example of a proof found after about thirty years:
https://arxiv.org/pdf/math/0108116.pdf
The final proof is only about two pages, assuming what was considered standard by then. This seems to be how things are simplified and subsumed in later work.
Another, slightly more complicated example:
https://arxiv.org/pdf/math/0401308.pdf
I am currently revisiting a topic from 1974-75. This process of learning also makes research fun.
Here is a monstrosity from me and Peter Scott:
https://arxiv.org/pdf/math/0703890.pdf
Waiting for it to be simplified.
https://arxiv.org/pdf/math/0108116.pdf
The final proof is only about two pages, assuming what was considered standard by then. This seems to be how things are simplified and subsumed in later work.
Another, slightly more complicated example:
https://arxiv.org/pdf/math/0401308.pdf
I am currently revisiting a topic from 1974-75. This process of learning also makes research fun.
Here is a monstrosity from me and Peter Scott:
https://arxiv.org/pdf/math/0703890.pdf
Waiting for it to be simplified.
No comments:
Post a Comment