- 172comments
- 157comments
- 11comments
- 159comments
- 9comments
- 148comments
- 85comments
- 26comments
- 78comments
- 29comments
- 401comments
- 111comments
- 1comments
- 49comments
- 29comments
- —discuss
- —discuss
- 277comments
- 53comments
- 376comments
- 2comments
- 1comments
- 66comments
- 30comments
- 130comments
- 9comments
- 180comments
- 286comments
- 127comments
- 268comments
I like this site of Mathematicians' biographies with some occasional quoted segments for extra flavor.
I also like how Serre wrote a book on linear representations of symmetry groups, because his wife needed a good exposition of the subject for her work on quantum chemistry, and that Serre described that as "fullfiling his duty as a husband" :-P
It's nice to have this perspective validated by someone like Serre! I felt like I was missing something when I first encountered that formalism. In fact, all of my introductory calculus classes sucked and turned me off of math for a few years.
He later participated in Bourbaki, who were known by their overly formal style, tough.
What's the alternative for explaining those concepts that's still reasonably rigorous?
Nonstandard analysis [0] [1] uses infinitesimals but is still completely rigorous. I haven't ever really used nonstandard analysis myself, but there's a fairly well-regarded textbook available online [2].
[0]: https://en.wikipedia.org/wiki/Nonstandard_analysis
[1]: https://math.stackexchange.com/questions/51453/is-non-standa...
[2]: https://people.math.wisc.edu/%7Ehkeisler/keislercalc-06-03-2...
When I first learned non-standard analysis, my reaction was that we don't need the axiom of choice to find the derivative of x^2.
The formalism is very simple symbolically. But the mathematical machine behind it is very complex.
Various algebras of dual numbers are used in most automatic derivative routines.
This is treated more rigorously and generically in the subject of synthetic differential geometry.
The European Mathematical Society just published an interview with Serre on the occasion of his birthday: https://euromathsoc.org/news/ems-magazine-no.-141:-celebrati...
Happy birthday “Tonton Serre”