2 ms·

This is really a good question. On the one hand the work of bourbaki was important, the foundation of math was shaky (I heard there were proof of some theorems

This is really a good question. On the one hand the work of bourbaki was important, the foundation of math was shaky (I heard there were proof of some theorems and the negative of the same theorem). But then it somehow seems to destroy the spirit of mathematics. Arnold wrote about it: https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html#:~:text=by%20V.I.,Paris%20on%207%20March%201997.&text=In%20the%20middle%20of%20the,to%20divide%20physics%20and%20mathematics https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html#:....

andi999 6y ago
To add: I dont know what the solution to this is. So lets say there are two types of approaching math. Approach one is formal/rigid (caring about Axiom of Choice, Set theoretical foundations ..:-)) the other one still (partially) rigorous but more classical in spirit. A big question for me is, how is actually research done? Is it more the first or more the second approach? So what are possible solutions? I dont know. If you are trained in the first approach, you usually loose the ability to gloss over the gaps in the second approach. If you are trained in the second you cannot (or very difficult) come around the first one. And then there is physics which uses the sloppy (and often not correct) version of the second approach. I once asked Serge Lang about this (phrasing:'what about physicist getting the right result with wrong mathematics' (thinking about renormalization)). Lang replied:'this is God's way of calculation'.
BlueTemplar 6y ago
Oh wow. So it looks like that the reason why I suddenly got 'bad' at math towards the end of high school might be due to the switch to this hyper-formal way of teaching mathematics, instead of using a more geometric/physic way ?
- andi999 6y ago
  Could be. Although high school (at least where I am) only teaches a tiny drop of mathematics (so the other style is also difficult.). But generally the is an adaptation problem/challenge in the first two semesters of math students where usually only solving a lot of problem and getting them corrected helps. But dont worry, these things can be overcome (do not fight them at your current stage if you are still a student). Just dont believe the 'hours needed' in the description of the modules (they are politically decided). Generously work around the clock for the first few years..... edit: more seriously: although working hard is important: go to the office hours of your TA and/or prof and discuss the work you are doing. Usually no student does that and you will learn a lot.

andi999 6y ago

To add: I dont know what the solution to this is. So lets say there are two types of approaching math. Approach one is formal/rigid (caring about Axiom of Choice, Set theoretical foundations ..:-)) the other one still (partially) rigorous but more classical in spirit. A big question for me is, how is actually research done? Is it more the first or more the second approach? So what are possible solutions? I dont know. If you are trained in the first approach, you usually loose the ability to gloss over the gaps in the second approach. If you are trained in the second you cannot (or very difficult) come around the first one. And then there is physics which uses the sloppy (and often not correct) version of the second approach. I once asked Serge Lang about this (phrasing:'what about physicist getting the right result with wrong mathematics' (thinking about renormalization)). Lang replied:'this is God's way of calculation'.

BlueTemplar 6y ago

Oh wow. So it looks like that the reason why I suddenly got 'bad' at math towards the end of high school might be due to the switch to this hyper-formal way of teaching mathematics, instead of using a more geometric/physic way ?

andi999 6y ago
Could be. Although high school (at least where I am) only teaches a tiny drop of mathematics (so the other style is also difficult.). But generally the is an adaptation problem/challenge in the first two semesters of math students where usually only solving a lot of problem and getting them corrected helps. But dont worry, these things can be overcome (do not fight them at your current stage if you are still a student). Just dont believe the 'hours needed' in the description of the modules (they are politically decided). Generously work around the clock for the first few years..... edit: more seriously: although working hard is important: go to the office hours of your TA and/or prof and discuss the work you are doing. Usually no student does that and you will learn a lot.