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One thing I don’t think is discussed enough is the process of how self-learners in math get critical feedback. Most advanced level math textbooks do not have so

One thing I don’t think is discussed enough is the process of how self-learners in math get critical feedback. Most advanced level math textbooks do not have solutions to check their work against nor do they have a way to get feedback by an expert and this is essential for learning. Least with programming, you can get immediate feedback and know whether what you did is correct or not.

yuanshan 7y ago
Usually, some people will post some or almost all of the solutions online if the textbook is really famous, for instance, baby rudin. Although rarely, some authors do provide solutions, like Knuth's books, Stephen Abbott's Understanding Anaylsis, etc. For immediate feedback, maybe you can checkout [0] to learn some formal proof by doing interactive proving. [0] http://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_game/ http://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_game... BTW, you can always ask questions on https://math.stackexchange.com https://math.stackexchange.com
clircle 7y ago
It's not immediate feedback, but you do learn when you right and when you are wrong. You learn when you are bullshitting yourself. You learn that you need to be able to justify every step in a proof, and if you can't do, then you are wrong. Trying to bullshit the right answer is the most common way to end up with a faulty proof. Of course, you can also end up with a faulty proof because you can't differentiate your own bullshit from truth, but this is less common.
chobytes 7y ago
Learn proofs well and you get pretty good and knowing when you’re right. Enough for almost any problem you’ll be likely to encounter in a math textbook anyway.
- TheTrotters 7y ago
  I strongly disagree. It's a little like saying "learn programming well enough and you'll know if some piece of code works as expected without running it."
  - inimino 7y ago
    > "learn programming well enough and you'll know if some piece of code works as expected without running it." That is 100% true. Obviously the code needs to be self-contained (not calling into other unknown code) but so do mathematical proofs.
  - abvr 7y ago
    That's what seperates them both, it's not about immediate formal checking from a compiler here, but rather if our proof is being justified adequately according with the rules of deduction and reasoning, it's a more intuitive approach in math, although you do end up knowing whether something is right or wrong, akin to programs.

yuanshan 7y ago

Usually, some people will post some or almost all of the solutions online if the textbook is really famous, for instance, baby rudin. Although rarely, some authors do provide solutions, like Knuth's books, Stephen Abbott's Understanding Anaylsis, etc. For immediate feedback, maybe you can checkout [0] to learn some formal proof by doing interactive proving. [0] http://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_game/ http://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_game... BTW, you can always ask questions on https://math.stackexchange.com https://math.stackexchange.com

clircle 7y ago

It's not immediate feedback, but you do learn when you right and when you are wrong. You learn when you are bullshitting yourself. You learn that you need to be able to justify every step in a proof, and if you can't do, then you are wrong. Trying to bullshit the right answer is the most common way to end up with a faulty proof. Of course, you can also end up with a faulty proof because you can't differentiate your own bullshit from truth, but this is less common.

chobytes 7y ago

Learn proofs well and you get pretty good and knowing when you’re right. Enough for almost any problem you’ll be likely to encounter in a math textbook anyway.

TheTrotters 7y ago
I strongly disagree. It's a little like saying "learn programming well enough and you'll know if some piece of code works as expected without running it."
- inimino 7y ago
  > "learn programming well enough and you'll know if some piece of code works as expected without running it." That is 100% true. Obviously the code needs to be self-contained (not calling into other unknown code) but so do mathematical proofs.
- abvr 7y ago
  That's what seperates them both, it's not about immediate formal checking from a compiler here, but rather if our proof is being justified adequately according with the rules of deduction and reasoning, it's a more intuitive approach in math, although you do end up knowing whether something is right or wrong, akin to programs.