Proofs remain inordinately difficult for me, although I have noticed a small improvement. To do MIRI-relevant math, proofs will need to become second nature. Depending on how I feel as I progress through my next book (which will likely be a proof-centric linear algebra tome), I’ll start trying different supplemental approaches for improving my proof prowess.
I had difficulty with proofs because of a tendency to ‘leave steps for the reader’ (because they were obvious to me, and I assumed they would be to others as well). I was also missing some TAPs, so I would get into situations like “how do I prove X? It’s just self-evidently true” without that triggering “so assume X is false and derive a contradiction.” Then a professor pointed me at a book on how to prove things, and that smoothed most of those rough edges.
Sadly, I don’t remember which book it was, but consider this an endorsement of reading a book on proofs directly, and a weak suggestion that you read How To Prove It.
Yup, that particular book is how I learned to prove stuff too.
(well, actually, there was a substantial time delay between reading that and being able to prove stuff, but it’s an extremely worthwhile overview)
I had difficulty with proofs because of a tendency to ‘leave steps for the reader’ (because they were obvious to me, and I assumed they would be to others as well). I was also missing some TAPs, so I would get into situations like “how do I prove X? It’s just self-evidently true” without that triggering “so assume X is false and derive a contradiction.” Then a professor pointed me at a book on how to prove things, and that smoothed most of those rough edges.
Sadly, I don’t remember which book it was, but consider this an endorsement of reading a book on proofs directly, and a weak suggestion that you read How To Prove It.
Yup, that particular book is how I learned to prove stuff too. (well, actually, there was a substantial time delay between reading that and being able to prove stuff, but it’s an extremely worthwhile overview)