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Comment by rahimnathwani | Hacker News Reader

I'm curious - did you work through this book on your own, or as part of a class or with help from others?

I started reading it, attempting most of the exercises at the end of each chapter, and some of the 'as you should verify' parts. I found the 'aha' moments during the text or when solving the exercises really enjoyable, but I got stuck often enough that I began to only pick up the book when I felt super-alert.

I stopped about a third of the way through, a few pages before the introduction of eigenvectors and eigenvalues. I would like to pick it up again, but am worried about how to maintain motivation the next time I'm faced with a page where I'm stuck/confused for 30 minutes.

EDIT: Thank you to the people who replied. Your empathy (~"you're not alone in getting stuck") and encouragement (~"you don't have to grok everything the first time through") have given me new motivation to try this again.

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Mathematicians are chronically lost and confused. It's our natural state of being, and it's okay to keep going and take what insights you can.

I suggest you don't worry too much about verifying every claim and doing every exercise before moving on. If it takes you more than 5 or 10 minutes to verify a "trivial" claim in the text, then you can accept it and move on. It's healthy, if you get stuck on such a problem, to think about other problems or come back to them later. It's not uncommon to find that by the time you revisit them you've literally grown so much (mathematically) that they're trivial.

> Mathematicians are chronically lost and confused. It's our natural state of being, and it's okay to keep going and take what insights you can.

This needs to be emphasized more in learning maths. Once I got over this fact and was guided by my interest rather than wanting to grok everything, I actually started understanding a lot more.

Someone should tell us that sooner then. I've been trying to get over math anxiety for a long time, and having professors that say "it's simple, what don't you understand?" when you try to get help didn't help much.

A common joke among mathematicians.

Two mathematicians are working on a problem and one makes a claim to which the other replies, "That's trivial!" The pair stare at the claim for ten minutes. The other says, "Is it trivial?" They go home, think about it all night, publish three papers about it over the next two years, and then they agree, "Yes, it's trivial."

I started reading it for a class but I wasn't assigned all the problems. Later, I managed to propel myself through it by building confidence with the problems of the first few chapters (which were easy by that point) and then embracing the sunk-cost fallacy to get through the rest.

One problem stood out. I forget the chapter, but I'll never forget the problem: prove that normed vector spaces are inner product spaces IFF the parallelogram law holds. It took about half a day to crack that problem and I was completely lost for about 90% of it. (That's not a strategy. The first paragraph was my strategy. My only point here is that you aren't alone in getting stuck.)

I actually skimmed the book over before I took my first course in linear algebra (doing some of the exercises on my own, but certainly not all--I skipped anything that seemed too hard or just too boring during this reading). At that point, there were definitely parts of the book that were challenging to me, and I just jumped over them.

Then when I took the actual course, I more or less ignored the main course textbook and instead tried to tie whatever happened in the last lecture with what I found in Axler.

I considered Axler my secret weapon. It honestly felt like I had access to secret insights that trivialized the class and granted me the same intuition the professor had.

I agree. I am also working through this book and feel the same as you. I think also part of the problem maybe not being able to discuss this with other people. I'm trying very hard to get through it but I think I miss being able to discuss problems with other students in a traditional classroom setting. These sorts of discusses can really help clarify things rather than just staring at the page for a long time.

A side note: how do you feel when you've lost your motivation? Is it common to barely be able to keep your eyes open? Or is that just me!

Not just you. I'm procrastinating on one of those too-damn-hard math problems right now!

It's not just you. It's probably easier to accept that I'm sleepy and should take a rest, than to acknowledge that I need to focus and think harder about the material.

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