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> Another thing that resonated deeply with me was how Newton studied a book by a French mathematician (I don’t remember which one): he started reading the book

> Another thing that resonated deeply with me was how Newton studied a book by a French mathematician (I don’t remember which one): he started reading the book – when he found it too hard, he started over. That’s what he did until he understood the whole thing. So, he didn’t go and read something more basic, or tried to found someone who could explain it. He just stayed with the source until he groked it. Approach this advice with caution. Yes, it might work great if you're working with a great book that has good coverage of all the fundamentals of the topic and presents it in a logical order. Many books don't do this. Starting over when you get stuck can just throw you into an endless loop if the required information just isn't in the book you picked to learn from. Know when to branch out to other sources of information instead of looping back. Don't be afraid to make a quick interlude to Wikipedia if you need to. (Personally, I prefer to just backtrack to the information I missed instead of starting over from scratch. Starting over seems to waste a lot of time, but if you missed one concept, there's a chance you missed more.)

shizzy0 14y ago
There's a lot to recommend for backtracking. Newton backtracked multiple times to understand the math from an astrology book he picked up. Also, if you're inexperienced, how are you to tell who the Master's are? I fear that whatever book is renowned for its difficulty will become the Master's book. The advice is like, find the steepest slope you can, then climb it. You may not get very far, but you'll feel good that you got anywhere at all.
silentbicycle 14y ago
Indeed. Many brilliant, groundbreaking work is produced by geniuses who are lousy writers, so sometimes secondary sources are necessary to get past roadblocks. Still, it's a good reminder to try reading primary sources, when so many people seem to be learning from screencasts and blog posts three degrees removed from them.
- silentbicycle 14y ago
  "Many brilliant, groundbreaking work is produced...lousy writers." I, um, yeah. Oops.
jwdunne 14y ago
I agree with this. I'm currently reading John McCarthy's paper "Recursive functions of symbolic expressions and their computation by machine" linked to in the article, which I've been meaning to read. I don't have any real formal maths/computer science education so looping over would have been futile in many cases and Wikipedia, namely http://en.wikipedia.org/wiki/List_of_mathematical_symbols http://en.wikipedia.org/wiki/List_of_mathematical_symbols, has been an invaluable resource for me in understanding the paper (and other things in the past). Another example is partial recursive functions, which I didn't know the definition of. A quick Google/Wikipedia search helped here. I've found myself looping over once or twice to make sure I haven't missed anything and, if not, proceeded to search for definitions or further explanations. I'm not entirely sure if this approach would work for other papers such as the Turing ones, since I'm familiar with Lisp already, but it's working very well for the paper I mentioned earlier.

shizzy0 14y ago

There's a lot to recommend for backtracking. Newton backtracked multiple times to understand the math from an astrology book he picked up. Also, if you're inexperienced, how are you to tell who the Master's are? I fear that whatever book is renowned for its difficulty will become the Master's book. The advice is like, find the steepest slope you can, then climb it. You may not get very far, but you'll feel good that you got anywhere at all.

silentbicycle 14y ago

Indeed. Many brilliant, groundbreaking work is produced by geniuses who are lousy writers, so sometimes secondary sources are necessary to get past roadblocks. Still, it's a good reminder to try reading primary sources, when so many people seem to be learning from screencasts and blog posts three degrees removed from them.

silentbicycle 14y ago
"Many brilliant, groundbreaking work is produced...lousy writers." I, um, yeah. Oops.

jwdunne 14y ago

I agree with this. I'm currently reading John McCarthy's paper "Recursive functions of symbolic expressions and their computation by machine" linked to in the article, which I've been meaning to read. I don't have any real formal maths/computer science education so looping over would have been futile in many cases and Wikipedia, namely http://en.wikipedia.org/wiki/List_of_mathematical_symbols http://en.wikipedia.org/wiki/List_of_mathematical_symbols, has been an invaluable resource for me in understanding the paper (and other things in the past). Another example is partial recursive functions, which I didn't know the definition of. A quick Google/Wikipedia search helped here. I've found myself looping over once or twice to make sure I haven't missed anything and, if not, proceeded to search for definitions or further explanations. I'm not entirely sure if this approach would work for other papers such as the Turing ones, since I'm familiar with Lisp already, but it's working very well for the paper I mentioned earlier.