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Comment by zafka | Hacker News Reader

This stuff is very cool, and I feel extremely outclassed. Is there a math camp for adults who just made it out of engineering school, but never absorbed the real beauty of math? People post this very interesting stuff, and I see something sparkly and say wow! I must say the writing of Feynman gives me a little hope, but so far most of the language of math is beyond me.

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I would recommend the Princeton Companion to Mathematics[1]. Its got a broad range of topics in short digestible articles. (though the first section has preliminary material for understanding the later articles)

[1]http://www.amazon.com/gp/aw/d/0691118809/ref=redir_mdp_mobil...

Thank you for that recommendation, I've been looking for a book like that for ages.

Thank you!

This is a good reference. It is basically an encyclopedia, so some sections are better than others. I'm not a big fan of Gowers' intro, it is very heavy and could have done much more in the way of explaining how to navigate the volume itself. It is generally assumed that you know integral and differential calculus.

If you are daunted by mathematical formulas and don't have a solid basis in math generally, I would recommend Pickover's "The Math Book"[1]. Very engaging; good short, non-technical descriptions of many of the same topics in Princeton; lots of pretty pictures.

[1] http://www.amazon.com/Math-Book-Pythagoras-Milestones-Mathem...

How deep does Pickover's book go? I read in the reviews that each topic is limited to one page only, so I presume the real mathematics would not be covered. In other words, after reading this, will I understand the topics or would just understand things about them?

I also see a Physics book by the same author, but have the same question there too: http://www.amazon.com/Archimedes-Hawking-Science-Great-Behin...

IIRC there are a few things that are simple enough to actually explain in a page, but yes, one page per...artifact? Very little real mathematics, you will just understand things about them. It is, however, the best written of these pop-math type books that I've come across. If you are comfortable with undergraduate-level mathematics, the Princeton Guide is a much better book for getting an idea about a specific topic. Pickover's book is more for getting a feel for what topics are out there. They were written for two very different audiences and I like them both for different reasons.

Learning math is pretty much like learning programming.

Sit down to read books, it gets boring. Get a real problem to solve, and you learn tons of things along the way.

Don't learn mathematics. It's not supposed to 'learned'. Math is basically what you indicate in notation without you would other wise denote in words while you explore something.

So don't learn, pick up a problem and explore.

I think that your point about learning being easier when you've got a problem is probably true. But as someone without such a problem immediately at hand, I could really use a list of interesting problems to give me a starting point. And, even if I had a problem I wanted to solve, I expect I might not even know where to begin on it (so then I'd have two problems, as they say). So in practice I'm not sure what to do with your advice.

Write simulators that use the mathematics you want to learn. One way or another you will learn the mathematics if you do this. A game engine with bone animation is great for really getting familiar with 3D vector mathematics. Electrical circuits simulator and a Physics engine are great follow ups. Fluid dynamics is another one. A symbolic math engine will get you even more familiar with lots of other pure mathematics.

Honestly speaking I've only built the circuits simulator, partially built the symbolic math engine and currently working on the physics engine. I have learnt a great deal though.

these nine videos are fantastic http://www.dimensions-math.org/Dim_tour_E.htm

here's a whirlwind tour http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar...

Can't recommend Ian Stewart enough!!

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