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In fact, the amount of math you need as a hacker is a lot less than most university departments like to admit. I don't think you need much more than high school math plus a few concepts from the theory of computation. (You have to know what an n^2 algorithm is if you want to avoid writing them.) Unless you're planning to write math applications, of course. Robotics, for example, is all math.

But while you don't literally need math for most kinds of hacking, in the sense of knowing 1001 tricks for differentiating formulas, math is very much worth studying for its own sake. It's a valuable source of metaphors for almost any kind of work.[3] I wish I'd studied more math in college for that reason.

Like a lot of people, I was mathematically abused as a child. I learned to think of math as a collection of formulas that were neither beautiful nor had any relation to my life (despite attempts to translate them into "word problems"), but had to be memorized in order to do well on tests.

One of the most valuable things you could do in college would be to learn what math is really about. This may not be easy, because a lot of good mathematicians are bad teachers. And while there are many popular books on math, few seem good. The best I can think of are W. W. Sawyer's. And of course Euclid. [4]

Everything

Thomas Huxley said "Try to learn something about everything and everything about something." Most universities aim at this ideal.

But what's everything? To me it means, all that people learn in the course of working honestly on hard problems. All such work tends to be related, in that ideas and techniques from one field can often be transplanted successfully to others. Even others that seem quite distant. For example, I write essays the same way I write software: I sit down and blow out a lame version 1 as fast as I can type, then spend several weeks rewriting it.

Working on hard problems is not, by itself, enough. Medieval alchemists were working on a hard problem, but their approach was so bogus that there was little to learn from studying it, except possibly about people's ability to delude themselves. Unfortunately the sort of AI I was trying to learn in college had the same flaw: a very hard problem, blithely approached with hopelessly inadequate techniques. Bold? Closer to fraudulent.

The social sciences are also fairly bogus, because they're so much influenced by intellectual fashions. If a physicist met a colleague from 100 years ago, he could teach him some new things; if a psychologist met a colleague from 100 years ago, they'd just get into an ideological argument. Yes, of course, you'll learn something by taking a psychology class. The point is, you'll learn more by taking a class in another department.

The worthwhile departments, in my opinion, are math, the hard sciences, engineering, history (especially economic and social history, and the history of science), architecture, and the classics. A survey course in art history may be worthwhile. Modern literature is important, but the way to learn about it is just to read. I don't know enough about music to say.

You can skip the social sciences, philosophy, and the various departments created recently in response to political pressures. Many of these fields talk about important problems, certainly. But the way they talk about them is useless. For example, philosophy talks, among other things, about our obligations to one another; but you can learn more about this from a wise grandmother or E. B. White than from an academic philosopher.

I speak here from experience. I should probably have been offended when people laughed at Clinton for saying "It depends on what the meaning of the word 'is' is." I took about five classes in college on what the meaning of "is" is.

Another way to figure out which fields are worth studying is to create the dropout graph. For example, I know many people who switched from math to computer science because they found math too hard, and no one who did the opposite. People don't do hard things gratuitously; no one will work on a harder problem unless it is proportionately (or at least log(n)) more rewarding. So probably math is more worth studying than computer science. By similar comparisons you can make a graph of all the departments in a university. At the bottom you'll find the subjects with least intellectual content.


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