A comrade asks whether to learn math. My first reaction is, "Sure!" — but then I have to stop and think.

Learning math — or rather, learning about math — is much like learning (about) music, history, language, art, literature, etc. It broadens one's base of human cultural knowledge, an Extremely Good Thing. It can be great fun. It might even lead to a new discovery or a new career.

But where to begin? My route commences with popularizations and broad surveys (if possible from a local public library). There are countless candidates; a few I've enjoyed include:

• collections of Martin Gardner "Mathematical Recreations" columns from old issues of Scientific American
• almost anything by Keith Devlin (see LogicAndInformation or MillenniumMath)
• Gödel, Escher, Bach by Douglas Hofstadter
• For All Practical Purposes, a PBS television series which has an accompanying book of the same name

Another approach is via focusing on an area of mathematics that has special appeal to you. Again, the list of possibilities is long: number theory ... probability and statistics ... complex analysis ... calculus ... differential equations ... game theory ... real analysis ... cellular automata ... set theory ... logic ... numerical methods ... combinatorics ... geometry ... topology ...

As a math dilettante over the years I've taken classes in some of the above, read bits and pieces about others, and worked on problems in still more. In all cases, the prime strategy that succeeds for me is to start with fun aspects of the subject: historical anecdotes, paradoxical concepts, subtle connections, or counterintuitive truths, and startling applications to real-world phenomena. Find a well-written essay or book and read it like a novel, skimming past the equations. Then and only then, if appropriate, go back and dig into the details, work on the exercises, and struggle through the harder parts.

Your mileage will definitely vary ...

TopicScience - TopicPersonalHistory - 2004-05-20

(correlates: Comments on WorthRemembering1, DelicatePower, ElectricalEngineer, ...)