What does a personal interest in math look like?

December 8, 2011 11:43 AM

A while back I read about an english professor who claimed to have a strong personal interest in mathematics. Assuming that he doesn't use math in a professional setting, how would this interest manifest itself? Completing math textbooks? Reading books about math? Memorizing the first 1000 primes? What would someone with an interest in math do?

I used to love math (I placed well in provincial contests during my first two years of high school), but some personal events caused me to miss a lot of material and after that I was never able to feel like I had mastered the material before being forced to move on. I recently discovered the Khan Academy and have been filling in some of the holes in my math knowledge, but I'm wondering what I'll do after I've finished the tree of math exercises that the site provides. I've taken statistics and I'm currently in calculus, but I don't know what I can do in math once I'm finished university this spring.

Perhaps a book or two about math could pique my curiosity, but I'm really interested in seeing what a long term math interest looks like. Personal stories about what your life with math has been like would be awesome. Thanks!

posted by Homo economicus to education (20 answers total)

Read books by Martin Gardner.
posted by caek at 11:46 AM on December 8, 2011 [5 favorites]

I have a lot of math geek friends, and when they get together they do problems. Simple math-based logic problems, probability problems, things that involve limit equations that I don't understand, etc.

You know that game Pass the Pigs? I have it, and busted it out a while back to play at a party (it should be noted that I obviously throw rockin' parties). Well, after a few rounds of play, these guys took the pigs and did a bunch of rolls, asked for some pencils and paper, and started busting out Monte Carlo simulations. An hour or so later, they decided the game was no longer fun because they had solved it. (Jerks.)

They also do things like this and this (scroll down) for fun. (Those are both links to friends' websites where they frequently write about math and probability and programming and other generally interesting stuff.)

Basically, for these people who are extremely interested in math, who have had a lifelong interest in math, who studied math seriously in school and didn't stop learning about math after graduation, EVERY scenario in life with more than one answer can (and will) be broken down into a math problem. For them, math isn't a hobby or a chore or an activity, but rather a way of looking at the world.

(I can tell you firsthand that it gets kind of tedious hanging around these guys when they really get on their math benders, but they seem to enjoy themselves, and who am I to rain on their parade.)
posted by phunniemee at 12:04 PM on December 8, 2011 [3 favorites]

phunniemee: I teach game theory. One of my housemates has this game. Last semester I kept meaning to assign the problem of solving this game to my class, but I never did.

homo economicus: you should visit a large general-interest bookstore (I'm thinking Barnes and Noble, but it appears that you're Canadian) and take a look at the section with math books. (If possible you want a bookstore near a university; in my experience their math-book selections tend to be stronger.) They will pique your curiosity more, and also perhaps give you some idea what mathematicians think about. I'm a math professor, and I keep saying that the day looking at those books doesn't make me happy is the day I quit.

(Also check out a university library, for the same purpose. You are a student, so do this now; but a lot of university libraries allow in members of the public, and even more allow in their alumni.)
posted by madcaptenor at 12:18 PM on December 8, 2011 [1 favorite]

I'm not as far into math as you are, but some of what I do is:
* When I have time to kill and can only use my mind to kill it, I do things like memorize squares.
* I mentally critique newspaper stories based on statistics, and similar stuff.
* Read science magazines and books relating to math, such as "Freakonomics" and "A Mathematicians Reads the Newspaper."
* Make up my own mini research and statistical projects, such as relating countries' distance from the equator to their standing in the Human Development Index.

You can also get a math-involved career without a math degree. For example, I'm planning to work in geographic information systems. Roughly speaking, this combines mapping and data analysis.
posted by maurreen at 12:23 PM on December 8, 2011

So here's an anecdote for you - when I did my masters in economics I had a professor, he was a professor in economics, he'd done a BA in finance and worked in investment banking for a while, went back to university to pursue postgraduate education. Became a professor of economics, a moderately renown one. Alas he loves to read. So he took a sabbatical to do a masters in English literature. He then went back to work and when he was teaching me he was relating the life story of a poet to introduce a concept of some description. I can't remember what the lecture was on, I can remember this unusual introduction.
posted by koahiatamadl at 12:26 PM on December 8, 2011

sorry, what I'm trying to say is that whatever your interests you can find a way to incorporate them into your life somehow.
posted by koahiatamadl at 12:27 PM on December 8, 2011

Well, I have an interest in... mathematicians? Pure mathematics, the philosophy and foundation of math... interesting puzzles... etc. I am not professionally a math person in any sense.

Some books to read:

The Man Who Loved Only Numbers by Paul Hoffman (About Paul Erdős, a pretty sweet mathematician and all-around character.)

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter
(I am currently working my way through this and it is perplexing and delightful.)

Neal Stephenson's books (especially Cryptonomicon and Anathem) are fiction with some fun simplified math bits in them. Also Alan Turing, and in The Baroque Cycle, Newton & Leibniz, as fictional characters!

See also:

The Mountains of Pi, a New Yorker article about the Chudnovsky brothers. (Note: you have to be a subscriber to read this, but it's available free elsewhere on the web.)
posted by Isingthebodyelectric at 12:29 PM on December 8, 2011 [1 favorite]

I think the interest can be kind of active the way phunniemee describes - trying to solve puzzles, or just looking at things through the lens of math tools. I always found that a bit off-putting even when I was studying maths (something very competitive in it often) but I love reading books about maths, and kind of absorbing the ideas, even if I can't fully use them myself.

I highly recommend Tom Koerner's The Pleasures of Counting as a collection of essays on various topics where maths is used as an integral part of the argument without becoming too dauntingly theoretical. I also like Davis and Hersh The Mathematical Experience as an interesting overview of the subject as a whole. There are tons of good "knowledgeable layperson" books though.
posted by crocomancer at 12:30 PM on December 8, 2011

David Foster Wallace wrote a book about infinity.
posted by gentian at 12:46 PM on December 8, 2011

Take a look at the website of the current exhibition of the Fondation Cartier in Paris, Mathematics: A Beautiful Elsewhere. There are a series of video links to the right, and they give you a great insight into how mathematicians relate to the world. I've been enraptured by the way they write -- their concept of beauty is crystal clear, without any need to classify or clarify it.
posted by bwonder2 at 12:46 PM on December 8, 2011

I satisfy my personal interest in math by answering random AskMefi questions.
posted by vasi at 12:48 PM on December 8, 2011

(It was so tempting to make that recursive, but I resisted. Be proud of me!)
posted by vasi at 12:50 PM on December 8, 2011 [3 favorites]

The kind of math you do in high school and most of college is all about giving you tools to solve particular kinds of problems. It's just the tip of the iceberg.

But there's a whole other world of math. Logic, axiomatic set theory, and abstract algebra are the foundations of that world. I don't have a particular book to recommend, but if you get an advanced undergraduate book on any of those and start reading, that's a good start. Even doing a lazy evaluation from Wikipedia works pretty well as a general introduction (start with a topic, say, incompleteness, and when you encounter a concept you don't know, open it in a new browser tab. Keep reading until you've closed all the tabs)

The history of modern mathematics really helps to put things in context, and it's actually kind of exciting. There was an explosion of development starting in the late 1800's that revolutionized math. Things we take for granted today (axiom of choice, anyone?) were subjects of heated debate. Bertrand Russell, Kurt Godel, Georg Cantor, and their contemporaries --- these are the guys to start with.
posted by qxntpqbbbqxl at 12:56 PM on December 8, 2011 [1 favorite]

If what qxnt is saying sounds interesting, try reading Logicomix.
posted by crocomancer at 1:41 PM on December 8, 2011 [3 favorites]

You can start pounding away on Project Euler
posted by shothotbot at 2:05 PM on December 8, 2011 [1 favorite]

I am a mathematics graduate student.

If you are interested to get a glimpse of the sort of questions that research mathematicians try to answer, I highly recommend the book Mathematics: A Very Short Introduction, by (Fields medalist) Tim Gowers. I may not be the best qualified to judge this, but it seems pretty readable to a non-specialist. And in my opinion it does accurately describe what doing math is really all about.

I guess I'd say to find out what sort of math you're interested in, and try to delve farther into that. Do you like things that apply to the real world? Purely abstract mathematics? Something in between?

For me, outside of my mathematical work, I enjoy playing the game of Go a lot. It's not really mathematical in itself, but its elegance and simplicity appeal to the same aspect of my nature as mathematics does. Also the game of Set. Origami is similar. And, perhaps surprisingly, word games like crossword puzzles, Scrabble, etc.
posted by number9dream at 5:31 PM on December 8, 2011 [1 favorite]

Check out what Vi Hart gets up to.
posted by divabat at 6:57 PM on December 8, 2011 [2 favorites]

Not super heavy math, but I enjoyed Everything and More: A Complete History of Infinity by David Foster Wallace.

My dad is a math hobbyist - he coached my high school math team for about ten years, read books, and frequently runs across little problems to solve, often via writing a computer program. A simple one was figuring out how many lights should go on each layer of our artificial Christmas tree for even distribution, a more complex one was figuring out how many unique cubes could be made from a set of foam cube puzzles (not my dad's site, same cubes). And then how many other ways there were to make various other shapes. Keep your eyes open for an interesting problem.

If the board game recs interest you, dad also had a Chinese chess / Shogi / Korean chess phase - they're similar to international chess, with some interesting twists. I helped him run an Asian chess info table at a local chess tournament as a teenager. We also taught a unit origami class at a math event for middle schoolers - unit origami involves folding a bunch of identical units (there are different types), which can then be assembled into interesting things.
posted by momus_window at 7:53 PM on December 8, 2011

Steven Strogatz, professor of applied mathematics at Cornell, was the author of a wonderful 15-part series in the New York Times. I loved this series because it explained deep mathematical concepts in a very simple manner. Each article also carried a number of further reading notes using which one could further explore particular areas of interest.

Despite moving out of a strongly mathematical undergrad background, I have retained some interest in math, which I indulge by playing around with recreational math (games, puzzles and so on). Most of these puzzles are typically solved in a moment of epiphany, an "Aha" moment when light dawns on you and all is beautiful with the world. Awesome, especially during a dull day in the office. In this regard, the articles and books of Martin Gardner have already been suggested in this thread - I will also recommend the work of Raymond Smullyan (check out his chess puzzles too!).

I find that keeping sharp with math is a bit like keeping sharp in basic computer programming. It doesn't get you very deep in the original area (ie, math or programming) but it is tremendously useful in giving you a leg up in your career of choice, where it can become a very strong differentiating factor. For example, knowing Benford's Law (see here) is really cool, but it can become incredibly useful if you are in a job that deals with the collection and analysis of any sort of data that may or may not be manipulated.
posted by rahulrg at 7:57 PM on December 8, 2011

If you are interested to get a glimpse of the sort of questions that research mathematicians try to answer, I highly recommend the book Mathematics: A Very Short Introduction, by (Fields medalist) Tim Gowers. I may not be the best qualified to judge this, but it seems pretty readable to a non-specialist. And in my opinion it does accurately describe what doing math is really all about.

Absolutely. If the last maths you did was in school, this is a great primer on what mathematicians actually do. Gowers's is a little opaque for the non-specialist, but I enjoy it anyway.
posted by caek at 1:42 AM on December 9, 2011