Hi I was recently introduced to the idea that the most successful scientists tend to have diverse interests outside of their specific disciplines, from poetry to mountaineering. However, I'm not sure that the most successful mathematicians have similarly diverse interests. Personally, every time I read stuff that isn't related to math, such as general non-fiction or graphic novels, I feel guilty about wasting my time on such trivial pursuits during my undergraduate years. What do you guys think? Does one have to be obsessive and live a life around math, to the exclusion of most other things, to be successful? For those mathematicians who have been successful in other fields, do you think their varied experiences have helped them become successful in math, or is their success in those fields merely reflecting their general intelligence or productivity?
closed as off topic by lhf, Thomas, Nate Eldredge, M Turgeon, Asaf Karagila Oct 1 '12 at 13:45
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While a number of mathematicians are "obsessive", this is certainly not the rule. I could engage most of my professors on topics not at all relating to math. (One of my professors gave me a list of his favorite used bookstores, and I frequently discussed theology with another one.) There are also several examples of prominent mathematicians who are successful in other areas. An example that comes to mind: Eugenia Cheng is a concert pianist.
If you are feeling "guilty" about pursuing other interests, you should ask yourself this: Are you doing mathematics because you want to be successful at it, or are do want to be successful at math because you love doing it?
If you are doing math to be successful, I think you're going to have a really hard time enjoying your work, and you won't have much to motivate you to care about the math you have on hand.
On the other hand, if you just really like doing math, there's nothing stopping you from liking other things as well. Feeling an obligation to do math when something else seems more enjoyable means you don't really love it, you feel like it's supposed to define you, and your time spent doing math determines your worth. This is a terrible attitude to have. On the other hand, if every time you sit down to read a book, you think "Actually there was that group theory problem I couldn't figure out, I want to work on that", then by all means, stop reading and pull out some paper and a pen.
I will say, having diverse interests is probably good for you as a person. But don't try to force it, one way or the other-- don't look for "other things to do" simply because you're supposed to, and don't stifle non-mathematical interests simply because you're supposed to be doing math. (Unless, of course, you have a test coming up or a problem set you've been slacking on.)
Also, you're an undergraduate... you have plenty of time to learn the math you need. Take it easy, enjoy it. Math is fun, beautiful and rewarding, but there are probably other things you find fun, beautiful and rewarding as well.
Many mathematicians contributed to philosophy. For example, Thales, Pythagoras and Bertrand Russell.
Newton was interested in Alchemy and the occult; Einstein enjoyed sailing throughout his life and also played the violin; Turing was an accomplished runner, etc.
There are many more examples of mathematicians having diverse interests. I wouldn't feel too guilty—these guys seemed to do okay! :)
As an undergraduate student of mathematics, my side pursuits of literature, art, music, and sports are sometimes the very things which keep me going on mathematics. I don't expect to contribute in any major way to these fields, but they provide me with some respite from the sometimes arduous and seemingly endless tasks put upon me by my schoolwork.
Don't worry that you spend time doing other things that please you. There will be times (or rather, I've had times) when you're (I'm) just not productive at all doing math. I take a break with one of these diversions, and afterwards I can take on any challenge. Just make sure that there's always something in math that interests you, and I think you'll be fine.