How do I motivate myself to do math again? [closed]

I have been thinking of asking for help for a few months now but posting in a public forum like this is intimidating. Still, I am currently in a university studying mathematics as an undergrad. I took quite a few knocks a few months back when I failed to qualify for the universities of my choice and all the hard work for mathematical olympiads and hours of practice went up in smoke.Out of frustration and disappointment, I left math for a few months,doing nothing but staring at the ceiling. After coming to the university,I then tried doing math again and after a months, I tried to study linear algebra and analysis. I studied 30 pages of Rudin and then stopped; and then I studied those 30 pages, each time those 30 pages seemed to be as difficult as before but less interesting and now I am stuck.

I came to the conclusion that I cannot do math OR I have lost the motivation to. How do I get back to studying math?

Thank you everyone for your answers and comments. I have read them and I will try to get back up.

Solution 1:

Disclaimer:

If you didn't consult your friends and/or parents on whether your situation is serious enough (i.e. requires specialist attention), then do it now. Major depressive disorder may have detrimental effects on your life and you should treat it accordingly. On the other hand, mild depression, melancholia, etc. may be temporary and may not require any professional treatment. Often those are normal human reactions and are nothing to be ashamed of.

Thanks to @EricLippert for his comment.

It depends on what motivates you generally. Naturally, first

• Get enough sleep (but not too much).
• Keep you body healthy (within reason, esp. if you have some disabilities).

As to the motivation, I observe three main factors:

1. Pleasure – Math is fun and beautiful.
2. Need – we (the world) need your math.
3. Community – there are some cool guys among mathematicians.

You need to find what exactly works for you, but here are some tips:

1. Math is fun and beautiful.
   • Look for some nice proofs, like those in Proofs from the Book.
   • Read Gödel, Escher, Bach.
   • There are also comics about math, e.g. Logicomix (one of the authors is a world-class researcher in theoretical computer science).
   • Find some other nice mathematical books, you can find some recommendations here.
   • Find some beautiful mathematical facts, you can find some here.
   • Try some nice online presentations like How to Fold a Julia Fractal.
   • There are even television series like Numb3rs; to put it mildly, it's not my favorite, but who knows, maybe it would work for you (it doesn't really matter what the IMDb ranking is, only if it remotivates you again).
   • Look at some highly voted questions and answers here, at math.SE, some are real pearls.
2. I don't think this needs much commentary. There are many, many articles on why math is important and why it would be good for you to know it (and I think that would be even more so in the near future). I've never been interested in those, so I'm unable to recommend any, but try searching for it.
3. Sometimes doing things is fun when in group, and math is no exception.
   • Imagine how music bands stick together, mathematicians very often collaborate and this is for a reason. One of them is that doing something with peers is just more fun than being alone in the cave.
   • Mathematicians like Tim Gowers and Terence Tao write blogs. You can learn a lot from them (but it might be complicated).
   • It's easier to get motivated when you have some examples of other motivated people (but be aware that you might also get demotivated).
   • Why don't you hang around with "us, the cool guys"? Answering and asking questions might also be a motivating experience (if you ignore those lazy bums that come only to get their homework solved).

Finally, this goes without saying, but I feel that is should be emphasized here: there are other domains, one of these might suit you better, do you really want to study math? If the only reason is that you do not wish to throw away all the hard work you did, then there are some good news: the skill you have acquired will stay with you in some form, or simply put, it made you smarter. Moreover, areas like physics, engineering or computer science use math a lot, and the math you know will directly help you there. Mathematics is everywhere, you don't need to be labeled as a mathematician to do mathematics.

I hope this helps and good luck! $\ddot\smile$

Solution 2:

Mathematics is difficult and if you lack confidence it'll be hard to keep going. Of course, not many people have confidence that they know a lot - actually most of us know that we know very little in the scope of things. However, I've seen that good mathematicians seem to be confident in their abilities to learn given enough effort and patience. Some learn fiendishly quickly and it can be discouraging to be among them but others like me really need our time to sit down and explore the definitions, theorems, etc. To survive in this game you need to be confident in yourself and a great thing to be confident about is work ethic. If you are able to put in a couple of hours into solid learning every day, you'll tackle almost any subject.

About studying itself - there are lots of different ways to go about it and some are more mind-numbing than the rest. The texts are dense, especially Rudin. You can't understand them the way you understand a novel when you read it. Actually, if the text is new to you, you cannot even read it with any appreciable speed. A good way to learn is to take it very slowly, sentence by sentence. Rip each sentence apart and see that you know each word and expression, and that you get the meaning of the words combined. Make diagrams and check your intuition. It takes keeping your foot on the brake because it's really easy to just run-off onwards and glaze over. It might seem like it would take forever to learn this way but it's more resilient.

You lost motivation in your studying because you faced many big failures in a short amount of time. Suddenly a lot of long hours of studying, writing applications and proof-reading letters seem like they have been for nothing. All of a sudden, you feel yourself burned out. I see nothing wrong in taking the kind of break that you took because it can be traumatizing. If you come back to math and feel still deep anxiety, I know how you feel. The problem is that math is difficult and we face a ratio of many failures for each success, and this seems to be mimicked in my friends' career paths too. This kind of ratio is absolutely toxic to confidence. You need to redefine what success means to you.

In my undergrad my successes were usually finishing an assignment, doing great on an exam, and occasionally solving a hard homework problem that bothered me for days. But as the years progress I faced more and more difficult problems. All of a sudden, assignments were incomplete, problems had holes in them, exams were not stellar, and hard problems remained unsolved. I lost a lot of confidence and was in a situation similar to yours several times. It's something a lot of math students face (at least among my peers). They all seem to meet their match that makes them or breaks them. What it takes is a shift of the mind. You are a mathematician and you can make your own definition and properties.

So here it goes. When there's failure in everything you do you gotta look for the small successes. You understood a paragraph - that's a success. You understood the idea behind a proof - that's also a success. You find an interesting property of some function - another win. One case down out of five - another success. Basically, when the stairs become too tall to scale, you gotta make your own ladder so you can climb up more easily.

When you focus on the small successes, there will be lot of them and failure will not bother you as much anymore. All of a sudden it wouldn't matter so much if the whole assignment is in or if you understand a whole chapter. You'll enjoy making the little steps and they'll eventually take you much further than trying to make bigger leaps.

I hope I'm not reading too much into your words. When I read your question I kind of saw myself as I was a few years ago and I wish someone would have told me what I know now.

Solution 3:

I highly recommend The Shape of Space by Jeffrey Weeks for its readability and fun factor. Imagine cross-sections of higher dimensional shapes! Build "impossible" surfaces with paper, scissors, and tape. It's a gentle, hands-on introduction to some important ideas in low-dimensional topology and differential geometry.

Solution 4:

Doing what you like is the most important thing. If you do things because you feel that you have to, you'll end up resenting them. Of course, it's okay in the short term - we all have obligations - but forcing yourself to do something you don't enjoy, in the long term, is not sustainable.

You're still an undergrad, so you should focus on a varied diet, rather than gorging yourself full of the first thing you find. Imagine that you are at a buffet with a lot of time on your hands. The best thing to do is to get a small taste of everything. And if, by chance, you find something that you really like, good! Sail with it for a while!

Even the best mathematicians go through dry spells sometimes. The intelligent thing to do, then, is to put down the books, and do something else that you like. Being happy is the most important ingredient to success - not the other way around!

Solution 5:

You could watch Numberphile video's on Youtube, I really enjoyed them!
It involves some pretty complicated math, but it's explained in such a way that's easy to understand, even if you're not a brilliant mathematician. http://www.youtube.com/user/numberphile