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I have a MsC and want to take a PhD in algebraic topology. Probably very few people in the world will have any interest of my thesis. They will pay me for doing my hobby. Its the only job I can think of which doesnt contribute to bettering the world somehow. I feel like I should get a real job like doctor or garbageman. I get bad conscience. How can I feel better for pursuing my dream?

John
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    Typically academic positions involve teaching as well as research, so that you would often have the opportunity to share your learning with others, not necessarily at the narrowest levels of attainment, but from everything that builds up to that level. – hardmath May 28 '15 at 10:45
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    Be selfish and do what you love. – JP McCarthy May 28 '15 at 10:48
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    I think "bettering the world" is very subjective. Somebody might think "x" improves the world, other people will think it makes the world worse. – wiskundeliefhebber May 28 '15 at 10:50
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    Note Applications of Algebraic Topology. – mvw May 28 '15 at 11:05
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    "Its the only job I can think of which doesnt contribute to bettering the world somehow." Seriously? I can think of tons of other examples. – Did May 28 '15 at 11:07
  • If you don't you are most certainly wasting your talents which is arguably worth feeling bad about. Especially when I and probably many others on the site could only dream of being able to pursue such a career. – Karl May 28 '15 at 11:13
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    Why are people taking this question seriously? – Asaf Karagila May 28 '15 at 11:21
  • @Did I added a comma and read the sentence as “It’s the only job I can think of, which doesn’t contribute to bettering the world somehow.”. – k.stm May 28 '15 at 11:21
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    @AsafKaragila Why not? It’s a real concern to some and I guess it can be a real mood killer if you’re considering spending 3–5 years working hard on one particular problem/question. Even though I don’t pursue a career as a mathematician, I can relate to this concern. Why not take it seriously? – k.stm May 28 '15 at 11:24
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    Well, you can be an academic from Monday to Friday and a volunteer barber of the homeless on Saturnday. Is there a reason why one should better the world for a living? If you do it for a hobby, you can actually choose what to improve in the world (and not just what others are willing to pay for). –  May 28 '15 at 11:32
  • By the way, I'm flagging this as "primarly opinion-based". –  May 28 '15 at 11:39
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    @k.stm: There are different ways to phrase a question. And I cannot, for the life of me, take this phrasing by an unregistered user whose only contribution to the site is this, as anything other than trolling. – Asaf Karagila May 28 '15 at 11:44
  • Maybe Tim Gower's talk on importance of mathematics might interest you. – Martin Sleziak May 28 '15 at 12:16
  • The premise of the question seems to be that someone is willing to pay you to do something that is of no use whatsoever. Really? – David K May 28 '15 at 12:22
  • There are bigger issues than the insecurity of not being useful to society: See for example http://www.math.wisc.edu/~miller/old/perils.pdf – hot_queen May 28 '15 at 13:00

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Perhaps you need to read G. H. Hardy's A Mathematician's Apology.

One of the main themes of the book is the beauty that mathematics possesses, which Hardy compares to painting and poetry. For Hardy, the most beautiful mathematics was that which had no practical applications in the outside world (pure mathematics) and, in particular, his own special field of number theory. Hardy contends that if useful knowledge is defined as knowledge which is likely to contribute to the material comfort of mankind in the near future (if not right now), so that mere intellectual satisfaction is irrelevant, then the great bulk of higher mathematics is useless. He justifies the pursuit of pure mathematics with the argument that its very "uselessness" on the whole meant that it could not be misused to cause harm. On the other hand, Hardy denigrates much of the applied mathematics as either being "trivial", "ugly", or "dull", and contrasts it with "real mathematics", which is how he ranks the higher, pure mathematics.

[bolding mine]

Somewhat ironically, some topics that were in Hardy's day the domain of pure mathematics now have very practical importance, eg, algorithms used in public key cryptography rely on things like the difficulty of factorization of large numbers, properties of discrete logarithms, elliptic curve theory, etc.

PM 2Ring
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    The argument is interesting, however he has been proven wrong some times the last century. Fields of mathematics which were thought to be very pure have become applied in several fields of engineering and science. – mathreadler May 28 '15 at 11:31
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Simple - you contribute to humankind according to your ability to do your job. Your ability to do your job is fundamentally affected by your enthusiasm for your job. It stands to reason that the people should be taking jobs doing things they want to do anyway, regardless of pay, perks, etc.

If you are making great contributions to algebraic topology, then that is what you should be doing. The small number of people being interested in your field means that opportunities might be limited. But if this is what you are determined to do, then you should be able to contribute. (Of course, always have a Plan B.)

If you pursue the medical or the sanitation arts despite showing no interest in either, you will not be able to contribute all of which you are capable. That robs all of us of your potential. Worse, you might get depressed over your inability to pursue your dream. Depression is expensive and does you no good. Better that you strive to be an algebraic topologist, where your contributions will be great and your happiness unbounded.

Never feel guilty about doing what you want to do for a living. It is a gift from a successful society.

Ron Gordon
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If you are going to take a "real" job as you say, without the will for it, you will feel even worse. This feeling may make you under perform and actually you can end up even contributing less to bettering the world as you expected, so your choice should always be what you really like. If you have an easy access to this PhD position I really recommend you going for it. Moreover, as hardmath pointed out you will be very useful by sharing your knowledge with students.

Alberto Debernardi
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It is worth noting that in the dim and distant past, graph theory was considered recreational math with no practical application to real life; however, now graph theory is essential to computer science, modeling the brain, and all sorts of other practical fields. So right now algebraic topology may seem abstract and nonapplicable, but in 100 years, your research could be essential to a new development in a field which has appeared, which no one foresaw.

nosyarg
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