Contribute to Society: Theoretical Math and Real World Applications

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In summary, while people who study theoretical math (or some other theoretical subject) think that their work has applications in the real world, the applicability of the work is subjective and depends on the individual's values.
  • #1
What do people who studied theoretical math (or some other theoretical subject) think about whether their work had applications in the real world? I study the subject since I really enjoy it, but I can't think of a good reason about why my work could be "useful" and how I can use it to help other people/make a difference in their lives. Of course there are the usual arguments about how long-term impact isn't something we can predict at all with various historical examples, but I can't help but feel that I'm avoiding the original question. What are your thoughts?

(hopefully this is appropriate for the forum - feel free to move somewhere else if this post doesn't belong in this section of the forum)

EDIT: All comments about this are welcome (didn't intend to limit to people studying such fields).
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  • #2
I'm not a mathematician. But, my opinion is that neither extreme is true. The 'truth' is somewhere in the middle (if there is any truth). By this, I mean, if no-one ever did any theoretical maths, then obviously a lot of today's technology would not be possible. And on the other extreme, if the government used 100% of the money it gets from taxes to fund theoretical maths research, then clearly we would not have hospitals or schools or roads or anything, and we would be in a terrible situation. So the right amount of money for the government to spend on research is somewhere in the middle of the two extremes. But exactly where to place it depends on your values really. There is no objective answer.

edit: honestly, as long as doing theoretical maths feels useful to you, then you should do it, and not worry too much. So... maybe what you are here because you want to be convinced that theoretical maths is useful?
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  • #3
I don't think so, but to be honest I'm not sure. I originally intended to study something that was much more "useful" and then ended up doing something else since I enjoyed that lot more. While I thought that the first topic was more "useful" for society, I really didn't enjoy studying it. I'm not too far from graduating from university and I started to think a bit more seriously about what it would mean to be a "real" person and how I would like to contribute to society when I'm not a student anymore.
  • #4
I take comfort in knowing that what I'm studying is an academic subject, but that's because I don't really believe it's possible for one to "contribute" to society in any meaningful way. Do what maximizes your utility!
  • #5
hehe, but people often get satisfaction from doing something that they feel is useful to society. So a significant component of someone's utility might be the feeling of contributing to society.
  • #6
Indeed, determining that component of utility seems to be the problem.
  • #7
BruceW said:
But exactly where to place it depends on your values really. There is no objective answer.


In my view obtaining knowledge about the nature (which includes abstract maths) is the ultimate goal in itself. Consequently, I deem working on a most esoteric part of pure maths to be worthwhile even if it is never going to be put to any 'pratical' use.

This pursuit of truth relies on a stable, wealthy society to sustain it. Any contribution to the society will indirectly benefit the scientific progress. Ideally, similarly to a professional who needs to strike a balance between productivity and learning, the society balances resources devoted to research at present and to improving the society which will increase the available resources in the long run.
  • #8
I did my Phd in theoretical physics. I do not believe that any of my work, or that of any of my fellow PhD students, had any relation to any problem considered relevant in "real life" (yet). Learned some real-world valuable skills like actually getting work done rather than fantasizing about possibilities, though.
  • #9
Knowledge always contributes to society.
  • #10
In my PhD I have made some small discoveries that would probably never become the basis of real-life products, but they might help others get some new ideas (or rather new perspective), choose the direction in which to explore further and eventually find something really useful. I however did a PhD in a relatively applied area.
  • #11
Do the arts contribute to society? I believe they do. And if so, then mathematics certainly does.
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  • #12
Ben Niehoff said:
Do the arts contribute to society? I believe they do. And if so, then mathematics certainly does.
I don't follow your logic. There seems to be some similarity between arts and math that's obvious to you, but which I don't find obvious. In what way are they similar such that, if we count the arts as a contribution we must also count math as a contribution?

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