1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

If you're a pure mathematician, why?

  1. Sep 1, 2012 #1
    Are there any reason compelling you to go into pure mathematics beside passion? Aren't you afraid that your discipline will not yield any practical benefits for mankind?
  2. jcsd
  3. Sep 1, 2012 #2

    No and by-no-means no.

  4. Sep 1, 2012 #3


    User Avatar
    Science Advisor

    Hey StJohnRiver and welcome to the forums.

    I think you should think about the idea that we all don't actually do things that benefit every single other person in a very direct way.

    It's not to say that people don't contribute: most people do but it's in a smaller way and the sum of all contributions is what you see in the cumulative effect of how things come about.

    Like every group of individuals, people congregrate together and help one another meet the same kinds of mutual goals that all members of the group have.

    Pure mathematicians are just another group with a particular focus. Just like any other group, they have the same goals in mind and collaborate to achieve those goals just like a sports team collaborate together to try and win against their competitition.

    Just like the sports team, they aren't going to benefit everyone directly and like the sports team, most people outside that little pocket of the world won't know they even exist.

    This is how it is everywhere. It doesn't make anyone insignificant, but it does point out that no single individual or isolated group is really that significant in a way where they affect absolutely everything or are more important.

    The thing about stuff nowadays is that collaboration is necessary to produce the things that are going to be used by many people: the computer and the internet was not simply something that occured by a small number of people and all at once. Lots of people did their own part and most people don't even know who these people are, let alone if they ever realized they helped create the stuff we take for granted.
  5. Sep 1, 2012 #4
    I disagree. A single applied scientist/engineer can still have HUGE impact. A chemist discovering a new drug/material/process or an engineer designing a new machine could definitely upset the tech world, even if now the new thing has to be small.

    But stuff like say... a new OLED material, could be more *directly beneficial* than say... a few more significant digits on the value of Boltzmann's constant or the mass of a photon.
  6. Sep 1, 2012 #5


    User Avatar
    Science Advisor

    I didn't say they can't, I'm just saying this whole idea of trying to be important is absolutely stupid.

    The problem is (and you are highlighting it) is that people have different ideas of what is important, and this is the core of what I'm trying to highlight.

    Everyone has their own idea of what is important, yet most people seem to think they know what is important and it just keeps going in circles.

    Again most of the things created in this world that do have a huge impact are made by people that no-body knows even existed and quite frankly most don't really care.

    The people that create a lot of this stuff don't need to worry about that: the people in their immediate vicinity namely their colleagues, fellow professionals, friends and family know and for the majority the achievement, the learning experience, the final product and a pat on the back from those surrounding people is enough.

    This whole idea of being more important is just a weird and stupid desire to satisfy some inner need to want to be recognized in a highly extreme way.

    Again it's not that what people do is not beneficial: I'm not saying this. I'm saying that this idea of people thinking they know how to rank importance in an extremely narrow perspective and to think that they know what is more important (and especially when they think they are doing something more important than another person or group of people) is just really stupid.

    As an experiment, you should ask a good random sample with high representation across all kinds of groups (not just the scientists, the engineers, the mathematicians: all people) who was involved in the stuff they use on a regular basis like the computers, the tablets, phones, music players, roads, and so on who was involved and you'll find most don't know or don't care, but they do appreciate in some form having those things (and if they don't know, they will when they have to go without for a short period of time).
  7. Sep 2, 2012 #6
    From the time of the ancient Greeks all the way up to about 30 years ago, the subject of factoring large numbers has always been of high mathematical interest, but with absolutely no practical value.

    Today, the difficulty of efficiently factoring large numbers is the heart of modern computer security. Factoring went from being a highly esoteric specialty in the most useless branch of math, number theory; to the very heart of e-commerce. Useless for two thousand years; and suddenly the heart of the global economy. I think this is a striking example of how useless math so often turns out to be incredibly useful, but sometimes not for years, even millenia.

    Hardy gave number theory as the canonical example of a branch of math that was supremely beautiful and totally useless. Would Hardy be disappointed if he came back today and saw public key cryptography? Or would he be amused?

    The great British number theorist G.H. Hardy wrote a book, A Mathematician's Apology, in which he answers the exact question you asked. He looks at his life and tries his best to explain why he's spent his life doing work that is totally useless, yet supremely beautiful. Everyone should read this book.


    Seven bucks on Amazon. Your transaction is secure because factoring pq is difficult.

    Last edited by a moderator: May 6, 2017
  8. Sep 2, 2012 #7
    so what are some hot research topics in pure mathematics?
  9. Sep 4, 2012 #8
    Not directly a field of mathematics -- but highly theoretical topics, such as string theory, heavily use pure math; in fact, some string theorists claim that more pure math is needed for us to fully engage in string theory. Pure math topics such as differential geometry are needed to understand some of the more complicated ideas of string theory like calabi-yau planes.
  10. Sep 4, 2012 #9


    User Avatar
    Homework Helper

  11. Nov 2, 2012 #10


    User Avatar

    It keeps me off the booze.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook