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Featured I How do you answer "So what's the practical application....?"

  1. Dec 21, 2016 #1
    I suppose you recognize, by title, the situation I am referring to. I don't know if physics people get it as often as math people.

    The situation of course is that I tell somebody that I am studying math, and if I mention some specifics, like mention Topology or Algebra, (which I have to sort of explain is not "college algebra"), or whatever. Then comes the question "So what's this used for in..you know, real life?"

    As I see it there are two extremes to answer this question:

    a) A speech or possible tirade about how this question is not really relevant. Possible comparison of science to art, i.e. "Well, what's the practical application of music?" Trying, perhaps in vain to explain how mathematics doesn't always seek applications but that they often find their uses later, then tell a story about number theory and cryptography. Another variant is that for me, I've studied mathematics for the joy of it and because I think the thinking skills I learned can be applied to anything.

    b) Just say some stuff I heard about what people might be using this for. "Topological data analysis!" "Cryptography" (again). "Something in physics!"
  2. jcsd
  3. Dec 21, 2016 #2
    Of course, Algebra is a critical tool in all engineering ... and it doesn't take much for a situation to involve "college algebra" versus the introductory stuff one gets in High School. So, for Algebra, it could be to assist almost any kind of engineering design team. Topology is another tool - not as often used as, say, trig. But you would expect a carpenter to have a hammer even in these days of nail guns - and know how to use it.
  4. Dec 21, 2016 #3


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  5. Dec 21, 2016 #4


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    Last edited by a moderator: May 8, 2017
  6. Dec 21, 2016 #5
  7. Dec 21, 2016 #6
    Well, but when I say "algebra" i mean group theory, rings fields, Galois theory. I don't know how people use this outside of mathematics.
  8. Dec 21, 2016 #7


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    Modern mathematics is widely applied in many fields, Physics included. If you are interested in those areas of Physics where its application is common then you probably would want to learn it. Modern Differential Geometry is intensely topological. Here is a quote from a physicist,

    The beauty and profundity of the geometry of fibre bundles were to a large extent brought forth by the (early) work of Chern. I must admit, however, that the appreciation of this beauty came to physicists only in recent years.

    — CN Yang, 1979 "

    Chern was a pure mathematician, primarily a differential geometer. One can not understand much about fiber bundles without some knowledge of topology.

    Here is some reading that may give you an idea of how mathematics is used in modern physics:

    - 'A First Course in String Theory" by Zwiebach. Brian Greene recommended this book to me.

    Or maybe you would like to read this review article.


    - Here is a Wikipedia article on topological Quantum Field Theories.


    - If you are interested in the physics of stars you may wish to learn about Knot Theory which is applied to understanding the formation of magnetic filaments.

    Munkres book is an elementary topology book. One way or the other you will need to know what is in it if you are interested in the mathematically intense areas of Physics. On the other hand you may wish to pick the math up as you go along rather than take time out. That is a matter of intellectual style.
  9. Dec 21, 2016 #8
    There is nothing wrong with inventing new tools before their specific applications are recognized.

    Math has a long history of examples where the tool is invented and the applications follow. Mention some examples.

    Kinda like Viagra: no one knew how useful it would be until after it was invented.


    Sildenafil (compound UK-92,480) was synthesized by a group of pharmaceutical chemists working at Pfizer's Sandwich, Kent, research facility in England. It was initially studied for use in hypertension (high blood pressure) and angina pectoris (a symptom of ischaemic heart disease). The first clinical trials were conducted in Morriston Hospital in Swansea.[38] Phase I clinical trials under the direction of Ian Osterloh suggested the drug had little effect on angina, but it could induce marked penile erections.[3][39] Pfizer therefore decided to market it for erectile dysfunction, rather than for angina. The drug was patented in 1996, approved for use in erectile dysfunction by the FDA on March 27, 1998, becoming the first oral treatment approved to treat erectile dysfunction in the United States, and offered for sale in the United States later that year.[40] It soon became a great success: annual sales of Viagra peaked in 2008 at US$1.934 billion.[41]
  10. Dec 21, 2016 #9

    I personally have no problem with any of this. I am asking how people deal with being asked this question by the uninitiated.

    -Dave K
  11. Dec 21, 2016 #10


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    I posted this on the wrong thread. Someone asked a question about Munkres book. that said maybe it is OK to leave it here.

    People often ask what is the usefulness of pure mathematics. To me this is a biased attitude that asserts that nothing is worth anything unless it has a practical application. That attitude rules out the importance of art, music, literature, much of philosophy, charity and compassion (since they lead to economic inefficiency) to name a few useless enterprises. Can you make a widget with a Rembrandt portrait?

    When the proof of Fermat's Last Theorem was announced on the front page of the New York Times a mortgage securities strategist at an investment bank said to me, " How much money did he make spending his whole life on this?" I said "None. He didn't do it for money." He shook his head and said,"What a waste." and walking away - no doubt to go do something practical.
  12. Dec 21, 2016 #11
    Yeah, it was still good stuff. :)

    Of course, I agree with you, and this is part of option (a). The question is, given that this attitude is so ingrained, and so prevalent, how should we respond?

    Clearly this bias is taught from the beginning. We are taught that we need to do math, because things can be numbered, thus counted, thus added, subtracted, multiplied, and divided. We create "word problems," idealized imaginary scenarios about things that people are doing in the world, in order to give the impression that arithmetic is a practical skill.

    To those asking the question, it's a simple question. They are not looking for a lecture. Is it a totally unfair question? Not really.

    We don't teach math the same way we teach art. We teach it as a means to an end, and so naturally people want to know what that end is. Of course, not all people appreciate art and music either, and will often question the legitimacy of studying either.

    The news cycle can be a big problem. I once saw a very amusing talk by a mathematician who worked on the Pizza Theorem, which is a very interesting problem in geometry with a long history. There was an article published about it in a mathematics magazine, and it eventually made it to a more mainstream journal New Scientist, with the title The perfect way to slice a pizza!

    The comments section has since been closed, but as you can imagine, it was littered with comments to the effect of WHO FUNDED THIS RESEARCH?

    -Dave K
  13. Dec 21, 2016 #12


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    Abstract math like topology and abstract algebra give you general rules that help you understand a large variety of specific mathematics and physics subjects more quickly and easily.

    That being said, if the person is asking how you use it, then the answer is that you actively seek out subjects to understand and abstract math helps. If he is asking how he will use it, then the answer is that if he sits at home watching TV and drinking beer, it is unlikely that applications will come knocking on his door.
  14. Dec 21, 2016 #13
    Thank you for saying that concisely. I've known this is true but my explanation was much more long winded.

    It is times like this that I wish life really were more like a musical. Then a band would start playing, I would sing a song called "math is everywhere" and then everybody would understand by the end.

    -Dave K
  15. Dec 21, 2016 #14
    I'm not big on trying to justify funding to non-experts. I'd just say the research had the full approval and support of those who decided to fund it. And of course, some of the best work is done for love rather than for money.

  16. Dec 21, 2016 #15
    Indeed. The pizza theorem guys spent something like 10 years working on the problem, but the length of time is owed to the fact that they did so mostly in their spare time.

    -Dave K
  17. Dec 21, 2016 #16


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    Did the pizza get cold?
  18. Dec 21, 2016 #17
    After 10 years I would not like to imagine what it got.
  19. Dec 21, 2016 #18


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    This problem already occurs in school math. When tutoring I sometimes just answered: because you need it for the next test, your school qualification or similar. I mean as long as things like "10 construction workers build a house in 20 days, how long ...?" can be found in school books, can we really expect to be taken seriously? The real question is: Why doesn't this question about profits arise in fields like history? As if mankind ever had learnt something from past events.


    I plead to return to the original meaning of mathematics. Let's strip it off the natural sciences and regard it as a relative of philosophy again.
    That doesn't solve the problem (what is it good for?), but nobody will expect an answer anymore. I mean, we've done it before: AC, the barber problem and we buried Hilbert's program.

    It's a bit like CERN. Many people (if they even know about it) consider it as a giant loss of money but at the same time, they are proud of the fact that mankind has achieved something like this.
  20. Dec 21, 2016 #19
    I don't think history is immune from the question actually, but people seem to relate to it better.
  21. Dec 21, 2016 #20


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    People know that every historical fact had at least one significant application -- when it was a current event. Fewer people will know any application of abstract algebra.
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