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Practicality of pure math branches

  1. Feb 27, 2009 #1
    Hi all

    I was wondering just for curiosity what exactly are the practical applications of pure maths branches like number theory. As mentioned above, just curious to know what the racket about pure maths is all about.
    Last edited: Feb 27, 2009
  2. jcsd
  3. Feb 28, 2009 #2
    The practical applications range from feeling good about ones self all the way down to giving lesser morals a certain smugness that only mathematics can supply.
  4. Feb 28, 2009 #3


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    Dead on. :grumpy: (NOT!)

    Anyways, lots of practical applications apply. All of mathematics, hence physics (math parts), started with Number Theory. For example, Archimedes was "integrating" areas of shapes long ago. He did it for plain pleasure... that is pure mathematics. Hence, a tool we now use everyday resulted from this.

    Pure mathematics is used all the time. No physicists can leave without us. The most important thing I think we do is supply tools. Other important things we can do for physicists is actually tell them a solution actually exists. That might not sound like a big deal... but I'm sure any physicists would agree that when you know a solution exists, that is priceless. You essentially know you are NOT chasing something that does not exist.

    Anyways, pure mathematics is not an instant gratification type of subject. Not once did I see my profs. or any respectable person in number theory/algebra and so on... think they were better than others.
  5. Feb 28, 2009 #4


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    One somewhat "recent" (within the last century) practical usage for something formerly an abstract mathematical mental exercise, is error correction code, which are typically based on nested finite fields. The lowest level are polynomials made up of 1 bit coefficients, grouped to form 8 to 12 bit coefficients for the higher level of polynomials, which are the basis for many error correction codes, such as Reed-Solomon. I recall a conversation with an company founder / engineer that recalls studying finite field math thinking it had no real purpose, only to end up using it for error correction code in the backup tape products his company ended up making.

    Normally though the analogy for this type of research is similar to climbing mountains, simply because it's there, with no intention of finding something practical. In many cases, the solutions discovered have no practical purpose, other than to further the study of the field.
  6. Feb 28, 2009 #5
    The creators of group theory in the middle 19th century thought it was so abstract that it would never find application in physics. Similarly for Reimannian geometry, and even for matrices, if you can believe that. In other words, history shows that yesterday's pinnacle of pure mathematical abstraction is today's bread-and-butter workhorse for our deepest physical theories.
  7. Feb 28, 2009 #6


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    Here's a course:
    "Number Theory and Cryptography"

    Here's an article:
    "The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google"

    a transcription of Wigner's "The Unreasonable Effectiveness of Mathematics in the Natural Sciences":
    Last edited: Feb 28, 2009
  8. Feb 28, 2009 #7
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