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Mathematics is used in statistics, physics, biology, finance, engineering, medicine, social science and more. Even in the 15th century, most mathematics was don

Mathematics is used in statistics, physics, biology, finance, engineering, medicine, social science and more. Even in the 15th century, most mathematics was done by non-mathematicans, it's not a new thing.

lokimedes 7y ago
To a physicist like me, the assumption that mathematicians are the source of mathematical revelations is the same as assuming that the best novels are produced by people who studied english.
- sls 7y ago
  That is by no means an apt metaphor. Mathematicians are in the business of creating new mathematics, not in studying the "language" in which mathematics happens to be written. Of course the history of mathematics is replete with contributions from physicists and others, particularly during the period when the educated could turn their hand to nearly any such discipline and find a problem on which progress could be made.
  - injb 7y ago
    Yes. In fact it has often been noted by physicists that when they make a new discovery they sometimes find that mathematicians have been there before them. Like Einstein and non-euclidean geometry etc.
    - sriku 7y ago
      ... with string theory (or M-theory as you wish) offering a break by having made its own contributions to maths.
    - ncmncm 7y ago
      It more often goes the other way, and more profoundly. Group theory. Laplace transforms were considered an irrelevant curiosity until somebody figured out they were isomorphic to the wildly effective Heaviside D operator. Then everyone did their best to bury Heaviside's demonstrations of their utility, and pretend that Laplace had done all the heavy lifting.
      - injb 7y ago
        Group theory was invented by physicists?
bjnord 7y ago
oblig.: https://xkcd.com/435/ https://xkcd.com/435/
- jasomill 7y ago
  There are, of course, many exceptions to this "rule". From the preface to my favorite calculus book: My aim is to exhibit the close connexion between analysis and its applications and, without loss of rigour and precision, to give due credit to intuition as the source of mathematical truth. The presentation of analysis as a closed system of truths without reference to their origin and purpose has, it is true, an aesthetic charm and satisfies a deep philosophical need. But the attitude of those who consider analysis solely as an abstractly logical, introverted science is not only highly unsuitable for beginners but endangers the future of the subject; for to pursue mathematical analysis while at the same time turning one's back on its applications and on intuition is to condemn it to hopeless atrophy. To me it seems extremely important that the student should be warned from the very beginning against a smug and presumptuous purism; this is not the least of my purposes in writing this book. - Richard Courant, Differential and Integral Calculus [1] Courant, who trained — under Hilbert, no less — as a pure mathematician, never tired of pointing out the importance of applications to pure mathematics and vice versa. In addition to the calculus books, see, e.g., https://www.ams.org/journals/bull/1943-49-01/S0002-9904-1943-07818-4/S0002-9904-1943-07818-4.pdf https://www.ams.org/journals/bull/1943-49-01/S0002-9904-1943... [1] https://archive.org/details/DifferentialIntegralCalculusVolI/page/n7 https://archive.org/details/DifferentialIntegralCalculusVolI...

lokimedes 7y ago

To a physicist like me, the assumption that mathematicians are the source of mathematical revelations is the same as assuming that the best novels are produced by people who studied english.

sls 7y ago
That is by no means an apt metaphor. Mathematicians are in the business of creating new mathematics, not in studying the "language" in which mathematics happens to be written. Of course the history of mathematics is replete with contributions from physicists and others, particularly during the period when the educated could turn their hand to nearly any such discipline and find a problem on which progress could be made.
- injb 7y ago
  Yes. In fact it has often been noted by physicists that when they make a new discovery they sometimes find that mathematicians have been there before them. Like Einstein and non-euclidean geometry etc.
  - sriku 7y ago
    ... with string theory (or M-theory as you wish) offering a break by having made its own contributions to maths.
  - ncmncm 7y ago
    It more often goes the other way, and more profoundly. Group theory. Laplace transforms were considered an irrelevant curiosity until somebody figured out they were isomorphic to the wildly effective Heaviside D operator. Then everyone did their best to bury Heaviside's demonstrations of their utility, and pretend that Laplace had done all the heavy lifting.
    - injb 7y ago
      Group theory was invented by physicists?

bjnord 7y ago

oblig.: https://xkcd.com/435/ https://xkcd.com/435/

jasomill 7y ago
There are, of course, many exceptions to this "rule". From the preface to my favorite calculus book: My aim is to exhibit the close connexion between analysis and its applications and, without loss of rigour and precision, to give due credit to intuition as the source of mathematical truth. The presentation of analysis as a closed system of truths without reference to their origin and purpose has, it is true, an aesthetic charm and satisfies a deep philosophical need. But the attitude of those who consider analysis solely as an abstractly logical, introverted science is not only highly unsuitable for beginners but endangers the future of the subject; for to pursue mathematical analysis while at the same time turning one's back on its applications and on intuition is to condemn it to hopeless atrophy. To me it seems extremely important that the student should be warned from the very beginning against a smug and presumptuous purism; this is not the least of my purposes in writing this book. - Richard Courant, Differential and Integral Calculus [1] Courant, who trained — under Hilbert, no less — as a pure mathematician, never tired of pointing out the importance of applications to pure mathematics and vice versa. In addition to the calculus books, see, e.g., https://www.ams.org/journals/bull/1943-49-01/S0002-9904-1943-07818-4/S0002-9904-1943-07818-4.pdf https://www.ams.org/journals/bull/1943-49-01/S0002-9904-1943... [1] https://archive.org/details/DifferentialIntegralCalculusVolI/page/n7 https://archive.org/details/DifferentialIntegralCalculusVolI...