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Courses The math level of computer scientists and physicists

  1. Dec 12, 2017 #26

    radium

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    I think people need to be very careful when they offhandedly dismiss something as being irrelevant or useless. To be a successful scientist requires one to develop a unique perspective that gives them an advantage when looking at certain problems. Most people are very specialized these days, but there are certain people (I can think of several physicists) who are able to make significant contributions in several different areas. They are able to do this because they have a wide base of knowledge and are able to use it to think of new creative ways to approach problems that never occurred to anyone else. For example, people have recently found connections between gravity and several different areas, which many people would first assume make no sense as they appear entirely unrelated. But actually there are very beautiful and intuitive arguments why this should be the case in many instances.
     
  2. Dec 13, 2017 #27

    FactChecker

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    I agree -- especially when a fast-changing field like computer science is involved. Who can anticipate what will happen in the next 40 years?

    That being said, there is a difference between saying that something like theoretical math will open doors for a person to do advanced research, and saying that it will be necessary to work anywhere in the field. There will probably be a lot of work and jobs in computer science that will not require advanced math. But several of the advanced research jobs will be off-limits.
     
  3. Dec 16, 2017 #28
    I am indeed a proudly philistine engineer.

    I'm being snarky but I'm also making a point; I think it is hard to decide what is the correct barometer for how much math one needs. If you use theoretical physicists at the Institute for Advanced Study, you will probably decide that modern physics is very much dependent upon exotic, complicated, inscrutable mathematical ideas. If you looked at what DFT people do, you would think that workhorse computer science and 19th century mathematics was representative. If you look at some machine learning theorists like Jordan, you might think that the subject is indistinguishable from mathematical statistics. If you read Hinton's AMA responses, you will think that you had better think intuitively like an old school physicist and that complicated mathematics is perhaps not that important.

    If you talk to a QA engineer at facebook, you would think that you need a stash of standard algorithms and very up to date knowledge on the relevant, specific software tools.
     
  4. Dec 18, 2017 #29

    bhobba

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    Actually he wasn't - he was downright sloppy - competent - but excellent - no. In later years he hired assistants to do that tiresome stuff.

    Compare him to an actually great mathematician like Von-Neumann and he was way ahead. What set Einstein apart from Von-Neumann, and Von-Neumann was one of the greatest that ever lived at this - in fact he was so great a guy like Poyla was genuinely scared of Von-Neumann (he mentioned in a class some theorem that nobody had yet proved - at the end of the class Von-Neumann gave him the solution) is his ability to see to the heart of a problem. Von-Neumann, like Feynman was simply a magician at it, but Einstein was supreme. He saw to the heart of things better than anyone - but yet his math was rather ordinary. It's this ability that is crucial - not mathematical expertise.

    That's not to say we should confuse students by leaving important concepts unexplained - in fact I think it crucial we don't - its just it's not the key thing in making progress.

    Thanks
    Bill
     
  5. Dec 18, 2017 #30

    bhobba

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    What one needs actually isn't much, and unless you are a mathematician you don't have to be good at it either. Like I said Einstein wasn't.

    But what we cant do is confuse thinking students - we must make sure some rather obvious inconsistencies are not left without comment - at least - yes this is non-sense but can be explained although it will take us to far from our main aim to do it.

    Thanks
    Bill
     
  6. Dec 18, 2017 #31

    FactChecker

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    That's harsh. If we compare everyone with geniuses, then no one was excellent except Gauss.
     
  7. Dec 18, 2017 #32

    bhobba

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  8. Dec 18, 2017 #33

    StoneTemplePython

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    I think having von Neumann as your bar is too high -- he was at once brilliant in pure and applied mathematics and fast. Outside of Olympiad settings its not at all clear that being so fast matters that much. (Gowers has written about this, I can dredge something up a link.)

    Einstein's Mistakes is a really enjoyable book (though people should be aware that the author, a physicist, takes cheap shots at engineers from time to time).
     
  9. Dec 18, 2017 #34

    bhobba

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    Its not his speed that made him great - it was his ability to penetrate a problem. For example he solved many of the problems on the atomic bomb project such as using a conventional bomb around the atomic material to reach critical mass and hold it there long enough for explosive fission to occur. Natuarally that's just one of many things eg he practically invented game theory.

    But yes he was so fast it was said he was the only person fully awake.

    Thanks
    Bill
     
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