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Being an autodidact mathematician?

  1. Nov 10, 2017 #1
    Would you guys say it could be done, to become an autodidact mathematician with the knowledge of a mathematical degree or higher?

    Obviously, it's not impossible, and it's not as easy as taking a degree in a university. But is it in the realms of a very motivated, 16 year-old. I have got no responsibilities other than learning, as I am homeschooled, but I teach myself.

    I am in a conundrum as far as sitting exams is concerned and I don't know if I would be able to get into a university. I am unable to sit physics exams for a-levels and GCSEs as it requires 'pratical work' and I am an external candidate. There is also other things holding me back.

    But the main question is, can I get to that level?
  2. jcsd
  3. Nov 10, 2017 #2


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    I think it is possible, but quite difficult.

    To me, the most important part of being enrolled in a university program is that it provides 1. a certain amount of discipline and 2. the possibility of critical feedback on your work. If you are not enrolled in a program, then you must find a way to secure these aspects for yourself.

    Also, unless you manage to prove something truly remarkable, a formal degree is usually better for your employment chances than pure self-study without any formal conclusion.

    Incidentally, here you can find some well-regarded articles about self-studying mathematics at various levels.
  4. Nov 10, 2017 #3


    Staff: Mentor

    I’d say yes but in today’s world the PhD paper is very important and may well be the primary piece of evidence of what you know when it comes time to being hired for your mathematical skill.

    I know Freeman Dyson is a professor of mathematics at the Princeton Institute for Advanced Studies and he does not have a PhD. You can find his interviews on YouTube where he talks about his life and career choices. He did it in a time where talent was noticed and nurtured before the time of big business standardized tests for everything.
  5. Nov 10, 2017 #4
    Thanks for the reply, I do definitely have the motivation and discipline, however, step 2 I am not so sure on. How would you suggest i get feedback? On forums? online contacts or?
  6. Nov 10, 2017 #5


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    Forums are a possibility, as are online contacts. However, you should be critical because the quality of the feedback you will get is going to vary a lot and may sometimes be incorrect.

    You could try it here, especially in the homework section. I like Math Help Boards as well. There is also Stack Exchange, but I am not very familiar with that. The best would be a serious real-life tutor - such as a retired academic - who would agree to help you pro bono (these exist) by meeting and discussing your work.
  7. Nov 10, 2017 #6


    Staff: Mentor

    For number two you’d have to gain a foothold at a university with one or more profs. I had a connection like this when I was in high school. I had a project to find the Lagrange points between then Earth and the Moon.

    When I hit a math snag, my HS teacher got me an interview with a geometrician named Prof S at the local university. He was quite helpful and asked if I had applied. I said no not yet and when I finally did, I think he helped get application approved.

    Initially, I was on a wait list, so my parents and I visited the school and the admin folks wondered why I didn’t ask for an interview as part of my application and I said well I talked with Prof S which countered that line.

    Finally my dad mentioned that he had mentored some of their social work students at the local public school district and I think that was the tipping point. To be fair my SAT English was atrocious (it’s my primary language) but my math was very good on the SAT..
  8. Nov 10, 2017 #7
    Do you mean that you got into some sort of mentorship program? or is that how you got into the university you were at?

    I am asking as I am wondering where or not it would be possible that I could get into a university by displaying my mathematical knowledge and any other academic knowledge to get into it? however I would doubt it sadly.. that being said, my dad is lecturing professor at a university for computer networking and security. But that is not the same field as mathematics..
  9. Nov 10, 2017 #8


    Staff: Mentor

    Here’s the thing, you want to be recognized for your work and the only reputable place to do that is the university setting. There is no other place, the PhD paper gives you a kind of authority to say you know certain stuff so that when you decide to publish your work in a peer reviewed journal others will take notice. Without the PhD title, you won’t get past the editors especially if you are a new unknown author.

    Checkout the career biography of Prof Erik Demaine. He was home schooled and is a recognized authority in computational origami math.


    I first encountered him while watching the Nova documentary called Between the Folds about all the ways Origami has affected the arts and sciences.

    Last edited: Nov 11, 2017
  10. Nov 11, 2017 #9


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    Is your T9 acting up, jedishrfu... ? . :biggrin:
    I'll bet that should read ?... " I first encountered him while watching the Nova documentary..."

    I would say jedishrfu is right... it probably is harder today, though .

    Here's a long list of people that were self-educated ...
  11. Nov 11, 2017 #10


    Staff: Mentor

    Thanks, I’ve fixed the typos. These are caused by my spell corrector malfunctioning and supplying alternate words to what I type. It’s my ghost in the machine giving me a semblance to humanity.
  12. Nov 11, 2017 #11


    Staff: Mentor

    That critical feedback is very important. Acting as both teacher and student makes me think of this quote by William Osler, "A physician who treats himself has a fool for a patient." When you do work as a student, it's difficult to step away and give critical feedback from the perspective of a more knowledgeable teacher.
  13. Nov 11, 2017 #12


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    You know, one of the biggest things is the problem of just being on your own, working on your own all the time. Cutting yourself off from your peers and contemporaries before you have even started may be a very bad idea.
  14. Dec 3, 2017 #13


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    Sure, it can be done. You have to be quite good at math though, as well as disciplined. My son started down this path, home schooling math from 8th grade on. He studied on his own, then branched out to taking an Art of Problem Solving class, then using their books, then auditing classes at local colleges.
    How difficult it is to find good self-teaching material depends much on what level you are at. AoPS stuff is quite good. Khan Academy stuff is decent. For higher level mathematics you have to pick and choose.
    I wouldn't worry too much about sitting exams. You need to be able to do it, but you don't need the results for anything. My son went to Cambridge on the strength of being good at math, not based on exam results (other than the required STEP exams to fulfill Cambridge requirements).
    I don't think anybody can answer that but you. What kind of results are you achieving so far?
  15. Dec 3, 2017 #14


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    I would say it can be dome to some extent, if you use the right books. E.g. one could advance quite far toward an undergraduate degree mastery, by mastering the calculus and analysis books of Apostol and/or Spivak, and maybe the algebra book of Mike Artin, and that includes both mastering the proofs and working the problems. But just reading in a desultory way through an average calculus book that doesn't have proofs won't help much.
    Last edited: Jul 20, 2018
  16. Dec 6, 2017 #15


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    This is, unfortunately, true. The first paper I published on my own was when I was still in grad school. The editor of the journal I submitted it to insisted on talking to my PhD advisor to make sure I wasn’t trying to sneak something behind his back.
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