Could a Lawyer become a Mathematician?

Discussion in 'Physics & Math' started by rpenner, Nov 17, 2010.

  1. rpenner Fully Wired Valued Senior Member

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    oz2 -- a user at PhysForum writes:

    My off-the-cuff response:

     
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  3. James R Just this guy, you know? Staff Member

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    Certainly it is possible, but if the guy has done no prior tertiary study in maths it may be difficult.

    Lawyers do generally tend to be academically able, and many of them could easily have gone into a science or mathematics career instead of law.

    Speaking personally, I have studied both law and science at tertiary level, so it's not as if you either have a law brain or a maths brain.
     
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  5. rpenner Fully Wired Valued Senior Member

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    Hmm. And for "Fundamentals" I should have written "Foundations".

    Thanks for the opinion, James. I have to say that given the background he described, I remain pessimistic, but I tried to point him at good sources.
     
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  7. quadraphonics Bloodthirsty Barbarian Valued Senior Member

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    I'd say the big question is whether he's willing to expend the time, money and effort to go and get the sort of schooling that a math career would involve - at a minimum, an MS in applied math. Depending on what he studied as an undergrad, he may need to also go and fill in a bunch of background at that level (at a community college or whatever) before applying to graduate school. If he's serious about a math researcher position, he needs to have several years to dedicate to pursuing a PhD, and probably the flexibility to move far away in pursuit of job openings.

    Also I would resist the tendency to group "science brain" in with "math brain." Sure, most sciences involve learning and applying a fair amount of math. But it takes a very different temperment to want to study math for its own sake, and publish it in its own terms, than is typical of scientists and engineers. In order of similarity to mathematics, I'd list fields like philosophy, computer science and maybe even law ahead of the natural sciences and engineering.
     
  8. CptBork Valued Senior Member

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    Karl Weierstrass flunked out of law school, took up a maths career at a much later age and ended up becoming one of the best. Fermat was a mathematician and a lawyer. So it's totally doable, the problem is it's gonna take a lot of patience, like possibly even a decade or more, to become truly proficient if you're starting more or less from scratch.
     
  9. iceaura Valued Senior Member

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    Both those guys were hooked on math from early youth, and were well prepared in math long before adulthood.

    Neither one began their serious study of math only after having completed years of legal education. Wierstrass flunked out of law school because he was screwing around with math full time and blowing off his legal studies.
     
  10. CptBork Valued Senior Member

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    My analysis textbook said he flunked out because he was too busy drinking and fencing, and that he became a gym teacher instead. He only entered the maths academic community after he turned 50. I'm sure he had some maths background before then, no idea how much, but my textbook said he was a genuine late bloomer, one of the only famous such examples in history, but one nonetheless.

    Anyhow, hopefully the person asking the question in the OP has at least, say, high school math under their belt, and is capable of recalling a decent amount of it after some quick review. Still, this stuff takes forever to learn in proper detail, I can't imagine trying to learn it all after I've turned 30.
     
  11. temur man of no words Registered Senior Member

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    Here is says that Weierstrass drunk and fenced because his mind was in a conflict where his father wanted him to study administration and finance but he wanted to study mathematics. His first major unpublished work was around 1840 when he was 25, and his first published major work was in 1854 when he was 39. He did not have much time for mathematics because he was a school teacher (who teach all kinds of stuff including gymnastics, history and biology) with lots of teaching load. While working as a teacher he developed a bad mental illness because he spent every precious free minute to work on mathematics, making himself over tired.
     
  12. iceaura Valued Senior Member

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    He was teaching math at the university level in Germany in 1843, when he was 28.

    The word "gymnasium" did not mean the same thing in Germany at the time that it means now.

    He had already schooled himself in cutting edge analysis, including the areas of continuity and convergence that later made him famous, and was a few years into an exploration of elliptic functions - this stuff

    http://en.wikipedia.org/wiki/Weierstrass's_elliptic_functions

    was what he was inventing, as a hobby, in his early twenties.

    He is famous as a late achiever because his early work was not until his twenties and recognized late, and because he did important and brilliant new work, different from his earlier work, late in life, which is very unusual in mathematicians. As Hardy put it: "Young men should prove theorems, old men should write books". Weierstrass just kept on proving theorems, important ones.

    He's not a lawyer, or even a law student, who changed course and became a mathematician.

    Neither was Fermat - he was studying math seriously by 1625, when he was probably 18, and began studying law some years later when he had already established some of the mathematical correspondence with friends he was to maintain all his life.
     
  13. CptBork Valued Senior Member

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    Ok then, I stand corrected, although Temur agrees with my assertion Weierstrass used to teach gymnastics (I just called it "gym"), among other things. I figured Weierstrass had to have at least a decent background in math when he was younger, I just wasn't sure how much. My analysis textbook called him a late bloomer, but there's a huge difference between switching subjects to study something you've never done at a high level before, and switching subjects late in life to satisfy some secret passion you've already been working ultra-hard at since youth.

    So basically we should tell this guy it's hopeless, no one's ever had a notable math career unless they already knew a whole bunch by the time they were 18?
     
  14. temur man of no words Registered Senior Member

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    Just to clarify on Weierstrass, he is considered late bloomer because his life circumstances did not allow him to publish and get recognized by the leading mathematicians until he is 40. He was teaching at some school (similar to technical college or high school) that concentrates on teaching only, and after he published his first paper in a good journal, he was quickly recognized and within a year he was offered all kinds of professor positions by famous universities around Europe. Until then somehow he did not estimate his work to be that good and was kind of working privately, occasionally publishing "outlines" of his results without much detail in obscure journals. As iceaura said though, Weierstrass wrote his first major work when he was 25 and gave it to his teacher Gudermann, who then wrote notes down to himself that Weierstrass was an exceptional mathematician but never said to Weierstrass about this. Weierstrass later knew about this note and told that if he knew this he would have published the result right away.

    About whether he was a law student, actually after a high school equivalent he studied law, administration, and finance at the insistence of his father for 4 years, during which he drunk and fenced because he did not want to study those thing but mathematics. He did not do much mathematics either because in some sense he did not want to directly oppose his father. So these years were wasted but in the end he decided to study mathematics, and quit his school, to a great disappointment of his father. His father put him in some technical college, where he studied mathematics under Gudermann. After graduating the only job he found was a teaching position with full time load, and he did it until he is almost 40, until he published something major and got recognition.
     
  15. CptBork Valued Senior Member

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    Yeah and I said he was 50 when he got famous, not 40. I should dig out the textbooks when I say this stuff, I just didn't find much in Wikipedia so I tried to go by memory. So much for that one.

    I've been making a lot of physics/math mistakes in my posts lately, I'll try to check my facts more carefully in the future... sorry 'bout that.
     
  16. quadraphonics Bloodthirsty Barbarian Valued Senior Member

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    If the bar for a career in math being worth pursuing is to be as "notable" as someone like Weierstrauss, then we'd have to tell everyone that it's hopeless. The kind of people who stand to have those kinds of careers don't go around asking strangers for advice on whether it's feasible - they're too busy being math prodigies. Supposing the person in the OP has more reasonable expectations of a math career (teaching at some college somwhere, and publishing a few obscure articles that nobody outside of a small circle of like-minded researchers will ever read), then I see no problem there.

    Again, I think the make-or-break factor here is whether the lawyer in the OP can afford to be a poor student for a decade at this point in his life. If he's got kids and a mortgage then this career path is right out. If we're talking about some 25-year-old that just graduated law school only to be faced with the gaping abyss that is current hiring prospects for recent law grads, then that's a different story. He'd still be deferring any income to speak of until his mid-30's, but that's hardly the direst position anyone's ever been in. I'd seriously worry about the prospects of paying off law school debt on a mathematician's salary, though (unless he gets into high-flying wall street econometrics or something).
     
  17. CptBork Valued Senior Member

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    Obviously it's not a good idea for anyone to enter something expecting to excel at it like the next Einstein. I just find it disconcerting that I can't locate any examples of well-known mathematicians who got a late start on the actual learning process itself. Weierstrass was always my golden boy for that, but now I'm told even he got an early start.

    Which begs the question: if money's partially the issue, who would want to go from a job where you can make $50 per signature, to a job where you hardly make $5 per original thought? And if it's been a passion from a young age, I presume the OP would already have a good background in math, and the remainder would be more about navigating bureaucracies to get the necessary student positions.

    I'm not even a lawyer and I got stressed out by that paragraph

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  18. quadraphonics Bloodthirsty Barbarian Valued Senior Member

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    Two reasons leap to mind. First, the $50 per signature job is soul-crushingly dull and requires you to work 60+ hours a week, every week, forever, all while being available on email/cell phone 24 hours a day - some law firms explicitly require associates to check their email every 6 hours, day and night, including weekends. Imagine having to wake up every single night at like 4 AM just to check your email. Second, it may be that he can't actually find employment in the law field. It's been famous lately for the collapse in hiring, especially of new graduates. There's no benefit of being in a field with $50 per signature pay rates if you can't get one of the jobs.
     
  19. temur man of no words Registered Senior Member

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    Here
     
  20. Farsight

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    So condescending.
     
  21. rpenner Fully Wired Valued Senior Member

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    Not if he is not specifically a trial lawyer.
     
  22. Human001 Registered Senior Member

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    Liebniz was a lawyer of some sort. But he was a ploymath involved in all kinds of interests.
    Augustus De Morgan was a lawyer.
    Cayley, too, was a Barrister in England. And I think his colleague Sylvester was too.

    But it probably isn't fair to compare 17th or 19th centuries with today. In Liebniz's time, it would be possibly for a learned man to be knowledgeable on all areas of, well, knowledge.

    I do, however, remember, not clearly, a lecturer at my university who had degrees in law and mathematics. (God knows how big his student loan debt must have been.)
     
  23. CptBork Valued Senior Member

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    Definitely there's nothing to say that being a lawyer and being a mathematician are mutually exclusive. My dad was an engineer-turned-lawyer and I'm told he was pretty good at math, he certainly inspired me to do what I do today. On the other hand, being a lawyer and having the ability to make clever, convincing arguments before the public, says next to nothing about technical skills and talent, though at least the requisite studying/learning skills and work ethic would probably be there.

    I think the bigger issue is whether they received early exposure to abstract mathematical structures, and axiomatic logical rigour. You can teach an old dog new tricks, or at least an old human, but it gets way harder when you're older and most of the neural pathways are firmly set. If they didn't have at least a year's worth of calculus under their belt before specializing in the law field, and haven't acquired that level or higher since in their own private independent studies, that would be one heck of a transition to make in later life.
     

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