<p>PS: Many students who do “theoretical” physics research are really just doing computational physics these days. Sure, some computational problems require genius, but many do not.</p>
<h1>==</h1>
<p>Anyways, back to OP: Okay, I <em>know</em> students who took 10th grade calculus who aren’t that great in math at all. School just artificially delays many people (pre-calculus is redundant, and many math courses take far longer than they need to take since they’re catered towards the slowest students anyways). As long as you have a CTY-ish level of intelligence, you’re probably capable of taking calculus in 9th grade/qualifying for AIME/800’ing on SAT Math IIC, as long as your school didn’t artificially delay you.</p>
<p>I motion that henceforth any person who posts in this thread list their background in the maths and sciences (a summary will suffice). Because anyone who has not taken much undergrad math (AP Calc BC does not count as undergrad math, nor do classes at a CC IMHO) has no business conjecturing on the difficultly of graduate level work.</p>
<p>I’m an astro/physics/math triple major who has read (or at least tried to read) all sorts of math/physics textbooks including graduate level ones.</p>
<p>in terms of qualifications, near the level of what’s assumed among applicants to grad school.</p>
<p>How are we defining “math genius”? Good enough to get a PhD seems like a reasonable way and would certainly solve this problem nicely.</p>
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<p>There’s no definitive way to define one. It’s much easier to define a math genius by objective standards (certain concrete achievements, or ability to get a high score on a particular set of tests or courses ) rather than by knowing that the person got a PhD. The difficulty of a PhD can vary enormously from one project to another project, and in some cases, the professor may provide the student with considerable assistance, giving the student little room to develop his own ideas. This is probably the exception rather than the norm, but it does happen.</p>
<p>The issue with this debate is that we are unable to objectively define either “math genius” or determine exactly how good one must be to get a PhD. Without any fixed values the debate is doomed to wander without any conclusions.</p>
<p>Background: HS Graduate, 6 years in the US Maths olympiad system (best result was an invitation to MOP Blue). Currently taking Abstract Algebra (Textbook is Dummit and Foote)</p>
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<p>There are certain tests/standards that can pretty much guarantee that someone is a math genius. Qualifying for MOSP can almost guarantee it. As is doing well on Harvard’s Math 55. Becoming a professor at a top math institution also pretty much guarantees it, as is publishing a highly-cited paper. </p>
<p>Of course, one could be a math genius and still fulfill none of the above. There are multiple ways to prove extreme talent. None of them will cover all cases, but there are some ways that will cover the majority of them without too many false positives. </p>
<p>I don’t think that getting a Math PhD would quite fit though. Nor would I think that USAMO qualifier would fit (I know people with AIME scores of 5-6 who aren’t that great in math, although they’re still better than most). Most people don’t qualify for USAMO simply because they have too many other things to do. A homeschooled(=hours and hours of free time to prep) student who isn’t exceptionally intelligent could probably learn enough AIME tricks to qualify for it.</p>
<p>==
By the way, I think a common logical fallacy that many people make is that people’s learning curves are similar. Some people naturally take longer to learn than others, but their skills can eventually plateau at a higher value if given enough time. Not everyone will plateau at a higher value - this is why many people can’t get higher scores on the SAT even after SAT prep courses and SAT retakes.</p>
<p>InquisitiveOne, obviously it is easy look at some people’s records and claim that they ar math geniuses (Zeb Brady for example) and things like IMO or Math 55 are example of that what is impossible to classify is where exactly the line between Very good at math and Math Genius lies…</p>
<p>Yes that’s true, it is quite impossible to classify where that line lies. My main point, in any case, is that “math genius” should always be considered an age-invariant metric. Even a non-exceptional student could probably study off Dummit/Foote in high school if he learned math at his own pace (through homeschooling, Stanford EPGY, or intense self-study)</p>
<p>And also I was mostly criticizing the “math genius is required for PhD” argument. Some people who get PhDs in math don’t even qualify for the AIME (or get horrible scores on it) - and I know some from my summer math program. In fact, many people who get PhDs in math were HYPMSC rejects.</p>
<p>So I think we can now all agree that math geniusness (I’m sure there’s a real word for this) [is</a> like porn](<a href=“http://en.wikipedia.org/wiki/I_know_it_when_I_see_it]is”>I know it when I see it - Wikipedia).</p>
<p>I honestly feel as if math geniuses are hard to establish in high school. Unless you have taken a (legit) proof class at a college and aced the class, I feel it’s inaccurate to say anyone is a “math genius” before then. You may be good at the application of math (applied math), but are you good as showing that something has to be true? Multivariable calc and linear algebra are the end of the “learning” stages of math. Just wait until college and just relax. Basing everything on high school statistics is not smart nor accurate. Not saying that you can’t see if you’re good (or even fantastic) at math in high school, but just not that you’re a math genius. I do disagree with the fact that you need to be a math genius to be a math major/get your Ph. D. If someone else can do it, why can’t you?</p>
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<p>Maybe because they’re smarter than you? You seem to have hit upon the premise of the thread.</p>
<p>e.g., swim2daend in all likelihood owns me at math haha</p>
<p>USAMO Qualifier = Math Genius</p>
<p>This is a ridiculous thread. Who even says you need to get a PhD in Math in order to get a job? There are tons of jobs out there for Math majors with a BS or MS. If you want to teach at a university, then yes, go for the PhD, and while I don’t think it is necessarily as impossible as a lot of you guys make it out to be (remember, you’ll have 6 years of prior experience working with math and theory), it will definitely be hard and that is just the sheer nature of a freaking PhD.</p>
<p>Hmm, for the most part an MS in math is only useful for getting a pay raise as a K-12 teacher.</p>
<p>Okay, well BS then. Actuary, statistical analyst, economic analyst, computer scientist, topologist, cryptology, etc…there are PLENTY of jobs for BS Math.</p>
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<p>Hm, do you (or anyone else) know of someone who spent hours and hours preparing for the AIME and still didn’t reach a score of >= 5? (doesn’t have to be USAMO-ish scores, but still decent scores).</p>
<p>if you cannot do MOSP or IMO problems, you are not a math person.</p>
<p>if these
<a href=“http://www.econ.umn.edu/~jmiller/mathlatex/math5616hw3.pdf[/url]”>http://www.econ.umn.edu/~jmiller/mathlatex/math5616hw3.pdf</a>
and
<a href=“http://www.math.umn.edu/~richter/math3262/exam/TestI.Spring94.pdf[/url]”>http://www.math.umn.edu/~richter/math3262/exam/TestI.Spring94.pdf</a>
and
<a href=“http://www.math.umn.edu/~reiner/Classes/8201_Fall10_midterm1.pdf[/url]”>http://www.math.umn.edu/~reiner/Classes/8201_Fall10_midterm1.pdf</a>
and
<a href=“http://www.math.umn.edu/~voronov/8202/hw6.pdf[/url]”>http://www.math.umn.edu/~voronov/8202/hw6.pdf</a>
do not look like something you could do easily and have fun with (all your time will be spent writing proofs), you should probably not become a math major and are probably not very math oriented no matter how well you did on SAT/ACT/AP math. if you think your graphing calculator will be useful for a math major, you probably should not become a math major.</p>
<p>also, if you are a genius in math, a PhD would be easy as hell.</p>
<p>^some of those are pretty easy</p>
<p>I dislike problems where you have to do a bunch of algebra with variables that are the same letter (and different subscripts).</p>