<p>From a A Mathematician's Survival Guide by Stephen G. Krantz. American Mathematical Society, 2003.</p>
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[quote]
A few years ago, a young fellow contacted our Graduate Director to say that he was interested in entering our graduate program in mathematics. He was already an M.D. (i.e., a physician) and he wanted to get an advanced degree in differential geometry so that he could study protein folding. ... </p>
<p>This student was in my undergraduate real analysis class; he seemed reasonably good. As his first semester progressed, things seemed to be going OK, but at the end of the semester he quit. Just like that. He told the Graduate Director that he had never realized that the study of mathematics was such hard work.</p>
<p>Bear in mind that the student under discussion already had a medical degree. He was certainly familiar with the concept of "hard work", but the study of mathematics was an entire order of magnitude beyond what he knew.
<p>I think the key here is that math is one of those things you either get, or you dont. Unlike med school, which with a reasonable will-power, good work-ethic, etc, im sure anyone who’s reasonably smart, can do it.</p>
<p>However, I dont think that all the will-power, work ethic, etc, can take you thru math grad school if you are not cutout for it.</p>
<p>I believe mathematics at graduate level must be challenging. But I don’t know if that student is a good example to show that math is hard when he is a physician. If he has an M.D., he must have gone through med school for a long time, and he may have forgotten a lot of math while he was studying human anatomy in detail, and then he comes back to study math at graduate level.</p>
<p>Still, I think math at graduate level must be pretty challenging, though…</p>
<p>This isn’t directly related, but my calculus teacher was telling us about the joys of math grad school one time.</p>
<p>He was sitting in class and just got back the first test he had ever taken in grad school. He looked down and saw a 25% and thought “Grad school is gonna be rough.” But then he looks over at the guy next to him who had apparently gone pale–that guy had gotten a -6%! My teacher ended up getting an A in the course.</p>
<p>Yes rigorous math is probably the hardest subject around. But like others have said, it all comes down to whether your brain is wired the right way. If it is, then math can seem completely straightforward. nontraditional, where did you take your courses? What degree are you working towards?</p>
<p>I so disagree with what Weasel8488 have posted: “it all comes down to whether your brain is wired the right way.” Please, give your audience some information to back up your premise.</p>
<p>I think people are much more capable of math than they give themselves credit for: the two largest problems, I believe, are lack of a proper foundational education in math and, quite frankly, lack of self-discipline. Some people definitely do catch on the concepts quicker, but that doesn’t mean those are are “slower” can’t learn it at their own pace: however, many people aren’t willing to put in this effort and simply think they’re just “not good” at math, even if they are by any reasonable measure. I’ve heard some incredible situations where people who failed math throughout high school studied remedial mathematics intensely at community college with low grades and, eventually, became engineers with high upper-level GPAs. It took all the time they had and grueling effort, but they did it. I think this would apply to most people.</p>
<p>I went out searching for some evidence on this. There are some various and sundry articles on both sides of the issue. To say that all it takes is hard work and self-discipline is foolish. To work at the highest levels of math is akin to being a renowned tenor or artist. People have innate talents that not everyone possesses. To say you can just plow through is a foolish statement. If that were the case anyone could be an NFL quarterback with enough hard work but we know that isn’t the case.</p>
<p>pmrlcomm took the words right out of my mouth. Different subjects require different forms of intelligence. Being good at sociology requires you to have good intuition about the way humans interact. This sort of intelligence is totally unnecessary for math; many math students would look at you like a deer in the headlights if you ask them if they think society is too heteronormative. So my comments apply to more than just math. But math is somewhat unique in that it requires a very high degree of the form of intelligence tested on IQ tests and not much else.</p>
<p>I also think there’s a lot of truth to what JoeTrumpet said. Many adults will say with a perverse sense of pride that they “don’t do math.” You would never here someone say “I don’t do English.” That’s not socially acceptable. So while I stand by what I said about mathematical aptitude being IQ-limited, I believe that most Americans give up on math before IQ ever comes into play.</p>
<p>“You can wire your brain to be good at things.”</p>
<p>Please elaborate.</p>
<p>“I went out searching for some evidence on this. There are some various and sundry articles on both sides of the issue. To say that all it takes is hard work and self-discipline is foolish. To work at the highest levels of math is akin to being a renowned tenor or artist. People have innate talents that not everyone possesses. To say you can just plow through is a foolish statement. If that were the case anyone could be an NFL quarterback with enough hard work but we know that isn’t the case.”</p>
<p>Are you kidding me? Go ask Wayne Gretzky or Tiger Woods about how they got to their level talent. Ask anyone who is at top of their field, and not a damn one of them is going to say “I was just simply born with the ability.”</p>
<p>No one is saying that hard work doesn’t matter. We are simply stating the rather obvious point that Tiger Woods and Wayne Gretzky also possess intrinsic athletic ability and that this ability played a major role in their success (ALONG WITH their hard work). Do you really think that if you, yes you personally, work hard enough, you can be the next Tiger Woods or Luciano Pavarotti or Andrew Wiles? Come back down to Earth and check [url=<a href=“http://www.despair.com/potential.html]this[/url”>Potential - Despair, Inc.]this[/url</a>] out while you’re at it.</p>
<p>I don’t think the analog of top athletes to the greatest mathematicians holds true. Sure, practice and dedication can help out but feel that some people are born with an extraordinary gift with numbers, be it an autistic savant or just a natural understanding. Heck, G.H Hardy and other mathematicians lamented over how they had lost their creative genius at their old age and their intellectual prime was only during their youth.</p>
<p>Most the top athletes carry a similar trait that they have practiced relentlessly and often started at a young age. In addition, athletics relies on physical attributes, something that can be conditioned over time. Mathematics, especially pure math, relies on a creativity and logical ingenuity that can be innate. </p>
<p>Of course, I specifically argue this point for the “Great Mathematicians” such as Ramanujan, who possessed a natural ability that astounded even G.H Hardy. True practice can make you a good and gifted mathematician but I feel that there is something innate that separates the good from the greatest.</p>
<p>You can’t use hard work to become gifted or talented. You either are or are not gifted or talented. You can use hard work to make up for a lack of talent but it’s either there or it isn’t. No matter your talent level you have to work hard but things do come more easily to some than others. To suggest that innate talent has no bearing is ignorant.</p>
<p>I think art is a very apt analogy (sports also be we can agree to disagree). I have no artistic ability whatsoever. I don’t care how long I practice or study I would never be able to be a Rembrandt, Dali or Van Gogh. They had talent along with their hard work. It is very clear that hard work will trump talent in most cases, unless the talented person decides to work as hard or harder than the non-talented one. I’m sure if Sergio Garcia worked as hard as Tiger (who is supposedly that hardest worker on the tour) he could be 90% of Tiger but Tiger has that talent level that we may have never seen before in a golfer. I would use scientist or mathematicians for analogies but I’m not that familiar. Sorry.</p>
<p>"“You can wire your brain to be good at things.”</p>
<p>Please elaborate."</p>
<p>Well, for one, as you practice a skill your brain builds synapses and neurons that are specific to the skill. That’s why you get better at things with experience and practice. (I’m not sure about the terminology above but I know it works like this).</p>
<p>I’m thinking of a major in math and this forum is really scaring me. Is there any way to know if I have a talent for math?</p>
<p>What it really comes down to is this: can you read and write rigorous proofs? Assuming you’re still in high school, you might try familiarizing yourself with epsilon-delta definitions of convergence, limit, continuity, and so forth. Once you’ve done that, maybe try to prove that every bounded sequence has a convergent subsequence.</p>