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<p>Hey, I’m sure that plenty of humanities and social science majors would also love to work in their fields as well, but they cannot. Many English majors love analyzing classic works of literature, but frankly, there aren’t that many jobs that will pay you to do that. Again, I don’t know why physics/math is being singled out in this respect.</p>
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<p>Alright, Projectile, I’ll offer you an alternative career path for math undergrads (albeit still within ‘academia’, broadly speaking), a career path that I happen to know fairly well. Enter a finance/accounting/economics PhD program to become faculty. The (perhaps surprising) truth is that you need to know very little about actual real-world finance/accounting/economics to enter and succeed in such programs, for they’re mostly mathematically based: indeed, modern-day economics and finance have been deemed to be little more than sub-branches of mathematics, and plenty of econ/finance faculty publish largely in math journals. {For example, recent Economics Nobel Laureates Robert Aumann, Roger Myerson, & Eric Maskin, don’t even have economics degrees at all - all their degrees are in math.} Accounting academia is little more than applied statistics/econometrics. Many of the papers published in American Economic Review, Quarterly Journal of Economics, and (especially) the Rand Journal of Economics, are practically indistinguishable from papers published in math journals, in that they inhere nothing more than theorems, postulates, and proofs. </p>
<p>And there is little doubt that economics and (especially) finance/accounting faculty are amongst the most well paid and sought-after faculty in all of academia. It’s quite clear that anybody who graduates with a PhD from even an average school in those disciplines will be able to find a decent faculty position somewhere, a similarly cushy NGO or government agency (Federal Reserve, ECB, IMF, World Bank), or obtain a lucrative position in finance or consulting. </p>
<p>Frankly, I’m quite surprised that more math majors don’t follow this pathway. There’s even an old saying that failed mathematicians become economists, and failed economists become finance/accounting professors. But such failures are ironically rewarded with more pay: economists are clearly paid far more than mathematicians, and finance/accounting professors are paid better than economists.</p>
<p>So, projectile, there’s your escape hatch, at least for math majors. I suspect that a similar avenue is available to physicists. Numerous PhD physicists were hired by investment banks and hedge funds before the crash, and I suspect that they continue to do so even today (albeit at a lower rate).</p>
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OK, so now we’re getting somewhere. Check out this link: [Top</a> 20 Countries in Mathematics - Country Feature - ScienceWatch.com](<a href=“ScienceWatch.com - Clarivate”>ScienceWatch.com - Clarivate) . American mathematics accounts for over 25% of all mathematics papers in the world; that’s more papers than from the second, third and fourth place countries combined. These papers get over 30% of all citations in mathematics (more than their fair share); that’s more than the second, third, fourth and fifth place countries.</p>
<p>Given this, I feel like mathematics leaving America would be bad for mathematics and, inasmuch as mathematics is good for the world, bad for the world. It could be bad for America as well, since aspiring mathematicians would either go overseas to study (and might remain there, since there’s no more mathematics in America) or choose to do something else, squandering potential mathematical talent. Europe and Asia will dominate mathematics, and top engineers - the ones who actually use mathematicians’ theories, from time to time - would move to the supply.</p>
<p>More fundamentally, I’ll second sakky’s point: why single out mathematics majors? Even if math were useless - it’s not - and even if we could get rid of it in America without potentially far-reaching consequences in America and the rest of the world - which I doubt - why not teach it? It’s an interesting subject, if nothing else, like fine wine and ancient Greek.</p>
<p>Here’s a provocative thought: the only reason people do engineering is to make it possible to pursue meaningful subjects, such as sciences and the liberal arts.</p>
<p>My son is studying applied mathematics with a minor in statistics. He’s hoping to become an actuary, because there is a shortage according to the people in the field he’s spoken to.</p>
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<p>What if one of the high school students sees a proof, or proof technique, in the textbook, and wants to understand if it can be used to solve a similar problem?</p>
<p>FWIW, my HS calculus class, and the math classes that preceded it, required proofs. I remember using limits to determine derivatives, for example, rather than just using rules. Several math teachers in my HS held MS degrees in math, at least. One guy held a PhD.</p>
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<p>I would add that the loss of mathematics academic leadership of the United States would almost certainly result in the concomitant loss of economics, finance, and (probably) accounting academic leadership of the United States: 3 academic fields where Americans clearly dominate. Heck, it’s hard for me to think of more than a handful of econ/finance/accounting departments that are not in US universities (and of the rare few that do exist, most seem to be in the UK). Now, whether you may think such dominance is good or bad for the nation depends on whether you think economics/finance/accounting is harmful for the nation (you could arguably make the case that they’re actually harmful for the nation), but undoubtedly it would be bad for all of the Americans who comprise the shockingly well-paid faculties of those disciplines. {A newly minted assistant professor of finance or accounting will probably make $125-250k a year to start including summer support, without need for a postdoc. Not bad for somebody in their mid-to-late 20’s}. Like I said, academic economics, finance, and even to some extent accounting nowadays are arguably just sub-branches of math. Frankly, most top mathematicians could walk in and quickly dominate most economics and finance departments.</p>
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Lol, proofs can’t be used to solve computational problems. I should know, I’ve tried solving computational problems in the pure computational calculus class at my school trying to use the techniques I learned in analysis I. What you’re saying is akin to an engineering student learning the mathematical proofs for string theory to help solve their engineering problems</p>
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Really? Did you ever have to use mathematical induction? Proof by contradiction? Because those proof techniques would never be useful in taking a derivative or an integral. Also, taking a derivative by first principle isn’t a proof nor are delta-epsilon “proofs”. Those are computations and at best algebraic excercises with notation and require no creativity or deep thinking to solve.</p>
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At first I was going to say that this was the most wrong statement ever. Then I realized that was hyperbole; your statement is less clearly false than, for instance, “false iff true” or “This is not a statement.” Still this statement is completely and utterly false, as false as those statements. It is very often the case that a constructive proof will imply a computational technique in computer science. Computer programs are equivalent to mathematical proofs via an isomorphism. [Curry?Howard</a> correspondence - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Curry–Howard_correspondence]Curry?Howard”>Curry–Howard correspondence - Wikipedia) . The idea that proofs can’t be used to compute something is an idea you need to abandon right now.</p>
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Where do I even begin? First, delta-epsilon proofs are proofs, even if you don’t find them particularly complicated. In mathematics, the proof of a statement x is a sequence of statements, such that the nth statement is either an axiom or implied by statements 1, 2, …, n-1 and some rules of inference, where the last statement is x. That certainly applies to delta-epsilon proofs.</p>
<p>Besides, who cares whether engineers need to learn how to do proofs? We rely on mathematicians to prove things, as it should be {if you consider computer science to be “engineering”, you should know that computer science majors do real proofs using the same kinds of techniques and reasoning as math majors, by the way; so if your argument is that nobody needs to know how to do proofs because proofs are useless, you’re lumping CS in with math, despite the seemingly fantastic opportunities for CS majors, even compared to engineering}.</p>
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I meant for the types of proving techniques available to a high school student or freshmen/sophomore math major, not the types of proofs and skills a math graduate student would know.</p>
<p>You really think a high school student would try to learn complex analysis and number theory just so they could do computations in a different manner in high school calculus?</p>
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Yes, by definition they are proofs. But qualitatively, no real math student believes delta-epsilon to be on the same rigor as other proving techniques learned in a proof-y math class such as analysis or set theory.</p>
<p>Engineers learn delta-epsilon proofs in their undergraduate calculus classes. So, can we then conclude that engineers “know how to do proofs” despite the fact you admitted the contrary in a previous post? </p>
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The simple fact that CS majors need to do proofs does not do much to support your argument. In industry when they are programming or in software development, are they constantly proving theorems on a day-to-day basis? Nope. Even Sakky mentioned in another thread that engineers do not use most of the theoretical concepts they learned in undergraduate from physics and math, and that a senior engineer couldn’t even remember how to take a derivative.</p>
<p>Projectile, I agree with your general point that most engineers do not need to know how to construct proofs or otherwise engage in theoretical complexities. But I would temper that by saying that the vast majority of people in the world do not really need to know whatever they had studied in college. Let’s face it - the vast majority of English majors will never actually analyze literature as a profession. </p>
<p>Theoretical mathematics knowledge is therefore probably useful only in academia. But again, that’s why I encourage you (and all other math majors) to seriously encourage using your math knowledge within social science academia, especially within in a business school. Like I said, business school professors are shockingly well-paid and enjoy arguably the best job prospects of any academic discipline. And believe me, they are deeply intimidated by anybody who knows theoretical math, as most of them don’t know it. The business academic journals become ever more mathematically oriented every year - to the point that qualitatively oriented business researchers bemoan the lack of publication (and hence career-advancement) opportunities. </p>
<p>In my previous posts, I failed to mention perhaps the clearest pathway for a math undergrad to enter business academia: enter operations research, which truly is just a mathematics subdiscipline. Many articles from A-leading operations journals such as the eponymously named Operations Research (the journal) and Management Science are truly indistinguishable from a math journal, consisting of little more than theorems and proofs. Basically, you can devote your entire career to what is effectively theoretical mathematics research while enjoying the luxurious salary and facilities of a business school professor of operations. Frankly, I’m shocked that more math professors and PhD students do not pursue this route (along with the aforementioned economics/finance/accounting routes).</p>
<p>To clarify my previous post and the others I have written on this thread, I am not necessarily endorsing the growing mathematicization of business academia or of the social sciences in general. In fact, I actually consider one of the greatest philosophical questions of the world to be whether the social sciences can be adequately analyzed mathematically, particularly in light of the fact that social phenomenon often changes without warning. {As an analogy, how useful would mathematical physics be if physical constants such as the speed of light not only changed repeatedly, but did so without warning?} </p>
<p>But be that as it may, whether we endorse or it not, the fact remains that social science academia has become ever-more-mathematical which therefore provides a no-brainer opportunity for the mathematically-trained to dominate the space. It’s a perfect ‘rent-seeking’ opportunity: conduct highly theoretical mathematical research not dissimilar to what the mathematics faculty does, all while cashing a paycheck of double or triple the amount as a supposed “business” or “economics” professor (while actually just being a mathematics professor in disguise). Granted, you do have to ‘teach’ business or economics courses, but the (sad) reality is that most research universities place little weight upon your teaching abilities anyway. And if you publish prolifically - which may well be possible if you’re mathematically skilled - you’ll probably be able to negotiate a light or perhaps even a zero teaching load anyway. Either that, or jump to a business-school or economics department at another university that won’t require that you teach.</p>
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<p>Projectile, after checking around, I can now verify that the avenue I delineated above is also available to the physics students. It’s not that hard for even a half-decent physics student to be admitted to an economics/finance/business/accounting PhD program , or perhaps a MFin/MFE. After the Phd, you should be able to obtain an academic placement at a business school or economics department, or after the MFin/MFE, you should be able to obtain a lucrative placement in the finance industry.</p>