Andrew writes:

As I’ve written before, I was a math and physics major in college but I switched to statistics because math seemed pointless if you weren’t the best (and I knew there were people better than me), and I just didn’t feel like I had a good physical understanding.

But every single mathematician, except one, is not the best (and even that person probably has to concede that there are still greater mathematicians who happen to be dead.) Surely that doesn’t make our work pointless.

This myth — that the only people who matter in math are people at the very top of a fixed mental pyramid, people who are identified near birth and increase their lead over time, that math is for *them* and not for *us* — is what I write about in today’s Wall Street Journal, in a piece that’s mostly drawn from *How Not To Be Wrong*. I quote both Mark Twain and Terry Tao — how’s that for appeal to authority? The corresponding book section also has stuff about Hilbert and Minkowski (guess which one was the prodigy!) Ramanujan, and an extended football metaphor which I really like but which was too much of a digression for a newspaper piece.

There’s also a short video interview on WSJ Live where I talk a bit about the idea of the genius.

In other launch-related publicity, I was on Slate’s podcast, The Gist, talking to Mike Pesca about the Laffer curve and the dangers of mindless linear regression.

More book-related stuff coming next week; stay tuned!

**Update:** Seems like I misread Andrew’s post; I thought when he said “switched” he meant “switched majors,” but actually he meant he kept studying math and then moved into a (slightly!) different career, statistics, where he used the math he learned: exactly what I say in the WSJ piece I want more people to do!

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I’d like to defend Gelman’s view and decision. When most of us decide whether to become a research mathematician or not, it’s not a question of whether we will be one of the great ones but whether we will be productive enough to have a satisfying lifelong career as a mathematician. Although you don’t have to be a genius to be productive, it’s still a rather small and elite subset of academic mathematicians who have enough of both aptitude and attitude to produce even only one significant contribution. You don’t have to be a genius, but you still have to be damn smart (and have enough grit) to have a successful career as a research mathematician. It’s arguably a lot harder to do this in mathematics than in other fields.

And what happens if you somehow get tenure as a mathematician but are no longer productive? Despite having lifetime security (the Chinese like to call this an “iron rice bowl”), it’s not necessarily much fun. You’re expected to focus your attention on your teaching and administrative duties, even though that’s not main reason why you pursued this career. Your more productive colleagues call you “dead wood” behind your back. You get minimal cost-of-living raises and maybe a higher teaching load than others. You have no grant, so if you want to go to a conference, you have to pay your own way. And you don’t really want to go to conferences anyway, because you weren’t invited to give a talk and you have to hang out with people who were.

If you’re lucky enough to see that this will be your fate when you’re still young, you can still try to switch to another career. But if you’re over 40, it gets a lot harder, especially if you have a family to support. I remember realizing that tenure was a trap not only for the university but also for the person who has it. And I remember not wanting to fall into this trap, so I was determined to enjoy as much as possible life as a research mathematician before I turned 40 and escaping after that.

So in that sense I see Gelman’s point.

The title of this blog piece is misleading: Gelman *did* stay a math major. From his CV, he got an undergraduate degree from MIT in math and in physics. After college he did graduate work in statistics. So he is an example of what you wrote about in your WSJ piece: he’s a math-major statistician. You want to see more people who major in math in college and then go off and do something else, and that’s what he did.

Maybe a better subject for the title of this blog entry would be Mankiw, who has written about his love of math when entering college, where he switched to economics after meeting some classmates who were far stronger than him in math: http://gregmankiw.blogspot.com/2007/03/my-life-as-student.html

Jordan, I’m going to go on record as saying that I disagree (in part) with your article. I’ll come back with more details when I have had the chance to read the corresponding chapter in your book.

KC, I think we all would have been better off if Mankiw had remained a math student.

I agree with you (at least up to a point – see the last paragraph), but the problem is that the NSF budget doesn’t, and the number of universities able or willing to subsidize research by its faculty (by competitive salaries, reasonable teaching loads, et c) keeps going down. This means job prospects for a pure mathematics PhD are a good deal worse than for most statistics or computer science PhDs, who have significant industry options that actually use their degree and allow them to continue research in some form. This doesn’t affect the more talented mathematicians who still can get good jobs allowing them to do some research, but it does affect everyone else.

This is a bad state of affairs for the mathematical community, but I don’t think the public cares.

At the undergraduate level, this is less of a problem because we still have a liberal arts tradition that values a broad education and employers who are willing to hire people well and broadly trained in thinking, reading, writing, and making sound arguments rather than specifically trained in the technical skills of the moment, but that employment market too is changing. It’s certainly true that those of the math majors here who do not have a more specifically vocational other major (most usually education or computer science) are having a good deal of trouble finding employment that actually requires a college degree.

Also, I’ve known some students who are very interested in mathematics and put hard work into learning it, but when, after repeated attempts and a reasonable amount of hard work at learning the concept, one is unable to recognize and use the equivalence of a simple implication and its contrapositive except when specifically told to do so, one has to give up at some point. In other words, while one doesn’t need to be at the 99th percentile in mathematical ability, whatever that means, to contribute to mathematics, I’m not sure one can contribute to mathematics if one is at the 30th percentile. I think a mathematics education still does such a student and the communities the student is a part of a lot of good, but I doubt the resulting improvement in intellectual skills from poor to mediocre will help the student get employment. The filing clerk, most of the secretaries, and half the people making airline schedules have already lost their jobs to the computer.

Jordan:

Hi, see the second and third paragraphs here. And, no, I don’t believe that there is a strict ordering of mathematical ability, but I do think there are people much better than I am at math.

Also, I don’t believe that “math is for them and not for us.” Math is definitely for me, and for thousands of readers of my books! I certainly wanted to

usemath, I just didn’t want to become amathematician, which to me was associated with proving theorems. As I wrote in my longer essay, I think this was a problem with the way math courses were taught in college: there was no sense of applied mathematics as a serious endeavor. I didn’t want to spend my time proving narrow little theorems, and I was pretty sure I wouldn’t be proving any deep ones, had I spent a career in pure math.KCd: I wish I’d known that about Mankiw; he appears in the book two other places and it would have been nice to bring that thread in one more time in this section!

galoisrepresentations: I think most of the book is pretty uncontroversial, but yep, this is one section where there’s a lot of room for disagreement, to the point that I found it a real challenge to write (because I’m aware of the arguments against what I say and feel their force.) WSJ specifically wanted a piece that people might want to argue about. Fighting = clicks. Anyway, please do come back and weigh in!

Andrew: thanks for that link! You write

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Ultimately I decided the problem was that, in the world of theoretical math, there were the Cauchys, the Riemanns, etc., and there were everybody else. I didn’t want to be one of the “everybody else.”

**

You want what you want, and obviously it’s worked out great — but I don’t want everybody to have the same approach you have, because if only the Cauchys and the Riemanns stayed in math, there would be, like, five mathematicians.

I guess I have a way of going off topic, but I wanted to say the following: We have to convince people that even if they aren’t math majors and don’t want to become mathematicians, they *can* learn (to do) mathematics and use it effectively in many different settings outside of mathematics itself. I don’t think we do this particularly well.

I do some consulting in the financial industry, and I am struck by how much of this work does not involve any advanced mathematics (stochastic calculus, PDE’s, and all that). Usually some elementary probability theory, arithmetic, deductive logic suffices. Still, it’s difficult to find anyone without a math PhD who is able to do such things properly. Worse, I’ve learned that even people with math PhD’s cannot necessarily be trusted to do these kinds of things correctly (and all too often they do try to use overly sophisticated tools to solve easy problems).

Of course, I believe that your book is trying to do exactly what I’m asking for. I’m really hoping it becomes a best seller and, more importantly, that people actually read it.

I also had another idea (going even further off topic): Any chance you and Danica McKallar want to create a joint blog (including videos) on math?

Jordan:

You write, “if only the Cauchys and the Riemanns stayed in math, there would be, like, five mathematicians.” True. Maybe it would help in undergrad math courses to give a sense of how the rank-and-file of mathematicians can make contributions, for example pointing out various counterexamples that were discovered by the non-greats. When I was a math student there was lots of veneration of Euler, Gauss, etc., and I got a real sense that in any given era there were the mass of mathematicians who were just screwing around and the rare Cauchys etc who did all the valuable work.

Couldn’t agree with you more. I really feel what you said in the article “One of the most painful aspects of teaching mathematics is seeing my students damaged by the cult of the genius. ” Thanks for writing this.

It seems to me that the existence of only five mathematicians would be inconsistent with the existence of mathematics itself. If your only real audience is a couple of contemporaries and a couple of dead people, you would get little useful feedback, little real reflection of yourself and your ideas in the mirror, little chance to affect the world, and little validation, hence self-validation, from others. Math wouldn’t happen or would at least be severely degraded. A language with few native speakers can not survive. And no one likes being the proverbial falling tree in the woods with no one around to hear them, or being seen as a babbler of seeming nonsense.

Here is something your department could do to broaden participation in mathematics. Take some of the money you have for postdocs, and use it to instead provide salary replacement so that people at other UW campuses (including 2 year campuses) can come to Madison and do a full year sabbatical. It’s fine if you need them to teach one class to make the budget work. Engage them in research the way one would with a postdoc. Provide them with travel funding, not just for that year, but for the following couple of years, so that they can go present the research they did. Keeping the faculty members involved engaged in research should help their students as well.

Good column. Speaking of precosity, perhaps you could find and post the article that the National Equirer ran when you arrived at Harvard as a freshman. It certainly scared all of us on the faculty!

There are certainly people who are better wired to do this stuff than the average bear. I’ve had the pleasure of working with a few of them, and when you see it at close hand it is amazing. But that doesn’t mean that the rest of us should give up.

I have been trying to find that National Enquirer piece, so far without success! All I remember is that the subhead was “He solves brain-busters even teachers can’t do!”

From the WSJ article:

But this is a rational calculation, precisely because mathematics is institutionalized as a highly competitive discipline. If those who score high on the SAT at 13 are 100 times as likely to make a scientific advance as those in the remaining 99% of the population, then there should to be roughly 100 times the opportunity for lower scoring individuals to make those advances than they currently have. But the jobs in academia aren’t there. Students see this and they make the rational decision to jump ship. (I was irrational and did not.) The cult tells students that there are no jobs for you unless you are the very best. And with fewer tenure track jobs in a dwindling, pedigree conscious market, the perception of the cult is correct.

As long as the STEM subjects remain a zero-sum game, with the overwhelming spoils going to the early bloomers, the winners should be satisfied with what they have already won in an unnecessarily and destructively competitive field. The rest of us are doomed to provide them support as members of the economic precariat at slave wages, if we are foolhardy enough to remain in academia. There is no honor in adding to someone else’s power law distribution–and less honor in exploiting the labor of those who didn’t advance as far.

https://screen.yahoo.com/wall-street-journal/paying-too-much-attention-child-173207193.html

THIS!!! He called you Ellenberger, by the way.

I think a lot of the people who use “I’m not the best” as a reason to switch out of math really mean “I’m not good enough”, that is, good enough to achieve the type of goals they set out for themselves.. so many young people have very high aspirations and it’s just more apparent early on that they won’t achieve such aspirations in a very concrete subject like math. You’ve all probably heard of those studies where they ask incoming freshmen how many of them expect to be above average and of course the vast majority of them will say yes.

It is too bad that people leave math for such reasons, but at least in many of the alternatives such as computer programming etc, if you fail to reach the upper echelons there are plenty of other opportunities. It’s not like they leave math to try to become Olympic athletes, rock stars, etc. But try telling an 18 year old “Well, if it doesn’t work out as a top-notch mathematician, you can always become an actuary! Or work for the NSA! Aren’t you excited???”

If mathematics and other STEM disciplines weren’t institutionalized as winner-take-all disciplines, or if this perception weren’t in the air, then perhaps more students would stay. (Winner-take-all is more accurate than “zero-sum,” and it is sufficient to get the point across.) This perception starts at the top of the field–it doesn’t spontaneously arise. But in a winner-take-all discipline, the winners should be happy with what they have won–the losers would be wise not to compound their losses (by becoming adjuncts or eternal postdocs, among other ways). We’re not even talking about top-notch mathematicians–just faculty. Many faculty working today who have a knack for self-promotion will suffer the same eclipse after their lifetimes that any number of popular artists and composers have in the past. Some obscure figures will turn out to be more important in the long run. But the way the discipline is institutionalized, this is becoming less likely.

So–I was an undergrad math major and did a year of grad school in math before leaving the field. You may have actually been my first big red flag–when I was a senior and realized that you as a freshman were taking the same courses, I started to see a bit of a divide between people who liked and understood math and people who really really got it.

It’s actually a bit more complicated than that. What I realized was that I found the results interesting, but that I did not seem to be terribly well cut-out for the process of finding new results. I’ve always been particularly good at taking advantage of low-hanging fruit–but I found math as a whole to be a field in which the lower branches were extraordinarily well picked-over already.

(For comparison–in a lab science, almost any experiment suggests a number of possible followups or modifications. But the time and effort cost of experiments means that only some of these can be done. My impression is that math offers relatively very few places where there’s a lot of reasonably obvious stuff to “do next”–there’s much less variation on a theme.)

In hindsight, academia was not where I really needed to end up. It just took me many years in another field to get that figured out.