I’ve heard this view shared by many of my math chums (IANA mathematician). The idea is that if a mathematician hasn’t accomplished anything (as in proved a theorem or made a discovery of some sort) by the time he’s 30, he’s pretty much never gonna be able to. In short, it’s over for him.
This seems a pretty bleak but (dare I say it) widely held view. So I want the experts on the SD to chime in with their own views.
Is this phenomenon real, and if so, why does it occur? If a mathematician hasn’t discovered anything by 30 – does it really condemn him to a life of teaching high school kids (sorry, couldn’t resist – will withdraw the quip now)? Is his (or her – I haven’t forgotten the ladies) life of mathematical creativity terminated?
And what about people who enter mathematics (as an academic discipline) at a later stage in their lives – say their mid-twenties – does the same rule still apply for them?
Doesn’t this apply generally to most professions? How many artists make waves late in life? Most are gone before their 20s are over with. It’s not a certainty, but I think most inovations are from the young.
Well, being a mathematician doesn’t require a lot of maturity and real-world experience and insight into people (unlike, say, being a novelist or a politician), so it’s the kind of field where one can accomplish great things at a young age, and there have been several famous examples of prodigies who have done just that (like Galois, who died before his 21st birthday). If a person has both the interest and the ability to do mathematical work, these generally would have shown themselves by the time the person reached young adulthood.
But there have been plenty of examples of mathematicians who have done significant work well into middle, or even old, age. So “over the hill at 30” is something of a myth. And maybe one source for this myth is the mathematician G. H. Hardy, who in his famous A Mathematician’s Apology wrote “No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game.” But then Hardy himself was sort of a Peter Pannish figure who didn’t take well to growing older.
This might be where that general stereotype comes from. . .
The mathematicians I know usually entered graduate school around age 22 (out of college), worked like hell for 5-6 years until they get their Ph.D, usually doing (to them) fun, exciting, new work.
Then, as they desire to get tenure, they continue to work like hell. The fortunate ones have done a lot of interesting publishing and gotten a tenure track position (if not tenure) by 35-40.
At that point, they don’t necessarily go into “auto-pilot” but they might be publishing advances in “their” area instead of exploring a whole new area. That might be the root of that thinking.
And when I say “work like hell” I mean it, too. To really be productive, some work 7 days a week, 9:00-5:00 and into the night. That’s a hard thing to keep up.
However, there are the real geniuses (like a Ron Graham, or a Noga Alon come to mind) who are very productive for long stretches of time. Usually these people seem characterized by their ability to work in a lot of different areas.
Then, there’s the goodly portion who get Ph.Ds in their late 20s and then take 9:00-5:00 jobs, or get less stressful academic appointments. They still do research and publish, but not with the fervor of the other groups I mentioned here. They might have done their most interesting work by their early 30s.
I think most mathematicians I know fall somewhere in between the first and the third groups.
This is absolutely wrong. Most artists who have made it into whatever canon you consider appropriate continue to grow and develop as artists throughout their lives. Late period works by Rembrant, Hals, Bernini, Van Gogh, and others show definite maturation of style over the decades of their lives.
Someone had to mention someone besides Grandma Moses, after all!
I always understood it to be referring to making some truly earth-shattering discovery. The line of thinking is that if you’re the type of mind that’s capable of revolutionizing a field of science, this will show very early in your career.
Most scientists, even highly successful ones, do not accomplish anything revolutionary during their careers. A lifetime’s worth of incremental advances in knowledge is still a significant contribution, so that’s hardly something to be ashamed of. There are a precious few, though, that turn a field on its head.
Most folks I’ve heard say this understand perfectly well that, to the extent it has any validity at all, it’s a tendancy rather than any absolute law.
No real answer, just props to the OP for asking a question based on the show proof. Really really good play by David Auburn, going to be a movie this December with Anthony Hopkins and Gwyneth Paltrow.
Or how about Kandinsky, who didn’t even really turn his attention to art until he was in his 40s?
There are lots of exceptions to the “under 30” rule among scientists and inventors, but lots of these guys are people who aren’t heard of much by the general public. Grace Hopper, for instance, whose work provided a lot of the basis for modern computing, did her most significant work when she was in her 40s. Or check outChien-Shiung Wu, who started doing the work she won the Nobel Prize for when she was around 45 years old.
Mathematicians, as has been pointed out, may do a disproportionate amount of work early for the same reason many other academicians do – because they’d better, or good bye tenure and a good job. But I’m sure that lifestyle plays a large part too. The parties, the drugs, the math groupies, the general expectation of the public for the mathematician-as-hellraiser image, that’s all been ingrained since the 1960s. “Don’t trust proofs from anyone over 30” was more than just a slogan, man.
I’m a grad student in physics, expecting to get my Ph.D around age 27, even though I went to college right out of high school and grad school right out of college. For someone to have published ground-breaking work before age 30, they would have to either have gotten their Ph.D at an earlier age than usual, or done something amazing in a very short amount of time, while still a grad student or post-doc. Perhaps the former can explain the observation that a lot of ground-breaking research is done before age 30 (assuming the observation is even true)–the geniuses who get their Ph.D’s at age 23 can do their amazing research at a young age, whereas us average people don’t publish until later in life, and because we’re dumber our work is of a lesser quality.
Unless it’s being suggested that even geniuses who get their Ph.D early burn out by age 30…then I don’t know why that would be.
Anyway, I suspect that in a field like physics or math, the genius factor is going to skew the statistics a little.
I’m not so sure I would have associated ‘‘drugs’’, ‘‘groupies’’ and ‘‘hellraiser’’ with mathematicians, but thanks for the new image anyways.
So I see the general consensus amongst this board is ‘‘it’s not true’’. Although I see a lot of late artists mentioned, I don’t really see a lot of late mathematicians mentioned (as in guys and gals who made most of their major discoveries late). So can anyone name a few?