Are there any (relatively) famous or well-known examples of mathematicians who have begun studying mathematics at a later (than expected) age?
Have any dudes who published mathematical papers ever begun studying math at a rather advanced age?
For example, clearly someone who began an undergraduate degree at the age of 25 is quite old to start studying mathematics (where you’re considered old news by the age of 30 - or so I’m told). So are there any documented examples of people who began studying math at such an advanced age and became successful (e.g. published, or held a university posting) mathematicians afterwards?
And are there ever any “mature” students in mathematics?
It seems to me that more and more these days that older folk tend to study stuff at university. For example, a history course I know which was packed full of people who were in thier fifties. According to the information I get (keep my ears to the ground and all that) it seems to be occuring more frequently in all classes, not just the Humanities.
There are a number of “returning students” in mathematics. The thing with this sort of student (in any field) is that either they’re doing it as a dilettante or for shoring up some job skill.
To elaborate on the “job skill” set: people working in engineering will get math or physics Ph.D.s, people working in religious education will get masters’ in theology, and so on. These aren’t the people who are going to turn around, join the academy, and start cranking out papers other than for specific job-related applications.
As for the dilettantes, a large number of people find they’ve got free time and money and want to go learn about something they’ve been interested in. They tend to work at the undergrad level and really are more there to hear about a subject rather than to do anything with it. How many of those 50-year-olds in that history course were embarking on a new career in history? Probably not many.
Further, the place where math research gets done is in the academy. There are vanishingly few mathematicians working on original research in their spare time or in industry (again, except for specific applications). Universities these days don’t really look at you as a good prospect if you come so late to the game. For one thing, you can’t give them as much time to work on results since you’ve already used up twenty years the guy next to you still has ahead. Whether this is “right” or not, it’s the way hiring comittees tend to think.
As a side note on the “washed-up by 30” bit: it’d be more accurate to say that if you haven’t made a big splash by 30 you never will. Plenty of mathematicians do great work after 30, but almost all of them also did great work before.
When I was an undergraduate, maybe three years ago, I had in a few of my classes a guy around 30 years old. I never spoke that much with him, so I don’t know what he had done since he’d left high school, but he had decided to go back to school to pursue a math degree. I think that when he finished, he decided to go spend a year in the School of Education to be allowed to teach high school. Many finishing math undergrads at my university did or are planning to do the same thing.
Then, a few years later, when I was taking measure theory as a grad student, we had in our class a fifty-something man with a rather complex schooling history. If I remember right, he had originally been in the Navy, and had studied at a Navy school, but when he left his diploma wasn’t recognized anywhere else. So he had to do a three-year bachelor degree, and chose math because that was the choice that required him to take the least courses. Now, some years later, he was trying to finish his honours mathematics degree to get admitted in a distance education master’s of astronomy program. I think he wanted to do this mostly for fun, since he likes astronomy and already knew quite a few things about it from his years in the Navy.
So there are people who do mathematics degrees as “mature” students. I don’t think most of them do it in the hopes of having a carreer in academia, though.
As for famous mathematicians who got into the subject at a later age, I have heard of Alexandre-Théophile Vandermonde, but he isn’t as well-known as some other famous mathematicians. I’m sure there are others who started math later in their lifes.
Yeah I guess that’s the part I find a little confusing. I couldn’t ever imagine studying a subject that technical without becoming involved in publishing or a future career path.
And starting for the first time in your fifties just seems a little too late to me IMHO. But then, who am I to judge?
What do you mean by “technical”? Depending on which branch of mathematics you decide to study, it may not be very technical. I’m sure there are people who would study algebra or logic, or even analysis, for their inherent beauty.
Well, if you’ve always liked math, but never pursued this interest, and now find yourself retired with more than enough money to live comfortably, why not go for it?
Just to be sure, I’d like to point out that I’m not complaining at all. It would certainly be a welcome break from the torrents of little bastards who just want the piece of paper so they can go work in daddy’s company and make a mint off my back.
I don’t think Douggy meant “applications-oriented”. You can’t seriously suggest that there isn’t so much technical (as in detailed and jargon-heavy) background needed to get to the level that one could do original work as to preclude anyone from reaching that level without intending to do so.
I would suggest that it’s possible to study mathematics without intending to make a career out of it. There is the example I gave earlier, of retired people who always liked the subject and now want to learn more about it. I also said that I know several people who, after finishing their honours math degree, went to get a degree to be allowed to teach in high school. They didn’t need a honours degree to teach high school math, but they did one nonetheless. Maybe that’s because they were intending to go to graduate school when they started, but it can also be that they were interested in hearing more about the subject before studying something more “job-oriented”.
Yes, mathematics is heavy on jargon, and it can get pretty frustrating, but it’s still interesting enough in its own right that I can see people studying it just for fun.
Again, the people you’re describing aren’t studying to the level of making an original contribution to the field, which is what the OP was asking about.
Actually, as I understood it, the OP was asking a few different questions.
Are there any famous mathematicians who started studying the subject at a later age? (Yes, we see that Vandermonde did just that.)
Are there any mature students in mathematics? (Yes.)
(In post 4) Is it possible to study a subject as technical as math without the goal of starting a career in it? (I claim that it is.)
I don’t think we disagree, Mathochist. If you study to the point where you’ll be able to make an original contribution to the field (that means learn about current research), it’s likely that your goal is to actually make a contribution. Maybe mathematics is a little more technical than other subjects in that regard (for example, maybe laypeople can read about and understand current research in psychology, while they obviously couldn’t do the same thing for current research in math), but I think that in all fields, being able to actually do, not just understand, original research, requires a commitment.
On the other hand, it is possible to study the subject up to the point where you can’t yet do a major contribution to the field, but still understand very well the “classical” stuff (up to the first decades of the 20th century), just for fun.
Actually, I think that there even is current research in mathematics that could be understood, up to a point, by laypeople. Some new things in graph theory, for example, aren’t that difficult to understand; it’s just that the proofs are long and have required a lot of trial and error. I don’t have any example right now, though.
The Millennium problems aren’t that hard to describe–there may be a leap to find them interesting, to a layperson. And Fermat’s Last Theorem, who can’t understand that?
The questions here are rather vague, so I’m not sure if any of the following statements answer the questions asked, but this is as close as I can get to answering them:
It’s not the case that no one has ever done their best mathematical work till relatively late in their career. There’s at least one case of a mathematician turning out his most important paper in his 50’s. He was already a good mathematician before then and had taught at a good university, but his best paper was written in his 50’s.
I don’t think there are any cases of someone who didn’t study any (college-level) mathematics till they were, say, 30 but who afterwards did study it and made an important contribution to mathematics, but it’s certainly not impossible that it has happened or will someday happen. I don’t offhand know of any cases of someone who didn’t study any (college-level) mathematics till 30, and who afterwards got a math Ph.D., but I suspect that there are a few examples of this happening. I do know of cases where someone started on a mathematics undergraduate degree just out of high school. They either finished their degree and took a decade or so off or they dropped out of college and took a decade or so off. In any case, they didn’t enter grad school until they were well into their 30’s and yet they went on to finish a math Ph.D. and work as a mathematician or a math professor.
I know of one case of a man who worked most of his career as a technician and an engineer without ever doing a bachelor’s degree. (This was in the U.K. in the 1950’s through the 1980’s, where it was possible to do some engineering work without a bachelor’s degree. He took a few courses part-time over the years, but he never got a bachelor’s degree in engineering.) At the end of his working career, he got more interested in mathematics and began taking some math courses part-time. In 1990, he finished a mathematics bachelor’s degree and was moved by the agency he worked for into a mathematician’s job instead of the engineering jobs he had been doing. He retired a year later.
I never said that the statements were difficult, but that actually proving new results (and even having a proper notion of a rigorous proof) is beyond the lay reader. My point is (and has always been) that though there are older people in some undergraduate mathematics classes, they are there more as tourists.
Further, even if they did intend to do research, unless they were independantly wealthy they would have to do it in their spare time around their day job, since the current culture of academia is stacked against anyone who has ever left the Ivory Tower at all.