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Is Math a Young Man's Game?
Bamafan77 writes "Slate has an interesting article on the relationship between the productivity of mathematicians and age. The conventional belief is that most significant mathematical leaps are all made before the age of 30. However, the author gives pretty compelling reasons for why this once may have been true, but is definitely not the rule now. Two of his more interesting pieces of evidence include Grigori Perelman's (probable) proof of the Poincare Conjecture at 40 and Andrew Wile's proof of Fermat's Last Theorem at 41."
I think 40 is probably the peak between the tradeoff between knowledge accumulation and physical decline. But stand for a psychologist or neurologist to correct me.
A bit like athletes maybe... experience vs. physiology results in a trade off.
I completely agree that math is a young man's game.
I'm so old, I lost count. Damn wippersnappers and their meaningless symbols.
When you get married and have some kids it is real hard do get any work done..
"Okay Dear I'll mow the lawn now"
I also suspect the growing complexity of screensavers as a factor..
Two of his more interesting pieces of evidence include Grigori Perelman's (probable) proof of the Poincare Conjecture at 40 and Andrew Wile's proof of Fermat's Last Theorem at 41.
Yes, but at the tender age of 22, I can not only add my bar tab together, but also figure an appropriate tip.
Young people can't do hard math my ass.
A century ago, mathematics was primarily a new field. New fields are characterized by inventiveness and a lack of prerequisite knowledge -- there isn't a lot of background to learn, and if you look at problems "the right way" you can get results very quickly. Most of mathematics is no longer a new field; in most areas, one must spend years studying before one can do anything new, and even then it's likely to be the result of long hard work rather than a quick new insight.
Computer science is moving in the same direction, but is many years behind. Thirty years ago, computer science was a new field; there were few if any courses teaching necessary background material; and someone with the right insight could find very important work very easily. Now, we're starting to see movement away from that -- there is a body of important work to build upon, and anyone who hasn't studied that work will have "new insights" which simply reinvent already existing work.
Mathematics is no longer a young man's game, and this is probably the last generation when computer science has been a young man's game. Next generation, the young will find a new field to excel in -- perhaps genomics?
Tarsnap: Online backups for the truly paranoid
0 to 5: Curious phase :-) ...: Irrelevant phase (atleast that's how it's treated by others)
5 to 15: Productive phase
15 to 40: Reproductive phase (some like to begin early and post longer
40 to 60: Consumer phase
60 to
After that brainwashing people aren't simply able to do anything outstanding anymore. There are some accidential great scores, but they are very rare.
I think we should change our mathematics education to tackle with this problem. And we should indeed already start in school were the first and the most foul foundations are laid. Instead of teaching children basic counting, set theory and algebra which draws in the whole rubbish of non-intentionistic mathematics, we should start with Lie groups and algebraic varities. Indeed most "Joe Adverage" problems can be reduced to Lie/algebraic geometry problems.
I can give a simple example why this is necessary:
Imagine the Kleinian bottle in R^4.
You'll say now: "That's not possible nobody can visualized 4 dimensional spaces."
But this is only because your basic mathematical education fucked up your brain.
If a decent education would start like mentioned above, we all would have no trouble at all to visualized arbitrary n-dimensional spaces.
And because of using different logical concepts wouldn't have to use the problematic axiom of choice. So, no trouble with the Banach-Tarski paradox, inmesaurable sets and non-holomorphic refractions in H^p_2.
This is even a serious political issue. Anyone into math research will agree with me that in the last 15 years we saw a rise of a generation of brilliant new chinese mathematicians. And why did we saw it ? Because China went back to its Confucian tradition in teaching which avoids the above mentioned problems in Western math education. So, if we don't act now we'll loose our technological leader within the next 30 years forever.
Owner of a Mensa membership card.
Frank Lloyd Wright did his most celebrated work after the age of fifty.
-kgj
Also worked on the proof for Fermat's theorem for 7 years in secret(which in the mathematics community is a rather odd thing to do). He was dreaming of solving it while he was still a child. There is quite a good book on the subject for anyone with any level of knowledge called fermats last theorem. I'd give you a link but i'm tired..
Why me?
" is there anything really brain demanding or innovating you can do after 30?"
Demanding: Writing the GPL, starting FSF, the Hurd, travelling the world over, believing in yourself despite others jeering you - RMS age 50.
Innovating: Buying an OS from someone, putting it onto someone else's h/w, building up a monopoly, driving out others (using suspect means), releasing newer and newer OSes that do essentially the same things, generate obscene profits, etc. etc. - William Gates, Age 45 (?)
Life begins after 30, methinks.
If you keep throwing chairs, one day you'll break windows....
Definitely this is the women-not-invited dept., as billed, but it reminds me of a conversation I had with a 98 year old woman in 1982. I was 28, had a toddler and an infant, and was very much afraid that motherhood would be the end of any other kind of creative work for me. (The exhaustion factor alone was daunting.)
Miss Mae said to me, in a Miss-Daisy sort of Southern accent, "Honey, women are not like men -- we get better with age. After all, you can't think straight until your parts settle. I promise, when you are 45, you'll know what you want to do with yourself, and it won't have anything to do with diapers."
She was right about women, or about me, at any rate. I'm 48 and in my first year of professional school while the "baby" is at his first year of college. (What this has to do with my "parts" I am less sure.)
What I notice is that my younger colleagues are quick and bright, but that what I lack in speed I make up in context. And all of us are passionate about what we are doing, but the flavor is a little different depending on age. When we are working well together, the combination of gifts is truly wonderful. Perhaps instead of framing the "game" (of math or of anything else) as a contest, we ought to be looking at ways to make progress that makes use of both the experience of age and the quickness of youth.
OK, now what?
Let's not forget that most pure mathematicians are University faculty members, and that the longer you're on faculty, the more committees you sit on and the more non-research responsibilities you end up stuck with.
Could it be because not so long ago
people usually didnt live
beyond 40?
What about young women?
/., is primarily an activity of men.
I know, I know: math, like so many of the things discussed here on
But it seems to me that we would be much better served if we talked about how to get more women in the field, not how we could keep old men in it. I mean, aren't there enough old men around anyway?
(spoken by a future old guy - hopefully)
It's simple: Young mathemetician's aren't getting laid -- so they work like hell on on their maths. Since male sex drive peaks at 18, the less sex drive you have, the less driven you are to find another way to spend the time.
Or maybe they got married and their wife nags at them to death and ruins their concentration.
When visiting mathtutor one can see that even 200 years ago, many important discoveries were done in the later stages of the Mathematicians career. Stories like the ones about Abel or Galois distort the picture.
More and more discoveries of younger mathematicians are achieved through collaboration or by standing on the shoulders of people with more experience (who tend also to be more generous with sharing their ideas without expecting credit).
Mathematical knowledge continues to accumulate in a fast pace and only few of this knowledge has been absorbed in books. Chances grow that a young mathematician will discover something already known or to be a special case of a much more general result. Fortunately, there are better and better online databases but it also needs more and more time to dig through that material.
The most productive age for a mathematician will grow also in the future. The same will happen in physics or computer science (as a previous post has pointed out already).
I can't believe that statement! I'll have you know that at 38 I'm just as...um...uh...what was I going to say? Hey, today's Saturday! The buffet has the early bird special today for dinner at 4pm! I'd better get the oil changed in my Oldsmobile first...
The truth is I don't feel any older than I did at 25 (still like the same age women as a matter of fact), I'm in better shape than I was then, and if coding skills are any indication I'm sharper than my 20-ish coworkers. So there!
Now if you'll excuse me I have to knock back my Ensure before I chase the kids off my lawn.
It can definitely be said that some mathematicians produced work at an early age. As the article said, many died early, some continued to produce work throughout their lives. And the body of maths has increased so much that it's much more work getting an good overview of a field.
Note also that before the 19th century, scientific research didn't have the same place in society: it has grown quite a lot.
But regardless of the mathematician's age, what has to be taken into account is the relationship between groundbreaking work, and sturdy, low-profile, everyday work that is achieved by the mathematics community as a whole.
Without that, the breakthrough cannot happen: it loses its value, as it has no ground to stand on.
This is of course relevant physics and astrophysics as well: if you didn't have people studying and cataloguing stellar spectra, you couldn't develop theories about distances, and, more crucially, n-dimensional cosmological models. Now remember, stellar spectra themselves are boring as hell, so are atomic spectra (the spectra that prompted quantum mechanics, etc.)
There are a lot of romantic ideas in the non-scientific public about science: I meet them every day. Sometimes they are just funny, but other times you wonder about the image that society has of your work. Of course I am by no means degrading the value of scientific breakthroughs and original thinking: any deep thought is a process that I consider to be mysterious in essence.
yours ever, fz.
He wrote about humanity's cleverness having outstripped its wisdom. In the story his hero sets up a foundation to retard the progress of scientific knowledge, to give our wisdom a chance to catch up.
About the widely spread notion that math, physics etc, are fields were only the young come up with the paradigm shifting insights... I have also read the suggestion that it is new arrival in the field that really counts, and that the older person who switches fields can come up with the paradigm shifting notion too.
My knowledge of pure math is not sufficient to know this. Are these two recent, famous developments really paradigm shifting? Or are they admirable accomplishments, but more developments of existing ideas? Can anyone set me straight?
Perhaps you should realize that since you've fulfilled your primary purpose as a human being (reproduction), all you're doing is taking up space and resources needed by the next generation to raise its offspring.
In other words, hurry up and die. Your life past this point is merely an exercise in selfish indulgence.
I assume this was just a joke, but...
Au contraire. Given that there are 6 billion people and growing on this planet, and given that a depressingly large fraction of them live in crushing poverty, overpopulation is a huge problem, and it's only getting worse. The solution? Fewer offspring. Nowadays, the selfish indugence is having kids. Sure, we want the species to continue, but there's no worry about that at the moment. (It's like spaying your dog or cat; there's no anger that there won't be kittens and puppies, so it's best for all concerned to spay.)
I'm not saying nobody should have kids. But if we want to have any hope of the people on this planet living in relative comfort and prosperity, we need to overcome that evolutionary programmed urge to procreate-- which is selfish on a species level, if not an individual level. Sure, evolution designed us so that our purpose is to reproduce, but unless we want the whole world to live in squalor, we now have to redefine that purpose.
So go on to professional school and develop your brain when you're older. Learn math, contribute to human knowledge even when you're past the age when "tradition" dictates you can make your best contribution. Bettering ourselves and our world should be the purpose of existence now, not just producing more and more kids to use the dwindling resources of this planet. Meanwhile, we need to figure out a way to seriously limit the number of kids produced each year while preserving as much personal freedom as we can.
-Rob
In a nutshell the grandmother can provide additional food resources to the weaned children of her child or her childrens mates (to increase their fertility) since she no longer has to provide those resources to her direct children and can produce excess to what she consumes.
Thus there is an evolutionary advantage to women surviving following their fertile years, and this advantage likely continues in different ways now.
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It took Andrew Wiles seven years to write a rigorous proof for Fermat's Last 'Theorem'. If he had started when he was 23 instead of 34, he would have proved it while he was 30, instead of 41.
The real problem, of course, is that it wasn't until Andrew learned about the Taniyama-Shimura conjecture that he figured out the method for proving Fermat's Last Theorem. He then waited for 2 years before starting.
Who I think is a better example of mathematician burnout is Yutaka Taniyama himself. He started his career at 28 - way old for a mathematician - and killed himself at age 31. A year after his mathematical prime. Coincidence? Maybe. But you never know...
We are not talking about life in general here. We are talking about maths.
Almost all the rich men have become rich late in their lifes. Most politicians are old, artists contibute throughout their lifes, most scietitsts are old, even.
Maths, due to the fact that it demands little interpersonal contacts (books are enough) and because it is almost entirely an act of the mind (unlike physics where you are related to the rules of the world), is generally assumed to be different.Intuition, originality blah, blah.....
.ACMD setaloiv siht gnidaeR
A counterexample:
Paul Erdös. Read about him in this book.
The man did math until he died of old age, at a pace of about 18 hours per day. He cared not for material things, as he lived out of a suitcase. He cared not for life's physical pleasures, as he (almost!) never even had a girlfriend, or boyfriend for that matter. He had his doctor perscribe speed to him, so he could work more hours on mathematics.
An amazing read about a guy who I am amazed by, but also whose qualities I am glad I don't have.
No, back to studying linear & nonlinear programming, stochastic processes, dynamic programming, and queueing theory for my qualifier on Monday.
Support a few technologists in Washington.
A highlight:
Small potatoes make the steak look bigger.
OK, I've got karma to burn so mod me down, but...
The abbreviation "math" really grates on me (outside the US it's called "maths"). It's not mathematic, it's mathematics.
Don't get me started on sulfur either...
Bob
Listen to my latest album here
A lot of very tallented mathematicians go down a dark road in their 20s, trying to prove the impossible, giving up prime years to fail at something and a few actually do prove something important and then are spent. Godel was nuts to start with and the work he did in his 20s pushed over the top.
Of course the real reason that scientists might make more discoveries at advanced age than in past times is simple. Viagra. What's more inspiring than getting some tail?
For great insights into the mind of a world class mathematician, please read A mathematician's apology by G. H. Hardy. Hardy was one of the top mathematician's of his era (1877-1947). Hardy is perhaps most famous for his discovery of Ramanujan and "A mathematician's apology" has a great Foreword by C. P. Snow documenting some of the details of the Hardy-Ramanujan collaboration.
Here are some nuggets from "A mathematician's apology". (Hope the copyright police are busy elsewhere.)
"No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game." [Section 1.4, page 70]
"Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty."[Section 1.4, page 71]. Also see Men of Mathematics for more on Galois.
"I do not know an instance of a major mathematical advance initiated by a man past fifty." [Section 1.4, page 71].
And later in the book,
"There are then two mathematics. There is the real mathematics of the real mathematicians, and there is what I will call the 'trivial' mathematics, for want of a better word" [Section 1.28, page 139].
Anand Rangarajan anand@cise.ufl.edu
As far as age and mathematics go, though, I'd have to agree that the effects of age are, if not disappearing, then at least being shifted back a number of years. Not long ago, I had the fascinating realization that after 3 years of college, I know more mathematics than Euclid, Diophantus, al-Kwahrizmi, Fermat, Newton, Leibniz, Euler, Hamilton, and Abel. This is not because I'm some sort of mathematics genius (I'm not even a math major), but rather because there is simply more mathematics to learn now, and I merely came later than those guys. For centuries, the situation was such that almost all of the human race's mathematics knowledge could exist in few enough books to carry in your hands- namely, Euclid's Elements and Diophantus's Arithmetica, eventually followed by a few others like Fibbonacci's Liber Abacci. In the 17th-19th centuries, mathematics used these simple foundations to create an incredible wave of new mathematics. (Just take a look at Fermat's annotated copy of the Arithemetica.) Now the number of books written on some specialized part of mathematics like Lie algebras or K-theory could fill a library.
Also, mathematics works a bit differently than the natural sciences- it's harder to create a general survey course in mathematics. Just look at the way these subjects are taught- you generally take high school science courses in physics, chemistry, and biology, but math courses in algebra, geometry, and calculus. The specialization has to start much sooner because eachthing builds off of the previous. In my high school chemistry courses, I remember covering some basic p-chem, some orgo, etc, and in my physics courses there was mechanics, E&M, optics, etc.. I of course returned to all of these in excrutiating detail in my college course, but the simple point is that you couldn't do a similar thing with math. In physical sciences, you can give a broad overview of a subject, and then later reurn in depth, because there isn't such an elaborate hierarchy connecting all of the fields. Conversely, mathematics works more like a pipeline, shuttling students from simpler subjects (basic arithmetic, simple Euclidean geometry) to harder ones (integral calculus, diff eq, set theory). The pipe opens up at the top- areas of specialization become apparent, and a frontier is reached where knowledge in one field is not necessary for knowledge in another.
In fact, there are so many fields and subdisciplines now that it has become incredibly difficult to become a polymath (in the quite literal sense of the term) in the vein of Euler or Gauss or Riemann. The idea of a single person making revolutionary discoveries in both, say, topology and number theory is steadily becoming more remote. If this were to happen, it would have to be someone who spent a long time mastering several disciplines, i.e., an old person. It's a sublime paradox- in the past, incredible leaps of insight that would connect disparate theorems and fields of math could only be made by the young mathematicians with the creativity and the daring to do so (or, if you're cynical, the neuronal plasticity), but now such individuals will still be in grad school learning the ropes.
Look at Andrew Wiles- it took him years to learn enough a
"FDA staff reviewers expressed concern about the number of patients who were left out of the study because they died."
Andrew Wiles' proof of the famous x^n + y^n = z^n equation having no proofs wasn't really just a breakthrough at the age of 41. He'd caught interest on this equation at the tender age of 10, and had been working on the thing his entire career. This was probably the dedication required to solve such a proof. Most people would have given up in the time it took him.
Anyway, read Fermat's Enigma, It's a great book, even though it's about math, it is surprisingly interesting
Anthropic principle: We see the universe the way it is because if it were different we would not be here to see it.
I think that the proposition that mathematical breakthroughs are predominantly made in youth, whether true or not, relates not to the vigour of youth, but to the settling in of dogma.
I've seen this proposition about physicists in more than one lay venue. It was made clear that most breakthroughs in physics were made by minds that had the flexibility to "think outside the box." The gist of the "youth" paradigm is that the more years dedicated to a subject, the more that the thought patterns get set in their ways, precluding the intuitive leaps that change the intellectual landscape.
That being said, Wiles didn't just make some brilliant leaps. He worked damn hard on the details. It may have been more than 10% inspiration for him to prove Taniyama-Shimura (the real achievement for which Fermat was a by-product). Still, from what I've read about his accomplishment, his work was definitely more than half perspiration.
Yes, we can learn the already discovered algorithms by the time we have a Math BS, but by then we are around 22. Our current system does not allow the best to advance at their own pace.
I was reinventing Calculus by 8th grade. I was about to win second place in an international math contest. (I was beaten by a 9th grade Canadian.) I usually ignored whatever was being taught in Math class, since I could literally get an A without waking up.
I was attempting to find the area under a curve defined by a formula. It seemed appropriate to do the work in math class. One day, my eight grade math teacher asked what I was doing. I showed him my current theory. He told me that there was already a proof that it was impossible, so I moved it from active work to the "known impossible, but cannot stop trying" category that includes a simple formula for discovering factorials.
If he had mentioned the word "calculus", I would have researched what was already done and continued with new discoveries. Or he could have encouraged me to repeat the discovery. Instead, he told me it was PROVEN IMPOSSIBLE.
Personal note: This was an important event in my life, because a few years later they tried to teach Pre-Calculus. I immediately absorbed the entire book, and then taught myself Calculus. But I could have done that a few years earlier. And it was the first time that I had proof an authority figure lied to me. The realization that adults have no clue even in their specialty was a major part of my maturing. Now I question facts even when the person giving them is the "top authority".
If our education system helped students that showed an aptitude for math to advance at their own rate, they would probably be finding better algorithms for known problems, with the possibility of discovering something new, as a teenager. Tiger Woods specialized in golf starting at age 3. Most Ice skaters, gymnasts, and dancers start before they are 6. Why should mathematicians need to wait until college before specializing?
---
Off-topic details: I was reinventing Newtonian Calculus. Newton invented a system about the same time the current system was discovered by the French. Both systems were used for a time, but further advances (Differentials) were only possible using the French version, so Newtonian Calculus was dropped. So it was unlikely my redicovery would help advance today's knowledge, since it was on a dead branch.
I spend my life entertaining my brain.
When a mathematician is in grad school or fresh out of it, she wants to publish as much as humanly possible, because having a 15 page CV helps one get tenure at a good university. So just about any thought she has that adds a tiny bit to the sum knowledge of humanity, she'll send to a journal. This is not to say she's not doing good work, just that she's publishing early and often. But that's what the tenure granting committees look for, so what else should she do?
But when she gets older, she can settle down and try to tackle harder and more time-consuming problems--that's one of the reasons for the tenure system, after all. So she may not look as productive, but she's contributing her time to mathematics in just as important a way as she did when she was younger. Also, her experience will allow her to supervise research more effectively, and she'll find that her time is well spent supervising a number of graduate students, giving them advice and help in their research.
On another note, remember that the vast majority of professional mathematicians will never solve a famous problem. And yes, every young mathematician tries to solve the Riemann hypothesis, but as he grows older he learns to spend less time on problems on which he's unlikely to make progress. There are exceptions to this, like Andrew Wiles. (And personally, if I had been on his post-tenure review committees during those 7 years, I'd have wanted to know what he was doing to justify a salary: mathematicians very rarely keep their work secret like that.) But while a mathematician in his 20s may be encouraged to try long-unsolved problems, he tends to grow out of it unless he's brilliant enough to have success with it.
Gates' Law: Every 18 months, the speed of software halves.
Prime numbers are exactly what Alan Greenspan says they are -S. Minsky
"But this is only because your basic mathematical education fucked up your brain."
No, actually, it is because of our world and our perceptual makeup. We live and interact in 3 normal dimensions (time is special form a perceputal point of view). When you look at something in the real world, you see three dimensions. Be it an inherant thing, a learned thing, or some combination of the two, you are equiped to deal with 3-dimensional perception.
Whenever you deal in higher space, you are limited by that in terms of visual representations. If you want to look at a 4D fractal you have to do it in 3D. You can do it is a bunch of 3D slices, a 3D image that you can dolly around the 4th axis, whatever, but you are still only going to see a 3D slice of it since there is no way to directly percieve more.
No way, dude. The original poster who said "A century ago, mathematics was primarily a new field" was way off base, and the follow up isn't any closer. Sophmore engineering students are pretty amazing, I know -- check out those concrete canoes! -- but their math curriculum encompasses about one percent of the math available a century ago.
The last person who might possibly have mastered the whole of mathematics as it existed in his era was Henri Poincare'. Incidentally, he did much of his most memorable work just about 100 years ago. The suggestion that today's undergrads might have a comprehension comparable to his, is just silly.
You can learn more about it from this book.
Happy people make bad consumers.
The article has a valid point. There is indeed an uphill battle against the popular notion that mathematicians are worn out by the time they are forty. But there is a reason for it to be this way: history. The fact remains that many of the legendary exploits of the people in the pantheon of mathematical heroes, particularly in the seventeenth through nineteenth centuries, were accomplished when the men (sadly, with few notable exceptions like Agnesi, Marie du Chatelet, and Sophie Germain, women remain anonymous) were in their late teens and early twenties. Gauss established most of the underpinnings of modern number theory in his mid-teens, publishing his authoritative tome on the subject, Disquitiones Arithmeticae, when he was only sixteen years old. Newton derived the vast majority of his relevant work in his early twenties and spent the rest of his life ruminating on religious matters, holding political office (including a seat in Parliament and running the Royal mint), and dabbling- and eventually poisoning himself into insanity- in alchemy. Similar stories hold for other eminent mathematicians (e.g., Pascal, Descartes, Riemann, Ramanujan, just to name a few) some of whom died while young. What is so often overlooked is that many of the prominent mathematicians in history- e.g., Newton, Gauss, Euler, and several of the Bernoullis, and Weierstrauss among them- remained mathematically formidable in their later years (Newton's invention of the calculus of variations relatively late in his academic career is one such example) and contributed many results that have revolutionized numerous fields in mathematics and physics. This oversight, in the popular consciousness at least, perhaps illustrates the fundamental flaw of relating age to mathematical brilliance: mathematical history has been transmogrified into mathematical mythology. That this should happen should come as no surprise. After all, is there not something romantic about a young mathematical hero opening up new vistas in knowledge (that there are instances of them dying in a metaphorical "blaze of glory" while still in their ascendancy compounds the heroic and tragic elements of the story) in comparison to what's viewed as to the steady, plodding course of old and stodgy men firmly rooted in the 'establishment'? The real tragedy in all of this is that the tenure processes at certain institutions of higher learning are still premised on a gross over-prizing of the brash intuition of youth and the promise of things to come over the gradual maturation and refining of talent; the environment is as unforgiving as it is off-putting and one can only wonder at how many accomplishments of the so-called "late-bloomers" have been denied to society as a result of it.
The article has a valid point. There is indeed an uphill battle against the popular notion that mathematicians are worn out by the time they are forty.
But there is a reason for it to be this way: history.
The fact remains that many of the legendary exploits of the people in the pantheon of mathematical heroes, particularly in the seventeenth through nineteenth centuries, were accomplished when the men (sadly, with few notable exceptions like Agnesi, Marie du Chatelet, and Sophie Germain, women remain anonymous) were in their late teens and early twenties. Gauss established most of the underpinnings of modern number theory in his mid-teens, publishing his authoritative tome on the subject, Disquitiones Arithmeticae, when he was only sixteen years old. Newton derived the vast majority of his relevant work in his early twenties and spent the rest of his life ruminating on religious matters, holding political office (including a seat in Parliament and running the Royal mint), and dabbling- and eventually poisoning himself into insanity- in alchemy. Similar stories hold for other eminent mathematicians (e.g., Pascal, Descartes, Riemann, Ramanujan, just to name a few) some of whom died while young.
What is so often overlooked is that many of the prominent mathematicians in history- e.g., Newton, Gauss, Euler, and several of the Bernoullis, and Weierstrauss among them- remained mathematically formidable in their later years (Newton's invention of the calculus of variations relatively late in his academic career is one such example) and contributed many results that have revolutionized numerous fields in mathematics and physics. This oversight, in the popular consciousness at least, perhaps illustrates the fundamental flaw of relating age to mathematical brilliance: mathematical history has been transmogrified into mathematical mythology.
That this should happen should come as no surprise. After all, is there not something romantic about a young mathematical hero opening up new vistas in knowledge (that there are instances of them dying in a metaphorical "blaze of glory" while still in their ascendancy compounds the heroic and tragic elements of the story) in comparison to what's viewed as to the steady, plodding course of old and stodgy men firmly rooted in the 'establishment'? The real tragedy in all of this is that the tenure processes at certain institutions of higher learning are still premised on a gross over-prizing of the brash intuition of youth and the promise of things to come over the gradual maturation and refining of talent; the environment is as unforgiving as it is off-putting and one can only wonder at how many accomplishments of the so-called "late-bloomers" have been denied to society as a result of it.
... that is almost totally abstract from math, but a valuable life lesson. "Authority figures" can and will lie to you, either a lie of ommission, a lie through ignorance (as your case sems to be), or a deliberate lie from another agenda you may not be privy to. With myself at a young age it was politics and "the news". What clued me was what I read and the "popular perception" that "everyone knows",as opposed to then getting the real information from some connected people who would be classed as "insiders" in government, some relatives, some just interesting adults who I think the notion of someone so young being interested in some subjects was enough to throw them off and perhaps they told me things they wouldn't have told an adult, but..I remembered, added it to the mix. Once your eyes are opened, you may see clearer. Removing the blinders is the hardest part for most people I think,or to even notice they have the blinders on.
Some people never even do that.
Ok, I'm a man, and I'm getting oldish (40) but it seems to me that the most brilliant of all the mathematics students (undergrad and post-) at "my" university are mostly female. And not necessarily under 40, either.