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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.
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
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.
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 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.
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
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 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.
Well, sorry teach, I do not recall anything from algebra that was ESSENTIAL for Calc.
Eh?
Can you demonstrate exactly how you'd go about calculating a limit without knowledge of algebraic manipulations? How about deriving/proving one of the rules for taking derivatives? What about any but the simplest of symbolic integration?
The only thing I can think of that you *can* do in calc without at least some knowledge of algebraic manipulation is taking simple derivatives. And even then, you'd be doing it without understanding why the rules work, and you'd be unable to do many of the calculations that make derivatives interesting.
There is plenty of more advanced algebra that is taught prior to calculus that teaches complex, laborious methods that are replaced by much simpler, cleaner ones when you learn calc, and you can argue that those could be bypassed. Personally, I found it valuable to learn the non-calc techniques first, both for what I learned for the process and for the appreciate it gave me of the ideas in calculus.
Note to ACs: I usually delete AC replies without reading them. If you want to talk to me, log in.
"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.
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.
Hmm...I think what the other guy was saying is that you may have knowledge of more fields of mathematics than Euler but you certainly don't have more knowledge of any mathematics than Euler. Euler had a vast knowledge of mathematics in many fields. I think that the University in St. Petersburg or some such academic place was still publishing works of his seventy years after his death. That's a lot of mathematics. No, I think it would take you many many years just to get to the same knowledge that Euler did never mind other mathematicians. I myself have a minor in mathematics and have taken enough graduate courses in advanced mathematics and I still would never claim that I know more mathematics than Euler, Gauss or whomever. Gauss probably knew more number theory than I even though I have a love for the subject and know of some advanced techniques.
"sweet dreams are made of this..."