## Is Math a Young Man's Game? 276

Posted
by
michael

from the women-not-invited dept.

from the women-not-invited dept.

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."*
## Not too young (Score:5, Insightful)

A bit like athletes maybe... experience vs. physiology results in a trade off.

## Re:Not too young (Score:3, Insightful)

## Re:Not too young (Score:2)

## I agree, math's a young man's game (Score:4, Funny)

I'm so old, I lost count. Damn wippersnappers and their meaningless symbols.

## Re:I agree, math's a young man's game (Score:2, Funny)

The conventional belief is that most significant mathematical leaps are all made before the age of 30.That sounds about right. According to another study, mathematicians reach their prime just before discovering sex, after which it is all downhill. It will give the old codgers some solace to know that they can expect a brief comeback after their wives

stophaving sex with them.## A young man's game? (Score:3, Interesting)

## It is obvious why this is the case.. (Score:5, Funny)

"Okay Dear I'll mow the lawn now"

I also suspect the growing complexity of screensavers as a factor..

## Re:It is obvious why this is the case.. (Score:5, Interesting)

Thinking, exploration, calculation, research, experimentation--all of these take a great deal of time. Relationships with friends, your SO, and eventually kids require a great deal of this time to keep healthy and strong.If you want smart kids/pets, that takes time as well.

No, I am not saying that one can't be productive or creative once older; however, it just becomes more difficult. Those that do it successfully usually do it though their profession. That is... you can do it though your job if they give you the freedom to do so.

I don't think all of this is so bad... most of us would rather have healthy relationships than awards/accomplishments as we get older.

Davak

## I prove you wrong! (Score:3, Funny)

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.

## Re:I prove you wrong! (Score:2, Funny)

A single example is not a proof. You can use a single counterexample to disprove a statement:

Note, however, that (3) does not prove tha

## Re:I prove you wrong! (Score:5, Funny)

A single example is not a proofEXACTLY!!!The proof comes from the side of the bottle. You should tip the bartender more the

higher the proof.I'm going to hell for that one...

## New field vs. old fields (Score:5, Insightful)

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?

## Re:New field vs. old fields (Score:5, Interesting)

Now, as the article says, you are a graduate student -- and probably not a new graduate student -- before you're even looking at other people's cutting-edge work, let alone doing your own.

## You've underestimated how much math there was... (Score:3, Informative)

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 curriculu

## Re:New field vs. old fields (Score:5, Insightful)

## Re:New field vs. old fields (Score:5, Insightful)

Hmm, so the Greeks, Euler, Descartes, and thousands of other mathematicians don't count? Math is one of the oldest fields I can think of.And yet, someone could learn and understand all of their most important discoveries before they graduate with a B.S. in Math. From what I've read of Andrew Wiles final resolution of Fermat's Last Theorem, it would take years of specialized study to understand.

Brian

## A poor education system does not help (Score:3, Interesting)

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 form

## Re:A poor education system does not help (Score:2)

My dream goal is to set up something like the school in x-men. Not the mutant part, but the school for the gifted.

I know that sounds so ridiculous, but I think it would be beneficial, and would help a lot.

I was so yearning for people to teach and help me when I was young, and I was lucky that I had a great headmaster at school who pu

## Re:A poor education system does not help (Score:2)

German. Not french.## Re:New field vs. old fields (Score:2)

## Re:New field vs. old fields (Score:3, Interesting)

In the middle ages people weren't very interestes in mathematics

Then we finally get descartes, Euler, Fermat end those dudes, who

## Re:New field vs. old fields (Score:3, Informative)

You neglect the contributions of the Arabic and Indian mathematicians at your peril. There's a reason they call them "Arabic numerals," and the word "algebra" comes from the Latin mistransliteration of the Arabic mathematician who first wrote a dicourse on it.

## Re:New field vs. old fields (Score:2)

## Re:New field vs. old fields (Score:3, Interesting)

## Re:New field vs. old fields (Score:2)

## Re:New field vs. old fields (Score:3, Insightful)

Definitely, computational biology (of which genomics is a subset) is a field which requires experience in a number of other fields, and that takes time. I spent eight years in the Air Force as a medic; and medicine is applied biology, so when I started taking bio classes, I had a much better feel for the way living things work than most of my classmates.

And I also did a lot broader work as an undergrad tha

## Phases of Life... (Score:4, Funny)

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

## The problem is with modern mathematics... (Score:2, Interesting)

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

## Re:The problem is with modern mathematics... (Score:3, Interesting)

In the meantime, WTF is a Lie group? WTF is an algebraic varity? Non-holomorphic sounds very impressive, but WTF is it?

You might be right; I've observed that certain Asian groups do seem to have a handle on maths that many Western brains don't, and I doubt it's entirely due to genetics. But if you actually want to change things, as opposed to sounding clever, people have to understand what you're on about. I don't, and

## Re:The problem is with modern mathematics... (Score:3, Informative)

## Re:The problem is with modern mathematics... (Score:5, Funny)

You'll say now: "That's not possible nobody can visualized 4 dimensional spaces."An architect, a physicist and a mathematician were asked whether they could imagine a 4-dimensional space.

The architect said: "That's impossible! I can't draw that!"

The physicist said: "Well, that can be done, if we say that time is the fourth dimension..."

The mathematician said: "Let us imagine an n-dimensional space. Now, let n equal four..."

## Check out "A mathematician's apology" by G. Hardy (Score:2, Interesting)

Here are some nuggets from "A mathematician's apology". (Hope the copyright police are busy elsewhere.)

"No mathematician s

## Re:The problem is with modern mathematics... (Score:2)

Since I wanted to know if you were trolling or if you were seriously trying to contribute something I looked at your posting history.Most of the posts were either classified as trolls or modded up as funny (though the posts seemed very similar to what you said in the post above).

Since I still have not figured out what you are trying to accomplish I have no other choice but to ask you to repost that in a Language atleast some of us can understand.

## Re:The problem is with modern mathematics... (Score:2)

Notice further down, where we start to see misspellings in the post come to light, and enough general inconsistencies. In fact, the parent's point simply has no legitimate claims (obivious to anyone who is even close to understanding the math involved), but everything is just close enough to be misinterpretted (comically) by charletan mathmeticians. A most excellent troll

## Re:The problem is with modern mathematics... (Score:3, Funny)

PretentiousMensa member, beware of the masturbation. For those of you in the first few rows, safety goggles have been provided.## Re:The problem is with modern mathematics... (Score:2)

taughtto solve, vs. the "answer one line later" of The Calculus.Algebra can be relegated to classes dealing with spreadsheets and accounting.

The counter "arguement" I have gotten from Mathematics teachers at all levels boils down to "the proper appreciation of [calc/algebra] will not be gained by t

## Re:The problem is with modern mathematics... (Score:4, Insightful)

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.

## Re:The problem is with modern mathematics... (Score:2)

## Re:The problem is with modern mathematics... (Score:2)

On the other hand, I think most of what is taught as "arithmetic" is useless.

## Re:The problem is with modern mathematics... (Score:2)

"That's not possible nobody can visualized 4 dimensional spaces."

But this is only because your basic mathematical education fucked up your brain.

I think you'll find that the problems that most people have with visualising spaces with more than three spatial dimensions is that our evolution has equipped us with excellent tools with visualising three-dimensional spaces, and in general found no need to help us visualise spaces with more dimensions. This should not really be surprising.

In short, the problem

## Ummmmmmmm (Score:3, Insightful)

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 ter

## Re:The problem is with modern mathematics... (Score:2)

"Indeed most "Joe Adverage" problems can be reduced to Lie/algebraic geometry problems."

No, most Joe Average problems are how to calculate 15% of a tab and how to bottom-line the monthlies on that house you're looking at and none of them reduce to abstract mathematical principles. It's great that there are a generation of brilliant new chinese mathematicians. It has nothing to do with

## Andrew Wile (Score:5, Interesting)

## Re:Andrew Wile (Score:3, Informative)

## Re:Andrew Wile (Score:2)

## Re:Andrew Wile (Score:4, Funny)

## The Book on Andrew Wiles and Fermat's Theorem (Score:2)

I wish he'd written more books; an Amazon search turns up little else than these two.

## Re:What an idiot (Score:2)

on a similar note, I have a proof for the grand unifying equation I just wrote. I'll get around to publishing someday

if I got the story of Fermat's last theorem wrong then this joke won't make since, so just ignore it.

## Re:What an idiot (Score:2)

After his death, his son found the book and decided to publish another edition of it with his father's margin notes included. The margins were full of assorted theorems with no or little proof that Fermat was satisfied with; over the years,

## Whose game? And who said it was a game? (Score:5, Insightful)

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.

## Re: Whose game? And who said it was a game? (Score:3, Interesting)

Hey, would somebody mod this up? I love women, they are so mysterious. I would love an intelligent discussion of the differences between men and women's intellectual development.

## Re: Whose game? And who said it was a game? (Score:5, Insightful)

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

## No Overpopulation Here! (Score:2)

What we need to do is give the world the tools to control their reproduction, and t

## Re: Whose game? And who said it was a game? (Score:5, Interesting)

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.

## Career path (Score:4, Insightful)

## Age or Exposure? (Score:2)

## Life expectancy (Score:5, Interesting)

people usually didnt live

beyond 40?

## Re:Life expectancy (Score:2)

Could it be because not so long ago people usually didnt live beyond 40?No.

The lifespan of a reasonably well-off individual hasn't been that short since the middle ages. Many of the youthful math geniuses of centuries ago died young because of various causes, but many of them also lived into their 70s and 80s.

Also, the fact that "average" lifespan was short during much of history does not mean that there weren't plenty of individuals who lived to a ripe old age.

## Young MAN'S? (Score:3, Insightful)

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)

## Re:Young MAN'S? (Score:3, Insightful)

But it seems to me that we would be much better served if we talked about how to get more women in the fieldIt depends on the reasons that women aren't going into the field. If it is because of some "old boy's club" keeping them down, then that is wrong. If it is because women in general, for whatever reason, don't necessarily want to go down that path then no one should push them on it. Just make it equal for the women who want to be mathematicians.

Women don't generally go to Star Trek conventio

## Re:Young MAN'S? (Score:2)

I find this to be horribly unfortunate. Why is it that for one sex to excel, the other pays a price? This isn't right.

## An evolutionary biologist says... (Score:5, Funny)

Or maybe they got married and their wife nags at them to death and ruins their concentration.

## Re:An evolutionary biologist says... (Score:2)

Or maybe they got married and their wife nags at them to death and ruins their concentration.Speaking from experience, there, matey? *wink* *wink* *nudge* *nudge*

Depending on what the nagging is all about, it might not be a bad thing, you know.

With mathematicians working

"like hell on on their maths", they may benagging about being neglected in the bedroom -- I wouldn't mind being nagged about that...

not at all...

## Re:An evolutionary biologist says... (Score:2, Funny)

## competing with discoveries from the past (Score:5, Interesting)

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 [ams.org] 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).

## Re:competing with discoveries from the past (Score:2)

weremade towards the end of his life and hence career...## Who thinks 40 is not young? (Score:5, Funny)

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.

## Re:Who thinks 40 is not young? (Score:2)

(still like the same age women as a matter of fact)That's because young women are better looking than old women, no matter how old you are.

## flash vs slow advances (Score:5, Insightful)

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.

## Andrew Wiles at age 41 (Score:3, Interesting)

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...

## Re:Andrew Wiles at age 41 (Score:3, Informative)

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.Actually it wasn't learning about the Taniyama-Shimura conjecture that was necessary, it was learning that Ken Ribet had proven that Fermat's Last Theorem was a consequence of the Taniyama-Shimura conjecture. Prove the latter and you prove the former. That didn't happen until 1986

## Re:Andrew Wiles at age 41 (Score:3, Funny)

>mathematical prime.

30 is not prime.

## In the spirit of mathematics: (Score:4, Interesting)

Paul Erdös. Read about him in this [amazon.com] 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.

## Interesting article on Fermat's Last Theorem (Score:2, Interesting)

A highlight:

## "Math" Arrrrrgggghhhh!!!!! (Score:2, Funny)

The abbreviation "math" really grates on me (outside the US it's called "maths"). It's not mathematic, it's mathematic

s.Don't get me started on sulfur either...

Bob

## Re:"Math" Arrrrrgggghhhh!!!!! (Score:3, Interesting)

## Generally it is, there are exceptions (Score:3, Insightful)

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.

## achievements before 30 (Score:2)

## Modern Elders of Science (Score:3, Funny)

realreason that scientists might make more discoveries at advanced age than in past times is simple. Viagra. What's more inspiring than getting some tail?## Wiles' proof of Fermat's theorem (Score:3, Informative)

Anyway, read Fermat's Enigma, It's a great book, even though it's about math, it is surprisingly interesting

## Expounding against the tide (Score:4, Interesting)

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.

## Had to say it (Score:2)

Is Math a Young Man's Game?Well, if virgins are men, then yes.

## Tenure and research productivity (Score:2)

I've worked in and around Academic departments and I can tell you that you can sure see it. The Assistant Professors are busting their butts, late nights and weekends on their research and that immediately changes the day they get tenure.

Some tenured Professors work hard on their research, those that really love the field. People who really love their field are wha

## Same for music? (Score:2)

Notable counterexamples are Haydn of the Classical period, who started writing his best symphonies after 50. Also, there's Beethoven, who wrote the 9th Symphony when fairly old and stone deaf.

A quote attributed to Marvin Minsky: "Ever notice that mathematicians tend to be good at

## You're looking at it the wrong way (Score:3, Interesting)

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.

## Senility (Score:3, Funny)

## No Reason to Live Long? (Score:2)

## I don't think it's biological (Score:2)

But, 10% isn't that bad.

So, I don't think it's biological. I think it's more to do with stuff like spare time, having a drive to do something, lo

## Raising the bar for Artificial Intelligence (Score:2)

There's an ongoing discussion about how "smart" computers have to be before they will be indistinguishable from

## A notable exception. (Score:3, Informative)

You can learn more about it from this [amazon.com] book.

## Frank Lloyd Wright (Score:3, Offtopic)

## Re:thelimitis30++ (Score:5, Interesting)

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.

## Re:thelimitis30++ (Score:3, Insightful)

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, bl

## Re:thelimitis30++ (Score:2)

## Michael outed (Score:2)

## Science, Math, and Age (Score:5, Interesting)

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

Elementsand Diophantus'sArithmetica, eventually followed by a few others like Fibbonacci'sLiber 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 theArithemetica.) 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

## Re:Science, Math, and Age (Score:3, Funny)

Briefly: Einstein is in the audience at a physics conference. The attendee next to him suddenly pulls out a small notebook, jots something down, and replaces it. Einstein asks, "What's that for?"

The other attendee replies, "I carry that in case I have an idea, so I can write it down and not forget it.

Einstein nods thoughtfully and says, "I see. Som

## Re:Science, Math, and Age (Score:2)

He was 26 years old at the time. This is amazing...Furthermore, he didn't have any higher education, let alone a completed degree on any level.

## Re:Science, Math, and Age (Score:2)

## Re:Science, Math, and Age (Score:3, Insightful)

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 mathe