Slashdot Mirror
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."
Check it out over at Simon Singh's website. Fermat's Last Theorem is great reading, not to mention The Code Book if you fancy cryptography, technology or just drama.
Not really,
Before the 20th century, science was just a wealthy-men's hobby and the they usually lived longer than the average people of that time.
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.
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.
-- Support Ometz le-Serev.
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
DMCA - Chilling free speech since 1998.
A Lie group is a set that has a multiplication operation defined on it (giving it a group structure) and has a topology defined on it (giving it a manifold structure) in such a way that multiplication is a continuous operation (so if y is close to x, then z*y is close to z*x for all z). For example, the unit circle in the complex plain, with the usual multiplication operation is a Lie group, with the topology being just the induced topology from the metric on the complex numbers (so two points on the circle are "close" to each other if they are "close" to each other in the plane in the usual sense).
A simple example of an algebraic variety is the complex plane itself. In general, an algebraic variety is something that locally looks like the set of zeros of some function ring, with some global compatibility conditions.
A function is "holomorphic" at a point in complex n-dimensional space if there is a neighborhood (think "little disk") around the point in which the function can be written as a power series (so it has a Taylor expansion around that point). Non-holomorphic means that no such expansion exists; for example the function f(z) = |z|^2 on the complex plane is not holomorphic.
Being 3/4 of a way through an engineering degree is not likely to help much, here. Algebraic varieties typically do not make an appearance in people's educations until they get to graduate school in mathematics; the other two concepts may appear in upper level physics or mathematics classes, but are of almost no use in engineering.
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.
... 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.
The mathematical community already recognizes you're probably "washed up" by age 40.
In fact, the Fields Medal, which is recognized as the equivalent of a "Nobel Prize in Mathematics", has the condition that "...the awards recognize both existing work and the promise of future achievement, it was agreed to restrict the medals to mathematicians not over forty...".
Supposing you were a typical Math graduate student who finally gets awarded his/her Ph.D. by age 26 or so, that only leaves about ~14 years to figure out something sufficiently mathematically mindblowing enough to earn a Fields Medal for, in between dealing with the hassles of competing for any of the scarce number of entry-level math postdoc/researcher/assistant professorships that you hope will eventually lead to a tenure-track full professorship.
No wonder some of the math professors I know just go around muttering bitterly about their work and the only real hope lies in recruiting new graduate students with the hope that a Good Will Hunting-type genius will show up.