31–40 of 73 posts
Most people use math less and less (even your average cashier will have issues if the machine isn't working). Will Myron Aub give us the feeling of power back? http://downlode.org/Etext/power.html by Isaac Asimov on just this topic.
I am a cashier. Never use math. I doubt anyone outside academia and parts of industry ever uses math in its proper sense.
Earlier quoted context omitted.
But sometimes the connection between "beautiful art project" and "practical tools" is totally unexpected. We often invest time in projects that seem simply like "beautiful art", and then much later stumble upon something practical. I think a great example of this is cryptography. The foundations of it come from number theory (prime numbers, modular arithmetic, elliptic curves), but the subject of number theory, befor…
That's a popular meme but its mostly false. See http://lesswrong.com/lw/4kt/the_value_of_theoretical_researc... The vast majority of "useless" mathematics really do turn out to be useless. In the rare exceptions, there's not much evidence that doing the work beforehand is actually an advantage. E.g. Einstein wasn't aware of most of the work on non-Euclidian geometry before developing relativity IIRC. Stuff like prime…
That's the worst example you could find, because Einstein didn't develop the mathematics for general relativity. He relied on the math invented in the XIX century for non-Euclidian geometry. If nobody had though about such a "sillY' geometry with "no practical value" it would probably take much longer because the necessary results would be out of the reach for Einstein.
Joy.... "Like having your brains smashed out by a slice of lemon wrapped around a large gold brick."
Earlier quoted context omitted.
>"The best way to teach real mathematics, I believe, is to start deeper down, with the elementary ideas of number and space. Everyone concedes that these are fundamental, but they have been scandalously neglected, perhaps in the naive belief that anyone learning calculus has outgrown them. In fact, arithmetic, algebra, and geometry can never be outgrown, and the most rewarding path to higher mathematics sustains thei…
> I've been starting into real analysis myself via Pugh's textbook[1] after not taking a serious math class since multivariable calculus Do you have recommendations for other books? I stopped at multivariable calculus as well. For what it's worth those yellow Graduate Texts in Maths books feel like reading TaoCP or CLRS; I'm looking for more approachable textbooks. I feel like I'm not even up to the 1800s, math-wise,…
Integrate concise and effect explanations into the relevant Wikipedia articles and you at least give future generations a good head start on understanding these things.
I read the SA article the blog refers to and I couldn't decide if that particular colossal theory on symmetry was just an isolated incident or that "deterioration" is really happening to many disciplines/theories of math. It is certainly an obvious fact that things become popular and then eventually forgotten and then sometimes brought back. There is also different levels of understanding: breadth vs depth. I recall…
Suppose there just isn't enough interest in the younger generation of mathematicians to study the proof, even if the old guard are able to organize it better before they retire. Then we may reach a situation in which CFSG will still be used as a proved theorem and not a conjecture - because it's so powerful and important in many fields of math - but its proof will be lost to collective memory. I'm not sure, but I think that state of affairs might be without precedent.
(Here's a quote from Gian-Carlo Rota's _Indiscrete Thoughts_ on forgotten and rediscovered math:
"The history of mathematics is replete with injustice. There is a tendency to exhibit toward the past a forgetful, oversimplifying, hero-worshiping attitude that we have come to identify with mass behavior. Great advances in science are pinned on a few extraordinary white-maned individuals. [...]
One consequence of this sociological law is that whenever a forgotten branch of mathematics comes back into fashion after a period of neglect only the main outlines of the theory are remembered, those you would find in the works of the Great Men. The bulk of the theory is likely to be rediscovered from scratch by smart young mathematicians who have realized that their future careers depend on publishing research papers rather than on rummaging through dusty old journals.
In all mathematics, it would be hard to find a more blatant instance of this regrettable state of affairs than the theory of symmetric functions. Each generation rediscovers them and presents them in the latest jargon. Today it is if-theory, yesterday it was categories and functors, and the day before, group representations. Behind these and several other attractive theories stands one immutable source: the ordinary, crude definition of the symmetric functions and the identities they satisfy.")
“In mathematics and theoretical computer science, we read research papers primarily to find research questions to work on, or find techniques we can use to prove new theorems.” This is why figuring out an elegant, concise, and powerful set of mathematical models which apply to multiple domains, and then devoting effort to simplifying, organizing, and explaining those ideas in an accessible way is so important. Incent…
> This is why figuring out an elegant, concise, and powerful set of mathematical models which apply to multiple domains, and then devoting effort to simplifying, organizing, and explaining those ideas in an accessible way is so important. This reminds me of this Von Neumann quote about the importance of mathematics having an 'empirical source': — I think that it is a relatively good approximation to truth—which is mu…
I'm only nitpicking because I recently started compiling a list of interesting quotes and intend to save this one :)
“In mathematics and theoretical computer science, we read research papers primarily to find research questions to work on, or find techniques we can use to prove new theorems.” This is why figuring out an elegant, concise, and powerful set of mathematical models which apply to multiple domains, and then devoting effort to simplifying, organizing, and explaining those ideas in an accessible way is so important. Incent…
But sometimes the connection between "beautiful art project" and "practical tools" is totally unexpected. We often invest time in projects that seem simply like "beautiful art", and then much later stumble upon something practical. I think a great example of this is cryptography. The foundations of it come from number theory (prime numbers, modular arithmetic, elliptic curves), but the subject of number theory, befor…
That's like saying that we should randomly start drilling holes in the ground because sometimes we will strike oil.
people arguing for it usually ignore the silent evidence of research that lead nowhere and also, more importantly, the potential research accomplishments those people could have acheived if guided to work on different problems.
Earlier quoted context omitted.
Most of the Wikipedia articles on technical subjects, and especially on mathematical topics, are terrible as introductory exposition. They are jargony, highly technical, and self referential. They usually contain much that is irrelevant, and they almost never properly explain the context for an idea. The main problem is that Wikipedia articles are tiny and atomic, so it’s difficult to synthesize and organize ideas in…
I think language and symbology is at the core of why they are so impenetrable. One major sin is taking new concepts and ideas and putting the primary discoverer's name on them. Such names yield no clue as to the interpretation or application of the idea itself. Another problem is the symbols used in certain mathematical texts. Everyone who uses them treats them like they're universally understood, but in reality the…
Integrate concise and effect explanations into the relevant Wikipedia articles and you at least give future generations a good head start on understanding these things.
Most of the Wikipedia articles on technical subjects, and especially on mathematical topics, are terrible as introductory exposition. They are jargony, highly technical, and self referential. They usually contain much that is irrelevant, and they almost never properly explain the context for an idea. The main problem is that Wikipedia articles are tiny and atomic, so it’s difficult to synthesize and organize ideas in…
Yet they are trivial(and often more helpful) as compared to the arcane material in a math text.