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Nearly every aspect of your modern life is fulfilled with help of science and technology that has some basis on concepts formulated in pure mathematics. Historically several topics in applied mathematics have started with abstract origins with little or clue on their eventual application areas during their early years.

I would suggest starting here: https://mathoverflow.net/quest...

If you still are unconvinced, I am sorry for your loss.

Was the output processed for bias? That might explain it. Creating a true RNG is trivial; simply reverse-biasing a PN junction in a transistor will create a good source of avalanche noise which can be converted into a bitstream. It has to be processed to account for bias though, like with the Von Neumann algorithm: https://mathoverflow.net/quest...

Math is also fascinating because of how it can often work around impossibility proofs.

E.g., what class of polynomials is solvable depends on what elementary functions are allowed. With Jacobi theta functions, you can exactly solve quintics.

http://mathoverflow.net/questi...

For another example, with cosine and acos, you can exactly solve cubic polynomials, w/o using cube roots. Better, if the solutions are real, then the solution does not require imaginary numbers, unlike if you solve with cube roots.

The integers extended by some irrational, say sqrt(2), requires use of real numbers but does not involve uncountable infinities or infinite information.

Only if you're limiting the accepted irrational numbers to a countable subset of R. That's not very useful. For example, it was demonstrated in a paper a few years ago that if you could have infinite precision real weights for the connections of an artificial recurrent neural network, that would allow super-Turing processing. However, your restriction would break that and any other such approaches (and, of course, physics also breaks it -- such a thing cannot exist in the universe -- which was my point).

It is just applying logical rules on various abstract structures. There is no requirement that they be "real" in the sense of being the result of some measurement in the real world. That also doesn't require assumptions beyond basic deductive logic working.

You seem to have missed the point. I was saying that humans cannot solve non-computable problems in the general case. Mathematicians have the same theoretical limits as a digital computer. The "just applying logical rules on various abstract structures" is not solving non-computable problems (siome of the simplest examples of these are listed in http://mathoverflow.net/questi... ); it's an action that can be mapped to a computational process (and even in cases where said process cannot be effectively simplified beyond an ab initio molecular dynamics simulation of mathematicians' brains and their environs, it's still computational).

Libertarians recognize rational thinking

i didn't know that was part of the definition of libertarianism, sounds like a "no true scotsman" fallacy, but let's encourage your embrace of rationality, because that's what i do when i say what i do

Can we apply the same reasoning to math & science? Because I always rather liked the idea of dividing when I see a + sign, and calculating a tangent when I see the symbol "cos". Because words change, man. Who cares that you've defined 'tan' and 'cos' certain ways? I like to swap them around!

wait, you're not doing rationality anymore, you're doing appeal to authority. you constructed a lame analogy that doesn't work because we are talking about political meanings which is not rational, at all. but to completely dismantle your lame analogy, yes: there are plenty of words in math whose meaning is ambivalent and changing:

http://mathoverflow.net/questions/7389/what-are-the-most-overloaded-words-in-mathematics

you have to understand human language. you have to get used to the fact that you can't, don't, and will never control the meaning of a word. you seem like someone who has invested a lot of passion in a starkly defined political philosophy which absolutely has to mean libertarianism. in your mind, sure. in society at large? no, sorry, you don't get to do that. you will never ever get to do that. especially an overloaded word with a complex meaning like "libertarianism" which will most certainly change in meaning over the passage of time, and most certainly does, and has. someone calling themselves a libertarian in the 1970s would look at you like an alien

from this page

http://en.wikipedia.org/wiki/Libertarianism

here's the third sentence, it should make your brain explode:

There is no consensus on the precise definition of libertarianism.

sorry dude

To original poster, I read the articles on: http://sciencedaily.com/ (all sciences- this is by far my favorite) http://spectrum.ieee.org/computing (computer science) http://mathoverflow.net/ (though this one is usually way above my head) http://extremetech.com/ (engineering) I also have Scientific American subscription, and although it occasionally has very interesting physics articles (the accuracy of which I couldn't tell you), I think there are better magazines.

Are you sure you want to do that? I can understand typesetting math in the browser, but typesetting entire TeX documents?
There's already an AMS-endorsed way of typesetting TeX math (Javascript-based) called MathJax (http://www.mathjax.org/), and it works pretty well (well enough for sites like http://mathoverflow.net./

There is an on-going discussion of note taking during lectures over at Math Overflow.

See: http://mathoverflow.net/questions/12638/taking-lecture-notes-in-lectures, especially Anton Geraschenko's comments on Live TeXing. It works!

See http://rjlipton.wordpress.com/2009/11/12/more-on-mathematical-diseases/ for unsolved problems which are all really simple and also really addicting to think about. For many of these, the best way to stop thinking about one of them is to start thinking about another.

I'm actually a bit puzzled as to why this is a Slashdot article. If I wanted to point to something new in the way people are doing math I'd point to Math Overflow http://mathoverflow.net/ where many professional mathematicians, grad students and others are active. It is essentially a centralized system for people to post math questions and get math answers from people who know. It is very cool. It also is highly addictive to read.