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Sun 25 Feb, 2007 04:04 pm
what is the most complex branch of mathematics -the one even hardcore mathematicians fear?
also why is philosophy and mathematics linked as one is about thoughts and ideas and the other is a "exact science" dealing with numbers - are accountants therefore philposhers? :wink:
ever seen a criminal investigation type of series called NUMBERS? if you havent, i suggest tuning into that sometime. the calculations the mathmatician performs on his chalkbourd are nitemarish...there is no way those formulas are easy to deal with...
The show NUMBERS is pure fiction. Any resemblance to real math is coincidental. There are a couple of things in that show that have something to do with real life mathematics, but the writers take a lot of liberties and you should take nothing from the show except entertainment. I do still enjoy the show, even though I know enough math to recognize they are mostly BS'ing.
I don't think that there is anything that mathematicians "fear". There are many areas that are interestingly difficult-- it depends on ones specific field to decide which ones are most interesting.
One interesting problem is factoring. The math that encryption is based on is assumed to be unsolvable... but no one has proven that it is unsolvable. If someone figures out how to factor numbers very quickly, it means that all of the codes that we use to send credit card numbers, or keep people out of files, or to send military communications ... would suddenly become readable to everyone.
ebrown_p wrote:One interesting problem is factoring. The math that encryption is based on is assumed to be unsolvable... but no one has proven that it is unsolvable. If someone figures out how to factor numbers very quickly, it means that all of the codes that we use to send credit card numbers, or keep people out of files, or to send military communications ... would suddenly become readable to everyone.
factoring is also a form of encryption? (if i read that right) if that means what im doing now in my math class is considered a type of mathmatical encryption i guess its true when people say you learn something new everyday...there has to be 2 different types of factoring b/c i cant see what im doing now can make military documents readable...
Wikipedia article on integer factorization
Quote:
Prime decomposition
By the fundamental theorem of arithmetic, every positive integer has a unique prime factorization. Given an algorithm for integer factorization, one can factor any integer down to its constituent prime factors by repeated application of this algorithm.
Practical applications
The hardness of this problem is at the heart of several important cryptographic systems. A fast integer factorization algorithm would mean that the RSA public-key algorithm is insecure. Some cryptographic systems, such as the Rabin public-key algorithm and the Blum Blum Shub pseudo-random number generator can make a stronger guarantee - any means of breaking them can be used to build a fast integer factorization algorithm, so if integer factorization is hard then they are strong. In contrast, it may turn out that there are attacks on the RSA problem more efficient than integer factorization, though none are currently published.
A similar hard problem with cryptographic applications is the discrete logarithm problem.
Yes. If you can find a quick way to factor very large numbers, you will become very rich and famous (even if you are honest and don't decide to make a fortune through theivery and blackmail). You will also make most of the encryption used today obsolute.
Many mathematicians believe there is no quick way, but this hasn't been proven so no one is absolutely sure.
Tensor calculus is pretty hard, at least for me.
Well Brandon,
You might find a more relaxed calculus is easier and more enjoyable.
ebrown_p wrote:Well Brandon,
You might find a more relaxed calculus is easier and more enjoyable.
I like differential equations and techniques of integration, but I digress.
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