8 math talks to blow your mind

Here is something for you mathophiles. There are several talks on different areas of mathematics.

TED Talks

Here is a mind bending video on the different sizes of infinity. There are more at the source link.

Mathematics is all about model building, creating the tools with which we operate on increasingly complex ideas. As such there is no (or just not yet) absolute "correct" way to explain things. Some models are more useful than others.

For example let's take the infinity thing. Sure, one can say that [2, 4, 6, 8...] has the same size as [1, 2, 3, 4...] because the function F(x) = 2x produces a one-to-one match. But while any natural number can be used for x not any natural number can be expressed as 2x. In other words, the input set is larger than the output set. Some people (perhaps most people) would say that it is more intuitive.

Instead of saying that they are of the same size, it is more useful and interesting to say that [1, 2, 3, 4...] is 2 times the size of [2, 4, 6, 8...] because of the coefficient of 2. As a rule, any function F(x) = Ax for some natural number A produces an output set whose size is 1/A of the input set, when we are dealing with natural numbers.

This is what happens when mathematicians think too much and get too deep.

3.142 to infinity and beyond!

Ah, I love things like this. I've been listening to university lectures on game theory, and hope to take a course in it after I finish my current coursework (because it's going to be too much trouble to register at two universities at the same time.)