Recent practical advances

Question

I love interesting and deep mathematical results, but on the other hand I cannot object when someone says that most likely all these complicating abstract theorem will not make a change to human kind (apart from more complicating math schedules ;) )

So I'm wondering what were mathematical results from the last decades that were put into real practical use - I mean there would be a noticeable difference without them (this most of the time can be translated to less productivity or money)???

(maybe excluding advances in numerics and algorithms which is easy to imagine. also proving theorems which give insights but yet dont change the world doesnt count.)

I heard about wavelets as one example. Maybe there is something in cryptography? What else? Is there something that seriously is likely to make a change during this century?

Answer 1

There are serious applications of algebraic topology in medical imaging and in robotics. If you want to learn about applied topology, a good place to start is Robert Ghrist's webpage -- he's got some free textbooks and things on there.

http://www.math.upenn.edu/~ghrist/

Answer 2

Take a look at this.http://en.wikipedia.org/wiki/Millennium_Prize_Problems

I feel some of the unsolved problems in math are world changing and might help humanity in one way or the other.Example the poincare conjecture which was solved recently by perelman might be used extensively to understand shapes of different kinds.some say it might be even used to understand the shape of the universe.

This is also interesting.http://weusemath.org/

Answer 3

Perhaps compressive sensing qualifies. For accounts of recent progress in mathematics see the series What's Happening in the Mathematical Sciences . The chapter on compressive sensing is here.