Topology isn't for everyone, but knowing the difference between your coffee cup and a doughnut is an essential workplace skill.
However, algebraic topology may be closer to us than you think. Drones, self-driving cars, and semi-autonomous AI are going to need it. And if you code, you're going to have to understand it. A little.
Unconventional mathematician Robert Ghrist rejects his field's "hippie aesthetic" in favor of suits and ties, loves medieval literature, reversed the usual way of teaching calculus in his popular MOOC, and is using one of mathematics' most abstract disciplines—algebraic topology—to solve real-world problems in robotics and sensor networks.
(Score: 5, Funny) by KritonK on Tuesday July 07 2015, @07:52AM
What difference? Coffee cups and doughnuts are homeomorphic [wikipedia.org] surfaces with a genus [wikipedia.org] of one. Even I know that, and I'm not a mathematician!
(Score: 2) by Dr Spin on Tuesday July 07 2015, @10:10AM
The difference is: <drum roll> Coffee on the nuts or not!
Warning: Opening your mouth may invalidate your brain!
(Score: 3, Funny) by FatPhil on Tuesday July 07 2015, @10:45AM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 0) by Anonymous Coward on Tuesday July 07 2015, @02:59PM
Neither the coffee cup nor the doughnut is a surface. Both are solid bodies with a non-empty interior. Although I'm not sure whether they are open or closed sets.
(Score: 2, Informative) by khallow on Tuesday July 07 2015, @07:07PM
Neither the coffee cup nor the doughnut is a surface. Both are solid bodies with a non-empty interior.
This is an important point. There are topologically distinct objects with the boundary of a torus (for example, the doughnut and a nontrivial knot bulked up with a little third dimension).
Although I'm not sure whether they are open or closed sets.
Depends precisely on whether you completely exclude the boundary or completely include it.
(Score: 2, Interesting) by khallow on Tuesday July 07 2015, @07:13PM