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When I'm asked about math there are a couple of things. Firstly, I ask them about Pythagoras. Most people know of it, and I phrase it in terms of cardboard cu
by RiderOfGiraffes 16y ago
When I'm asked about math there are a couple of things.
Firstly, I ask them about Pythagoras. Most people know of it, and I phrase it in terms of cardboard cutout squares. Take three squares cut from a heavy material, and make them so that A and B together weigh the same as C. Arrange them so their sides lie on a triangle. Not only is it always possible, but the triangle you get always has a right-angle.
Why? How do we know? As it happens, the reasoning as to why it's true is wonderfully elegant, and totally accessible.
Secondly, I ask - do you think mathematicians know about numbers? Here's something. Take any positive number. If it's even, halve it. Otherwise, triple and add one. Keep doing this, and what happens. So far every number anyone has every tried ends up in a ...->1->4->2->1->... cycle. Does it always happen?
No one knows.
Possibly it's useless, but there's a bunch of stuff people thought would be useless, and they've given us micro-processors, SatNav, cryptography, error-correcting codes, and a million other things.
Who knows what will be useful? After all, if we knew what we were doing, it wouldn't be called "Research".
- shasta 16y ago> Possibly it's useless, but there's a bunch of stuff people thought would be useless, and they've given us micro-processors, SatNav, cryptography, error-correcting codes, and a million other things. You're missing part of the argument, which has to do with the nature of the kinds of structures that mathematicians find interesting. Otherwise you can use this reasoning to justify anything at all.
- xyzzyz 16y agoOh, Collatz problem. I usually use Goldbach or twin prime conjectures to explain the difficulty of seemingly simple problems, but come to think of it, Collatz is even better, because it does not involve any complicated concept at all -- Goldbach and twin prime conjectures are about primes, and sometimes people do not even know what primes are.
- rfurmani 16y agoHow about the problem of, given a polynomial equation in at least two variables and integer coefficients, figuring out whether it has any integer solutions. This has directed a lot of modern mathematics and, on the face of it, doesn't seem like it should be so hard. Plus you can build off of this. They may remember that for two variable quadratics the real solutions form an oval or hyperbola or quadratic or two lines. In general you'll get some higher dimensional surface, and the "shape" of it (and how many "holes" it has) is closely tied with how many integer solutions there can be.
- kenjackson 16y ago"How about the problem of, given a polynomial equation blah blah blah blah blah ..."
- RiderOfGiraffes 16y agoIf you try that you get: * What's a polynomial? * What are variables? * What's an integer? * ... a completely blank stare. You're absolutely right about the usefulness, but most people really won't get past the word "polynomial".
- deleted 16y ago[deleted]