Maths is about understanding something the right way. And I'm guessing this kid did not take the seven seconds to do anything complicated. He just factored 32. i.e. 2^5. Then noticed that 999,999,999 + 1 = 1,000,000,000 = 10^10 = 2^10 * 5*10 which clearly contains a factor of 2^5. So 32 goes into 1,000,000,000. So the remainder after division of 999,999,999 by 32 is 31. I think you need about 2 seconds for that once you realise the correct way to think about it. So he took 5 seconds to work out what he should do. Quick kid!

Good point, but sadly faster than light communication allows messages to be sent back in time (due to special relativity). So once we invent FTL communication were going to be more worried about some severe problems with causality than about aliens many light years away.

I'll be saving my champagne for Epoch day 16,384 (otherwise known as 2^14). A little under 4 years to go...

Yes, you are.

Excuse me for replying to my own post. I should also mention that Poincaré's conjecture was not about 'a method for determining whether a three-dimensional manifold is a spherical'. It is simply the question of whether there are non-spheres in 3d which have all loops contractible (for a more accurate description, see the parent). The question about methods/algorithms for determining whether or not something is a 3-sphere is in itself very interesting though.

As someone who's job involves research into geometry and topology, I would like to point out that the summary is wrong in a couple of places. The Poincare conjecture states (in simple terms) that:

Any closed smooth three dimensional space ('manifold') without boundary where all loops can be contracted to a point is 'homeomorphic' (essentially the same as) the three dimensional sphere (that is, the unit sphere in 4 dimensions).

The words "homologous" and "boundless" have little/nothing to do with it.