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Is number theory more natural than calculus and kinematics?
By Thomas Mooney (P3048) on Sunday, October 15, 2000 - 07:44 pm:

All the calculus and kinematics is good and all but I just had a thought that the only natural maths is Number theory, topology etc. You know its like this is the maths of Gods universe (thus is very deep and complicated) and is not a synthetic man creation. What I mean by this is that the foundations of Kinematics is abitrary unlike the foundations of number theory which is not invented like areas such as kinematics but which is discovered. What do you think. Also for the first time when I read a number theory book , I felt as though I had already the entire contents inside my mind and that it was the most natural thing in the world to me . It just had to come out. Has anyone else felt this?.

By Dan Goodman (Dfmg2) on Monday, October 16, 2000 - 12:15 am:

I'm not so sure number theory is any less arbitrary than physics, it seems to be very much rooted in our experience of the world, for instance 1 lemon + 1 lemon = 2 lemons, etc. You might be right about something like group theory, where the assumptions are absolutely minimal, but not for number theory.

By Sean Hartnoll (Sah40) on Monday, October 16, 2000 - 01:33 pm:

In fact, I have always found number theory artificial and the results more like curiosities than deep relations, but certainly many of the 'great' mathematicians would agree with Thomas. As for physics, as one does more advanced stuff, the number of assumptions gets smaller and smaller and also more natural. Now, to make the statements more natural you need to use more powerful mathematics. So for me, the 'natural' mathematics are those that give an elegant description of phyiscs... so if we are counting sheep, then the natural numbers are the place to go, but if we want to do GR, the theory of differential manifolds becomes the most elegant and profound way of stating things, and for QM we need the whole apparatus of infinite dimensional vector spaces (Hilbert Spaces), etc.

Perhaps something else that is 'natural' is the way much of maths ends up being related, a simple example if the fundamental theorem of algebra (that a polynomial in the complex plane has a solution), this can be proved straightforwardly using complex analysis but can also be proved via a topological approach or also using group (Galois) theory.

Sean