Which is the most abstract maths subject? Why ?

Answer 1

All good choices. I'm going to go with Algebraic Topology because it is an abstraction of both topology and abstract algebra, both of which are already abstractions.

Galois is essentially an abstraction on abstract algebra, so I'll give him second place.

Differential geometry ranks up there, but it has so many practical uses in physics (26-dimensional universe theories and such) that I can't put it higher than third.

I hesitate to classify a new set of axioms as an "abstraction". It's not really extracting the relevant data from an old system, it's just rewiring the old system.

All my opinions of course.

Answer 2

Algebraic Topology. Differs from point set topology as we translant spaces into equivalent algebras based on what paths are homeomorphic to. For example a sphere is simply {0} as all paths reduce to a single point. (A dog on a retractable leash could run all over the place and his leash could still retract.) A donut (torus) is Z (the set of integers under addition) . (A dog on a retractable leash could run away the hole several times and thus each path around the hole is the equivalent of adding one.) The Kleine bottle is... I forget. I think it is Z2 (The set {0, 1} under modular addition but I forget why)

Or a graduate course I took called simply "Linear Curves". Sounded straightforward but i was totally lost from day one.

Answer 3

Differential Geometry. Tensors.

Answer 4

Abstract Algebra.

Pls visit this website for detail : http://en.wikipedia.org/wiki/Abstract_algebra

Answer 5

Galois Theory. Why do you think they call it Abstract Algebra?

Answer 6

Topology
See :http://www.chez.com/alcochet/toposi.htm

Answer 7

I've heard there are inconsistent but complete axiom systems that are being investigated. (Since by Gödel's theorem that any axiom system is either incomplete or inconsistent.)