What is the most advanced math subject of all time?

Post Reply New Topic

There's one question I always wondered about...

What happens to be the most advanced math subject of all time currently? I honestly don't know since I tried to look it up but no luck was found besides finding a subject called Multilinear Algebra, an advanced course in college that involves multiple dimensions.

If you guys have any subjects that are HARDER than the one I said, please feel free to comment what it is!

I'm really curious to know!

https://en.wikipedia.org/wiki/G%C3%B6de ... s_theorems

I recall a gifted math teacher saying that the brightest minds were working on completeness theorems--until Godel proved you couldn't do that! As I recall, most of us who took his BC Calculus course aced the exam for college credit.

Do you mean 'topic' not 'subject'?

When I was in grad school, the toughest course offered (probably in the entire University) was Real Analysis. It was a two semester course and if you made A's in it back then, you were really doing something.

The toughest I encountered was graduate Topology taught using the Texas Method. I also took Topology using a regular textbook and taught in a normal manner and found it quite pleasant.

I did well enough in the one analysis course I took, along with the two calculus classes I took for engineering--to be admitted to the math Honor Society!

Probably anything that's currently in development, I guess (elliptic curves, functional analysis, knot theory, etc.) It's very hard to say, because "advanced" is a very subjective term that's open to interpretation. Who's to say axiomatic set theory is more "advanced" than high school algebra, for example? By what criteria?

There is no special single branch of mathematics that is harder than all others (than itself).

Chaos theory and non-linear dynamics can bet hair. The theory behind the Navier-Stokes equation is very difficult. In fact there is a million dollar prize for anyone who can come up with a general numerical method that can approximate a solution to the Navier-Stokes to any prescribed degree of accuracy. Navier-Stokes describes turbulent systems.

Topology in its advanced form is difficult (algebraic topology) and knot theory can be very hard to untangle.

Keep up the replies you guys! I'm starting to see what it could be for what at least one of the most advanced math concepts is!

If you have an answer to this question please comment on this topic!

I think the most advanced is where multiple dimensions and the black holes come into play who knows!

The difficulty can be measured by how hard it is to prove the central theorems and solve the outstanding problems.

I would not venture to introduce a course in Zermelo-Frankel set theory in grade school. In American elementary schools students have a hard enough time with the watered down version of Euclid's Geometry (a subset of Euclid's Elements, Book I). The concept of proof is beyond most school kids and only the ones interested in it go on to advanced mathematics.

"advanced" can mean "cutting edge" - where the latest discoveries are.

Or it can mean "most difficult". Those arent necessarily the same areas of math.

Not a mathematician but had the impression the the current cutting edge in math is fractal geometry. Or maybe that was some years ago. and something else is now.

You may find "Combinatorics" a very hard subject, because you do a lot of induction , contrary to other maths where you mostly do deductive reasoning.
https://en.wikipedia.org/wiki/Combinatorics

I think this is the first math where I had to do inductive proofs.

Fractal geometry is a subset of chaotic dynamics which also includes turbulence. To this day there is no general way of approximating a solution (numerically) to the Navier Stokes equation. The is currently a one million dollar prize for anyone who can come up with a general numerical method for solving the Navier Stokes equation which is a classical math differential equation that describes turbulent flow perfectly. The problem is there is no general numerical method that solves all cases.

Taking the definition of "advanced" and accepting computability in computer science as sufficiently advanced and difficult, not to mention mathematical. P vs NP is up there, but you can't bring that up without mentioning that it is a member of significant "bounty" problems - The Millennium Prize Problems.

https://en.wikipedia.org/wiki/Millennium_Prize_Problems

A champion mathematician at the moment is Peter Scholze

https://en.wikipedia.org/wiki/Peter_Scholze

Inter-universal Teichmüller theory
https://en.wikipedia.org/wiki/Inter-uni ... ler_theory

If it's taught at college, it's elementary to some people. The most advanced math is the new elliptical theory Andrew Wiles developed in the process of proving Fermat's Last Theorem.

The only "math" that is at deductive is the exercises they give students. That's not real math, that's just application of math.

A: Trickle-down economics in the real world

j/k