What is the hardest level in math?

Answer 1

Research.

When taking classes, you know that the quetions are based on the material in the book and can be answered using the ideas you already know. When doing research, you don't know which ideas are relevant or whether the problem can even be solved with what you know. You are stepping into the dark and hoping there is something solid there to hold you up. At times, you stumble around for *months* trying to find something to stand on. This is far, far harder than taking any class.

Answer 2

There are a lot of difficult areas of mathematics. But I think it's safe to say some of the hardest areas must be the open questions, because nobody has figured them out yet! Here are some examples.

1. Goldbach's Conjecture: Can all even numbers greater than 2 be expressed as the sum of exactly two prime numbers in at least one way?
2. The Riemann Hypothesis: Do all nontrivial zeros of the Riemann zeta function have real component of 1/2?
3. Twin Prime Conjecture: Are there infinitely many prime numbers p such that p+2 is also prime?

Answer 3

I think the hardest level in math is number theory, where mathematicians try to solve problems such as, "Find a number that is not the sum of A^4 + B^4 + C^4 + D^4 where A,B,C, and D are any integers, including zero." I just made that one up, but that's the kind of thing they worry about.

Answer 4

Usually differential equations, partial differential equations, multiple integrals, and/ or linear algebra. 3D surface descriptions, coordinate transforms, Fourier transforms, and Zernike fits are cool too. Polynomial expansion series get pretty good also. Don't forget advanced statistical processes. These are very powerful.

But in a the hardest level of math is always the next chapter in your book. Keep up with it!

Answer 5

A question of relativity ...... for a person at the entry level, it itself is the hardest, and for a researcher, a level higher is harder. There is no end for any subject.

Answer 6

Well, for me it was Topology and/or Non-Euclidean geometry (lines aren't straight, planes aren't flat, ect...) Now those are grad level 500s in college, if you are talking High School, it would have to be Calc... but if you are not a visual and logic type of person, then Geometry class can suck too!

Answer 7

just speaking of math classes from hardest
calc2
calc1
calc3
differential equations
algerbra/geometry/trig

and not of any very specific topic

Answer 8

Anything that the student sees as "pointless". For me it was topology, for some it will be equations, or calculus, or fractions, or elliptic curves, or complex analysis, or anywhere in between - in short, it's totally subjective.

Answer 9

For me, it was metamathematics (that's the study of mathematical proofs and mathematical logic). But, as someone else said, Topology (especial infinite dimensional Topology) had its moments ☺


Doug

Answer 10

Neocalculus with antiphysic interpolation