# Least Studied Field of Mathematics

1. Apr 7, 2007

### Dragonfall

What field of mathematics is presently the least popular? I'm not talking fields like Euclidean geometry that's 'old and complete', but of fields that are unknown or in its infancy.

Also what about the MOST popular? Number theory?

2. Apr 7, 2007

### SeReNiTy

Algebraic topology is the future, me thinks.

3. Apr 7, 2007

### quasar987

Why do you think that, might I inquire?

4. Apr 7, 2007

### arildno

That is somewhat difficult to know, isn't it?

5. Apr 7, 2007

good one.
lol

6. Apr 7, 2007

### MathematicalPhysicist

i would think something like catastrophe theory and category theory to be the new theories in the past 50 or so years, but is it new enough for you?

7. Apr 7, 2007

### Dragonfall

Relatively unknown. Like this "catastrophe theory" posted above.

8. Apr 7, 2007

### quasar987

What is it by the way? How does "catastrophe theory" stands as a branch of math in its own right?

9. Apr 8, 2007

### leon1127

Quantum Information. A lot of mathematics will go in there; it also requires concrete knowledge from physics, engineering, and chemistry.

10. Apr 8, 2007

### SeReNiTy

Catergory theory is a piece of crap...

11. Apr 8, 2007

### MathematicalPhysicist

quasar, as it's relatively new i myself dont exactly no more than is being described in the web. (such as wikipedia, etc).
but as far as i can tell it's included in applied maths, more specifically to dynamical systems.

12. Apr 8, 2007

### MathematicalPhysicist

this is why it's being implemented in cs and physics, they need this sort of crap from mathematicians. (-:

13. Apr 8, 2007

### Hurkyl

Staff Emeritus
And, ironically given SeReNiTy's tastes, the algebraic topologists need it too. (That's why they invented it!)

14. Apr 8, 2007

### ILEW

I heard algebraic topology was also one of the hardest grad maths courses around. Is that true?

15. Apr 8, 2007

### MathematicalPhysicist

i think that every topic being covered in grad (short for gradient, lol) school is tough, btw how do you want someone to compare courses if as it's not humanly possible to cover all the mathematics courses which are offered by the school. (it's possible but you wont have time to research and specialise in a specific field).

16. Apr 8, 2007

### Crosson

Consider the following differential equation:

$$x'(t) = r - x(t)^2$$

If r is negative the every solution has $x \rightarrow \infty$ as $t\rightarrow \infty$, if r = 0 then x = 0 is a semi stable fixed point, and if r > 0 there are unstable and stable fixed points at x = + and - r respectively.

These changes in the qualitative features of solutions as we vary the parameter r are called bifurcations. When there is more than one parameter, the changes can happen in interesting ways, and this is the subject of catastrophe theory.

Not only is catastrophe theory entirely dead, but it has always been part of the "Nonlinear Dynamical Systems" branch.