# Least Studied Field of Mathematics

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?

Algebraic topology is the future, me thinks.

quasar987
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Why do you think that, might I inquire?

arildno
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Dearly Missed
but of fields that are unknown
That is somewhat difficult to know, isn't it?

MathematicalPhysicist
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That is somewhat difficult to know, isn't it?
good one.
lol

MathematicalPhysicist
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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?

That is somewhat difficult to know, isn't it?
Relatively unknown. Like this "catastrophe theory" posted above.

quasar987
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What is it by the way? How does "catastrophe theory" stands as a branch of math in its own right?

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

Catergory theory is a piece of crap...

MathematicalPhysicist
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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.

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

Hurkyl
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this is why it's being implemented in cs and physics, they need this sort of crap from mathematicians. (-:
And, ironically given SeReNiTy's tastes, the algebraic topologists need it too. (That's why they invented it!)

Algebraic topology is the future, me thinks.
I heard algebraic topology was also one of the hardest grad maths courses around. Is that true?

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

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