Here's a list of math jokes. They are compiled from various sources on the internet, including AMS notices, MathOverflow, reddit, aperiodical, and the Dabney spam mailing list. I've tried to credit some of the jokes, along with jokes not from the above mentioned sources, at the end of this page. Almost all jokes are of the question-answer format.
What is green and homeomophic to the open unit interval? the real lime
What is the contour integral around Africa? zero, all the Poles are in Europe
What couldn't the Möbius strip enroll at Caltech? because we require freshman orientation
Why did SO(3) leave Caltech after one week? because it can only do rotation
What do you call a young eigensheep? a lamb, duh!
What is hallucinogenic and exists for every group with order divisible by p^k? a psilocybin p-subgroup
What's yellow, linear, normed, and complete? a Bananach space
What do you call the category of Banach Analytical Manifolds? BanAnaMan
What is brown, furry, runs to the sea, and is equivalent to the Axiom of Choice? Zorn's lemming or the Well-Ottering principle. They're equivalent in the ZF Sea.
What tastes like oranges and is differentiable in the whole complex plane? a clementire
Who knows everything there is to be known about vector analysis? the oracle of del phi
What do you call a function with a negative derivative, that makes things cleaner? Degreasing
What is black and white ivory and fills space? Piano curve
Why did the mathematician name his dog "Cauchy"? because he left a residue on every pole
Why did the Klein bottle's relative start taking off its clothes? it was a Möbius stripper
Or, what doesn't have an orientation and likes taking off its clothes? a Möbius stripper
Why do Maclaurin polynomials fit the original function so well? because they are Taylor made
Why didn't Newton discover group theory? because he wasn't Abel
Why can't you grow corn in Z/6Z? because it's not a field!
Follow-up: Why can't you grow corn in Z/5Z? because it's an abstract mathematical object
Follow-up: I hear Grothendieck once grew corn in Z/57Z, although he had to devise a clever scheme first.
Follow-up: And you can't grown corn in Z/7Z either, because we grew corn in it last year, so you have to rotate the crops and grow soybeans this year.
What is often used by Canadians to help solve certain differential equations? a lacross transform
What did the calculus instructor say to his hungover student? Know your limits, and Don't drink and derive.
Why did the mathematician put his null space in the microwave? to make popcorn! (kernels are hard to eat)
What do you get if you cross a mosquito with a mountain climber? You can't cross a vector with a scalar.
What do you get if you cross a rat with a mosquito? |rat|*|mosquito|*sin(theta)*unit vector
Why did the polynomial plant (whose zeros all had zero real part) wilt? its roots were imaginary
Which family of functions \N->\N is the most excited? multifactorials!!!!!!!!!!!!
Which big cat is good at linearly approximating a differentiable function? a tangent lion or a straight lion
What do you call a destroyed angle that kinda looks like an equiangular quadrilateral? a rektangle
What happened to the indeterminate form that got sick in calculus? It went to the L'Hôpital.
What's purple and commutes? An Abelian grape.
What is purple and all of its offspring have been committed to institutions? A simple grape, it has no normal subgrapes.
What is lavender and commutes? An Abelian semigrape.
What's purple, commutes, and is worshipped by a limited number of people? A finitely-venerated Abelian grape.
What's purple, round, and doesn't get much for Christmas? A finitely presented grape.
Why was 6 afraid of 7? because 7 8 9
Follow-up: Why was 7 afraid of 8? induction
Why was Fibonacci afraid of 5? because 5 8 13
What kind of map would you take with you on car trips? automorphisms
What is an anagram of Banach-Tarski? Banach-Tarski Banach-Tarski...
What is an anagram of Banach-Tarski? Ransack habit
Why did the matrix finally become identical to her conjugate transpose? it was her mission
What does the little mermaid wear? an algae-bra
What is an owl's favorite kind of math? owl-gebra
Why are math books often sad? they have lots of problems
Or, why are math books so swoll? they get lots of exercises
What do you call an angle that is adorable? acute angle
What is polite and works for the phone company? a deferential operator
Follow-up: What fakes politeness and works for the phone company? a pseudo-deferential operator
What do analysts and number theorists throw into the fireplace? (really any mathematician does this, but computer scientists and chemists do not) natural logs
Why do analyists and number theorists like parks? Because of all the natural logs.
What do you call a ring theorist's parrot when it hasn't been fed? poly-"no meal"
Why is it hard to grow large-sized corn in an injective map? the kernels are small
What does the "B" in Benoit B Mandelbrot stand for? Benoit B Mandelbrot
How did the matrix whose eigenvalues summed to zero disappear? It vanished without a trace.
What do you call small, shiny disks which are made with precision? Exact sequins
What do prime numbers and stoners have in common? The higher they get, the more spaced out they get.
Who was the roundest knight at King Arthur's round table? Sir Cumference.
Why did Emil Artin's necklace keep falling off? It had a descending chain condition.
What do you call a lot of money that commutes? A-belian dollars.
At Christmas time, how do you perform the inverse operation to exponentiation? Yule log.
What do group theorists hang on their door at Christmas? Wreath products.
What is yellow and equivalent to the Axiom of Choice? Zorn's lemmon.
What is woolly, spits, and is equivalent to the Axiom of Choice? Zorn's llama.
Why do nurses use 1-to-1 functions so much? Injections.
Why was Gollum obsessed with Z/6Z?
Why are algebraic geometers always coming up with evil plans? They really like schemes.
What is a pirate's favorite field? R or C.
What is a pirate's favorite measure on a locally compact topological group? Haaaarrrrrr measure.
Where do you grow degree two polynomials? In quadratic fields on quadratic farms.
What do you call a banana with a hole in the middle? A bananulus.
What transform do you apply to turn a sphynx cat into a Norwegian forest cat? The furrier transform.
How do algebraists actually eat their corn? By modding out the kernels.
What is the best response to a harmonic analysis joke? Hardy Haar Haar.
How do algebraic topologists remodel their porch? With deck transformations.
What did the topologist say when s/he wanted to stop playing their hand in poker? man-i-fold.
How do linear algebraists settle arguments about matrix transposes? With a dual.
What did the geometer studying k^n say when asked about their career? It's affine job! (k^n is affine n-space over the field k)
Which LaTeX package should you avoid when you go hiking? Tikz
See also here for some pictures (joint with Matthew Weidner).