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Thread of top 10 kinky math objects <a target="_blank" href="https://twitter.com/Simmy16242170/status/2041308054528913628" color="blue">x.com/Simmy16242170/…</a>
10. You know we need to start it easy with the classic kinky math object, the leather of math objects. You know it, you love it: it is the Weierstrass function. This function set the standard of kinky math objects and all the nonsense in real analysis that can follow.
9. Should have put Weierstrass above this but I have a bias. This looks so innocuous, like your first time with the spanking paddle before realizing yes it is pain. Enjoy your land of finitely generated groups? Say hello to the earring space, the originator of wild topology.
8. Fat Cantor set I just applied inflation fetish to the cantor set and made it more fucked up. Not only is it still countable, nowhere dense, and empty interior, but now it has positive measure. I'd also like to mention the cantor step function as its kinky incestuous cousin.
7. Petersen graph This graph is like the objectphile. Nothing so taboo, just, weird in in an otherwise normal thing. It doesn't make sense, graphs are supposed to be nice so why is this very particular graph such a common counter-example and ingredient of such?
6. Hopf fibration How can you nontrivially wrap a 3-sphere around a 2-sphere? The hopf fibration finds a way to do so and complicate homotopy groups of spheres. Yet it does it so prettily. The hopf fibration is like shibari, wanting to show an artistic side of freakness.
5. Fourier Series I know, it sounds vanilla. But they're a secret freak. They are happy to play vanilla but look at the smooth lines they form, all made up of kinky curves. They require divergent sum techniques to deal with this kinky expansion. Plus those curves look kinky.
4. Alexander Horned sphere Maybe I've messed up my ordering, but I have a particularly kinky fondness of this space. It reminds me of tentacles. It just showcases how by using the infinite, you can create some very kinky things in topology. Can I be the seedbed of this space?
3. Nonstandard Models Set theory might as well be a game of human centipede, where set theory is used to study the models of sets and models used to study those and so forth. I mean, ZFC has a countable model. Sure. And now actually treating that object seriously? SURE!
2. Exotic R_4 R_4 is like the Folsom gathering of geometry and exotic R_4 are like the exhibitionists. Only for n=4: not 3, not 5, do we have nondiffeomorphic homeomorphic spaces. Despite manifolds being aesthetic like rubber, somehow these topological kinks emerge.
1. Sporadic groups The above kinky objects exist in the human realm of kink. But these kinds of groups are a kink that only a higher Lovecraftian being like Cthulu could know how to enjoy. It is a demonstration our world of desires is merely our own, and greater freaks exist
