The 7 Levels of Mathematics

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Chapters:
0:00 Intro
1:56 Level 1
2:32 Level 2
3:03 Level 3
3:35 Level 4
4:16 Level 5
4:57 Level 6
5:36 Level 7

[the_realtajgames]

I always tell whoever wants to do higher and abstract maths that theyre going into competitive and professional schizophrenia.

[JohnHargis-evyh]

Physics major at Uni. Stuck in between level 4 and 5. have heard horror stories about level 6 but never took any classes on them. Although I will call myself a level 7 because topology was not mentioned.

[revengeofspoon]

There's no way bro got past level 6 in 2nd grade he must be a super genius. I would've killed for that system though, I remember getting in trouble EVERY SINGLE DAY at school and getting sent to the principal's office for goofing off in math class because I already knew the content.

[TyPh]

Level 8 - Arithmetic Geometry.

Sounds like something you'd learn at grade school rather than a subject that demands a working understanding of nearly half of graduate level mathematics.

[GermanSeverin]

I am incredibly jealous you could take algebra in 3d grade.

[haseebahmeds]

2:02 maybe divide's photo is crazy 💀

[parl]

In the thumbnail, S^3 ≃ R^3 ∪ ∞ means that the space of the surface of 4d sphere is isomorphic to the space of real 3-dim space (with added infinity point). For those who wondered.

[gargamel]

Bro is not 19 years old, but the video is amazing ❤😂

[aleatoire_]

Level 8: you got 0 on yout math test but you know that's because the teacher didn't understand 😅

[iAtomic]

I just finished Calculus 3 yesterday. Can’t wait to start Linear Algebra 😃

[kruentis]

End of level 4 bro called me out word for word 😭😭

[farkas]

I am an econ master's student. I was always good at maths, but never really exceptional. For economics, it felt like some difficult tool that I needed to learn how to use. However, everything was weird and arbitrary and I sucked at solving problems because I always made careless mistakes and misunderstood the task. Then, I took real analysis last semester, full of proofs and only abstract shit, I fell in love with mathematics. I am aware that I might be very unique in this sense, but actually, I love the way how you are extremely rigorous about these abstract objects and it is possible to make sense of shit like infinity. This is mind-boggling to me. I also scored a 100% on the exam as finally, mathematics did not involve reading comprehension and stupid calculations.

[J-xj]

When I become an engineer, I think I will be on LVL 4-5, which is fine for me because I will still be still better than 99% in maths with that result.

[Nothingx]

5:47 there are more levels of mathematics and in the 22nd century there will be even more 😊

[patrickgambill]

Level 4 at the end, you talk about matrices and eigenvalues not being helpful. This is how SVD works! You have so many clustering algorithms in machine learning from these. You can solve systems of ODEs (like multiple springs attached to multiple objects), you can use eigenvalues and eigenvectors for image compression, and so much more!

[noone.]

I am 19 and probably at Level 4 transitioning to 5, and I absolutely love mathematics. I love mathematics, because it is never wrong. For example, it is crazy to think how Taylor expansions work! I mean defining cosx, sinx, e^x etc. in the form of polynomial functions is crazy asf, Physics and Mathematics are love❤️

[FabiFuu]

Level 1: learning counting

Level 5: learning counting (by rigorously define natural numbers and successor function)

Level 6: learning counting (ordinal numbers) all the way up to the omega, omega + 1, ..., epsilon zero, ..., Gamma zero (feferman-schute ordinal), and so on. Until you run out and start using ordinal collapsing function with weirder fundamental sequence

[amogus]

Showing British India while saying "devide" is so true i just laughed at it 😭

[obiedatv]

I am a first-year Computer Engineer student. I have A LOT of math classes in the coming years. I will say I am around level 5!

Math is not my favourite subject, but it is the most fun one to study, and solving problems is quite relaxing—not particularly fun, but just relaxing!

[adrienkaufman]

Mmm I'd say :
- level 6 : basic topology, intermediate differential equations, intermediate set theory, modular arithmetics, prehilbertian spaces and metric spaces, intermediate linear algebra (~endomorphism reduction), intermediate calculus (vectorial fonctions, parametrized integrals), ...

- level 7 : general topology, advanced differential equations, transforms (Fourier analysis, Laplace, ...), measure theory and intermediate probability theory, group theory (normal subgroups, modules, ...), distributions, set theory, some set theory, basic theoretical computer science (computability, lambda calculus, ...), statistics, tensors, ...

- level 8 : differential geometry (manifolds, connections, ...), complex analysis (holomorph functions, ...), some group theory (Lie algebras, Galois groups, finite groups, ...), stochastic calculus (continuous processes, Brownian motion, ...), theoretical computer science (formal systems, decidability, ...), topology (of Banach spaces, ...), set theory (ordinals, Zorn, AC, ...), ...

- level 9 : algebraic topology (homotopy and homology groups, ...), De Rham cohomology, stochastic calculus (Ito calculus, stochastic control, statistical manifolds, ...), some category theory (monads, closed categories, ...), theoretical computer science (randomness, type theory, ...), complex analysis again, some operator theory, advanced arithmetics, differential geometry (fiber stuff, vector fields, ...), transport theory, ...

- level 10 : algebraic topology again, advanced category theory, topoi and higher algebra, non commutative geometry and index theory, algebraic geometry, advanced computer science (Homotpy type theory, Thales theorem, categorical semantics, ...), flat earth and all the previous subjects in a fancy way

(Personal tier list obviously)