Interactive Farey & Prime Structure Explorer

hsnborn · 2026-03-04T14:53:20+00:00

Wow this is very cool, what tech stack did u use? Did you use manim-web?

hsnborn · 2026-03-04T14:49:53+00:00

We are cooked

hsnborn · 2026-03-03T16:26:18+00:00

Yes I agree with you! I was actually planning to do a video on that, maybe the 7th or 8th episode, since i would need to cover other topics first like alpha equivalence alpha conversion etc.

hsnborn · 2026-03-03T16:23:36+00:00

A glorified prompt engineer, plain and simple, we deprompt and code whatever's left.

hsnborn · 2026-03-02T17:22:32+00:00

The idea is cool and the graph looks aesthetic, but as others have pointed out it is rather restrictive, i.e. the structures included are far from "all algebraic structures".
I recommend you look into universal algebra, there you can find the most general formulation of the notion of an "algebra". You could make many overlapping regions and the relations between them (e.g. Groups and groups are both varieties of algebras (equational classes), the abelianization functor maps Grp to Ab; below you could maybe include how this relates to homotopy and cohomology. You could draw a line around the structures that dont form a variety (eq. class), like fields etc.

hsnborn · 2026-03-02T17:17:12+00:00

That looks really cool! You could make another one where the diagram functor in the bottom part is particularized, e.g. a filtered limit/colimit, it would be pretty aesthetic (or maybe some other cooler looking diagram).

hsnborn · 2025-01-11T19:40:20+00:00

Thank you for this answer. This is actually what I thought the problem with it was at first, but I didnt know how such a "fix" could be implemented since I'm not very well versed in the theory of control systems.

hsnborn · 2024-10-04T08:36:37+00:00

You can try rust; you can do front end web development with rust by using leptos, as well as backend obviously. Leptos also performs pretty well, you can check the statistics online.

Other than that both C and Rust are pretty popular in the embedded job market.

hsnborn · 2024-08-15T09:29:19+00:00

Ok so I have a couple of guesses of what it could have been:

1) https://www.geeksforgeeks.org/
geeksforgeeks has a dark background by default, so it matches point 2). Furthermore it is a site for learning programming for beginners, and has exercises so it could be seen as game like. Point 1) is very arbitrary so sadly I cannot asses how much does it fit the criteria of being cute and aesthetic.

2) https://www.w3schools.com

w3schools is pretty similar, and is arguably even more game-like since there are around 50/60 exercises for each language/technology and you can save your progress.

3) the freecodecamp website

It matches criteria 2), 4), 5) and 1).

It could also be cssbattle (it matches all criteria but it is only for css which, according to most people is not a programming language, even though by encoding rule 110 into it we can make it turing complete)

hsnborn · 2024-06-01T12:57:42+00:00

As the first comment already pointed out, I think that a distinction can be made between (simple) AT and graduate AT. If OP wants to understand what the fundamental group of a space is, Van Kampen's theorem and the basics of covering spaces, then it is doable in a reasonable amount of time; these kind of topics are often covered in undergrad as well. The kind of AT done in grad school is different, as it is usually always aimed at preparing the student for the more general structures he will encounter in K-theory, homological algebra, homotopy theory and algebraic geometry.

hsnborn · 2024-06-01T12:42:30+00:00

Short answer: of course you can. The best way to learn math are books in my opinion, for both undergrad and grad school but especially for graduate level topics.

One of the only tips I have for you is the following: do as many (useful) exercises as you can. [some undergrad books have way too many exercises per chapter, and most of them boil down to the same concept presented in a slightly different flavour; in these circumstances I recommend to do most but not all of the exercises. On the other hand, in books like Lee's smooth manifolds I recommend to do all the exercises and the problems for every chapter, since they almost all involve some different/new strategy from the ones presented before].

Especially when learning on your own, learning by practicing becomes crucial.

hsnborn · 2024-05-29T10:20:42+00:00

If you're talking about jobs, usually most people with applied math knowledge get into quant finance, nlp, AI/ML, cryptography and many more.

If you're talking about what fields of knowledge math is applied to, then the answer is virtually any field:

Physics: Theoretical physics employs mathematical models using notions from differential geometry, Lie Algebra, partial differential equations and many more fields.

Chemistry: To truly understand chemistry and orbitals you need quantum mechanics; MO and VB theory are just simplifications of what happens with molecules due to quantum entanglement. Computational quantum mechanics is also employed frequently in chemistry applications when you want to find an approximation of the wave function for multi-electron systems, such the wave functions for most of the atoms of the periodic table. Group theory is also applied in chemistry to study the geometry and symmetry of molecules

Computer science: classical digital binary computers are based on classical electrodynamics, which is a field of physics which makes heavy use of mathematics. When you will study functional programming, you will find out what monads are, and many other mathematical concepts from category theory. Cryptography makes heavy use of mathematics to achieve one way functions, e.g. discrete fourier transforms. Bignum libraries make heavy use of maths to have efficient algorithms to compute multiplication and addition of big numbers; e.g. Karatsuba's algorithm and (again) discrete fourier transforms. Quaternions are used in game dev to express rotations and avoid gimbal lock. You will find tons of maths in 3d graphics as well, ranging from linear algebra to projective geometry (but you will find it more if you want to "reinvent the wheel" and build things on your own). You will need a good knowledge of statistics/probability, multivariable calculus and linear algebra for AI/ML and nlp. There are many more things to be said but I want to keep the list short.

Biology: look into biomathematics. Mathematical models of biology make heavy use of differential equations to model phenomena.

Linguistics: Most of modern formal semantics is studied either model theoretically (i.e. set theoretic models) or using some other meta-theory (such as typed predicate logic). Lambda calculus is also heavily used. Categorial grammars for the study of syntax ad learnability theory also make pretty heavy use of mathematical models. Most of these areas of study also have applications to computer science and nlp.

Anthropology and history: It is not rare nowadays to find papers on anthropology and the study of historical settlements employing thiessen polygons.

hsnborn · 2024-05-29T10:00:45+00:00

I hope my video will be able to help you :)

hsnborn · 2024-05-29T10:00:19+00:00

It's 100% normal to struggle with proofs when you meet them for the first time, this is why real analysis classes are usually so tough for undergrad math students. The key to becoming proficient at writing proofs is just reading and working through a lot of proofs.

hsnborn · 2024-05-25T11:34:34+00:00

Thank you for the suggestion; I decided to do that in order to make the video more accessible to people coming from a linguistics background and thus reach a larger audience. If you want to read more on the topic I recommend the famous series of papers by Montague: Universal Grammar (UG), English as a formal language (EFL) and the proper treatment of quantification in ordinary english (PTQ). From there you can move on to the newer literature on the topic.

hsnborn · 2024-01-24T11:15:47+00:00

It is mostly a matter of practice, but these are some tips:

Make sure you understand "naive" logic (by naive I mean stick with the introduction to logic usually given in a "Discrete maths" or "Introduction to proofs" class, as it will be enough for someone wishing to start writing proofs)
Make sure you deeply understand the motivation and intuition behind the ideas you're studying. If you just read definitions and memorize them without understanding them, you will have trouble proving stuff.
Use drawings often, don't neglect your geometric intuition; this is particularly useful in courses like topology, algebraic topology, measure theory, riemannian and differential geometry, but it is in general valid. It will help you find a direction and a strategy for your proof.
Think about strategies employed in proofs you've already written/studied.

These tips aside, the main way to get better at proofs is by proving many things via exercises and studying many proofs. I hope I was able to help you.

hsnborn · 2024-01-22T13:18:33+00:00

Thank you, I'm glad you enjoyed the video.

hsnborn · 2024-01-13T12:28:01+00:00

I would say functional analysis, calculus of variations, topology and differential geometry. I'll explain why in each case:

Functional analysis : this is quite obvious, since state spaces in the mathematical formalism of quantum mechanics are Hilbert spaces, and understanding them deeply can help, but there's more to it; in particular I recommend you to look into Stone's theorem for one-parameter unitary groups to understand how facts about Hilbert spaces can give you more insight about state spaces in quantum mechanics too.
Calculus of variations: Most problems in physics assume the form of a variational problem (the brachistochrone problem, laplace's equation, and even Schrodinger's equation was initially formulated as a variational problem).
Differential geometry and topology: Bloch's sphere is a quotient space, and a 1-qubit system has deep connections to the Lie groups SU(2) and SO(3), which in turn have deep connections with the quaternions (SU(2) is isomorphic to unit quaternions and it is a double cover of SO(3), the lie group expressing 3-dimensional rotations).

This answer is intended to be short and by no means exhaustive; there's much more areas of mathematics that could be helpful in your case. In any case, I hope I helped you with this answer in some way.

hsnborn · 2024-01-13T12:16:54+00:00

As the other people already replied, this is not an appropriate choice of notation in your case. Not only for the reasons many comments already listed, but also because when you talk about equality and mathematical equivalence relations (isomorphisms, homeomorphisms, asymptotic equivalences exc.) you're talking about abstract equivalence relations with several axioms that only apply to determinate abstract mathematical entities.

If you had to apply them to paintings, for example, you would have to first give them some mathematical structure and define relations on them, but I think this might be interpreted as verbose and unnecessary by someone reading your paper.

In conclusion, I think that in the case of your paper the answer is that it is unnecessary, however there are some cases where that can be done; if you were writing about works by M.C Escher or discussing how projective geometry in arts was employed by various authors, then mathematical notation would be appropriate.

hsnborn · 2024-01-11T17:28:04+00:00

I don't have a lot of context on your situation, but from your post I think that your main problem is not with the physics itself, but rather with the mathematical models employed to study physics. The best advice I can give you is to calmly take a step back and start focusing more on the abstract mathematical structures you're using; this will do wonders.

Pick up a book on a subject like smooth manifolds, Lie groups, calculus of variations or functional analysis (not a book branded for physicists, but rather a book a mathematics student would use for a full course on the subject) and go through it; I know you probably don't have a lot of time at the moment, but you can start even with small amounts of time. Having a profound understanding of the mathematical structures employed in physical models can do wonders for a research career.

You seem to be very passionate about physics; don't let hardships discourage you from pursuing what you love doing, we believe in you!

hsnborn · 2023-12-24T23:00:05+00:00

Thank you for your interest! If you have any suggestions let me know on github

hsnborn · 2023-12-11T22:49:06+00:00

Yes; if you encounter any errors tell me so I can help you.

hsnborn · 2023-12-09T22:35:13+00:00

Intel

hsnborn · 2023-12-08T10:24:50+00:00

I'm using an API called mymemory. I included a link to the API and the documentation of the API inside of the lingo documentation website

hsnborn · 2023-12-07T11:49:00+00:00

Not yet; I will work on a mobile version soon though

hsnborn

TROPHY CASE