If you're in a philosophical mood, there's a great book on the philosophy behind category theory, ''Tool and Objects''. Time to invest in a rocking chair and a pipe!

Many abstract ideas get lost in formalism, the teaching of categories often suffer from such fate. Thankfully, William Lawvere identified the problem and made the subject into a very intuitive one. Lots of visualizations, examples and focus on a conceptual presentation.

''This is not piano, this is dreaming''.

Finally, a series of lecture on differential cohomology and physics. And don't worry, it's fine if you don't get it the first time, take your time, work on it, you'll get there.

youtube.com/watch?v=7kIoB8…

To add to Sen Hu lecture notes, here's a lecture series on Chern-Simons theories for abelian gauge fields.

- Introduction to 2+1 dimensional Chern-Simons Theory, Gregory Moore

youtube.com/watch?v=PSA8QX…

Chern-Simons-Witten Theory is a very interesting frame work in physics, a 3 dimensional topological quantum field theory, an idea related to De Rham cohomology. I found these lecture notes by Sen Hu, which are helpful. More supplementary than pedagogical. You take what you can!

So you wanted to up the abstraction level, kid? Here's Saunders Mac Lane ''Introduction to Topos Theory'' using sheaves in geometry and logic as a gateway to this very abstract idea.

Basics about categories are covered, the Grothendieck related material as well.

If you ever wondered what exactly is a sheaf and never got it because of the abstraction level required to get it , I found this very intuitive demonstration of what a sheaf is, used as a framework in data science. My ComSci friends will love this one.

youtube.com/watch?v=65y4Uy…

Before Godel and the question of completeness, logician were subject to the ''logocentric predicament''.

Hard to find a more underrated pianist/jazz musician than Komeda.

The essence of the Hegelian automatization of the future. I know of very few ideas worst than this one.

By the good graces of the youtube algorithm, I was blessed with this exposition of the fundamental group of the circle, a center piece in mathematics, very useful in physics as well. Also, best explanation of homotopy i have seen in a while.

youtube.com/watch?v=CFtXsm…

I recommended it before, by Selman Akubut's 4 manifolds is a great document for a more advanced study of 4 manifolds, in a topological framework. Very modern, clear text, full of colored examples, which is great for 4-dim examples. Physicists, check it out as well.

Having a background in topology, TQFT always felt like home for me. For those for whom it may not be the case, Topological Quantum Field Theory and Four Manifold by Labastino/Marino is a solid place to start. Chpt on Donaldson invariant, Seiberg-Witten and chpt 5 are quality.

Pierre, patiently explaining to us, what exactly are motives, a fairly abstract and advance concept that finds itself everywhere in mathematics. As an aside I truly enjoy the Franco-Flanders accent when spoken in English.

youtube.com/watch?v=V8Xp16…

My favorite introduction to number theory, David Burton's Elementary Number Theory. If you're interested in improving your dealings with numbers or have an interest in cryptography, it's a great place to start. It's even got bits of mathematical history.

Hermann Weyl, on scientist and their relationship with philosophy

Hegel, as the philosopher of the Prussian autocratic bureaucracy.