Recently, I am unsatisfied about spending a lot of time on consuming knowledge, rather then producing. As soon as I get to some level of expertise in some area, the benefit of passive reading approaches zero. So I plan to write more and code more (mastering Julia for mathematics and CS) in 2020.

A few titles I enjoyed this year:

"An Invitation to Applied Category Theory" by Brendan Fong, David I. Spivak. It was fun to dig deeper into categories and read how you can apply thinking in them to different domains: databases, signal processing, circuits. Some mathematical background is probably required. It is available for free as a PDF: http://math.mit.edu/~dspivak/teaching/sp18/ or if you are, like me, love collecting good titles in paper, a hardcover copy is nice with good paper and colour pictures: https://www.amazon.com/Invitation-Applied-Category-Theory-Co...

"Can't Hurt Me" by David Goggins. https://davidgoggins.com/book/ It helped me to start running, and I keep doing it. It improved my mindset about overcoming physical discomfort, inspired to cultivate a savage mindset within. I lost a few kgs as well. There is an audio version of it.

"Turn the Ship Around" by David Marquet http://davidmarquet-com.3dcartstores.com/Autographed-Book-Ha... A book on leadership, told as a story of transforming the team on the nuclear submarine USS Santa Fe. Not that boring like usual leadership titles.

Thank you for your answer and advice!

In pure mathematics - I found most interesting topics around algebraic topology. Next year, I plan to look into homology. These fields also have computational aspect and some applicability outside of pure maths: computational homology and Topological Data Analysis.

This autumn, I finally looked a bit into category theory (applied) using this good book: https://www.amazon.com/Invitation-Applied-Category-Theory-Co..., and, unsurprisingly, found it exciting.

Regarding PhD in an applied area: I tend to agree with you, and also keep thinking about focusing more on computational / applied mathematics so that my studies could be somehow related to my work. My tech focus at work is around data processing: with interest in distributed databases and computations.

Heh, I see that distributed systems, algebra, topology, and categories are similar in mental representation in my head, they cause same kind of excitement when I study them: visualising, analysing, and playing with the systems of structures, connections, defined rules and operations :)