Do you think this is legit?

I am a mathematics professor with PhD in math and a bachelor’s in philosophy. I am looking for easy-to-read nonfiction books about math. I am looking to replace my scrolling time with something equally effortless, but for me it has to be something a little more cognitively stimulating than fiction (but not too much!) Some fiction is very intelligent, but I want to scratch the logical and systematic part of my brain. For example, I recently picked up Linnebo’s introductory text on Philosophy of mathematics and enjoyed it immensely. Is there something you’ve read lately that you think I would enjoy?

Please, please… I know how much some of you love math but I am NOT looking for technical books that are on the easy side such as undergraduate mathematics texts. I do plenty of very difficult mathematics between the hours of 9-5. I am instead looking for something relaxing to do during my off-hours and weekends.

I’m coming from a geometric analysis background. So the only category theory exposure I have is whatever needed for basic graduate level algebraic topology.

What is the level of knowledge , say measured in years of learning for a postdoc level mathematician, that I will need in order to start doing research in it?

Thanks!

I took a look at my progress bar graph I keep where I track the scores of some mock tests. Over the course of 2 months, I have nothing. No improvement. At all. My score is still floating around the same range. 2 months of hard work, of dedicating my time and effort into this, and just nothing.

I had a mistake log, I practised every day, I tried my best to think about problems but often times would just end up staring and then seeing the solution. What more could I have possibly done? This feels like my dream of being a great problem solver and being able to learn the language of the universe is shattered. There must be something in me, something fundamentally broken that I haven't improved even a little bit even after giving my heart and soul for this.

And I break down every time I think about it. Honestly, I dont even know how many of these I can take. I dont know how long I can tolerate feeling this stupid, even when Im doing everything I can. I just never have the first step and end up staring at the problem, even when I change up the difficulties.

I don't want to give up, I really don't want to, but Im not sure if I'll even get somewhere if I keep going, maybe I'm just not meant to.

Have you all ever felt like this due to Math? Sounds stupid to ask, feeling so shattered because of a subject, but if you did and got through it, hearing it could really help right now

P.S: And for context I've been doing Olympiad styled Math:D

These are cute facts that I didn't know about somehow until just now encountering them on Wikipedia.

• \sum_{k perfect power, excluding 1} 1/(k-1) = 1
• \sum_{n=2}^{\infty}\sum_{m=2}^{\infty} 1/n^m = 1

In the first sum, perfect powers are taken without repeats: e.g., 3^4=9^2 appears only once as k. In the second sum, of course, repeats do occur.

Anyone have a rigorous proof for the first sum equalling 1? Wikipedia outlines Goldbach/Euler's argument, which certainly doesn't meet modern standards of rigor.