The art of reading math books

boredom is a sign to switch, struggle is a sign you're learning

"Nothing is more unreadable to me than books (and papers) on mathematics."

— Kunihiko Kodaira, Fields Medal (1954)

Reading math books is hard. They are very dense and technical. It’s easy to get stuck on a random detail on page 2, become exhausted, and put the book away.

In this issue, I'll share some strategies I’ve picked up to learn from books without losing motivation.

Work on One Hard Problem

Pick one hard problem (no more than one!) and sit on it for a few months.

Become immersed in it. Make it your world.

Struggle with it, try different approaches, compute examples by hand, maybe run computer experiments.

What you read, you forget. What you do, you remember.

(Tip: To find a hard problem, go to the last exercise in each chapter of a textbook. That's where the hard problems live.)

If It's Boring, Put It Away

Reading math should not feel like medicine. It should be fun.

So if you're reading a math book and it's boring, find another book.

Don’t "push through". Find something so fascinating that you can’t stop thinking about it. That’s when the real learning happens.

Get to the End as Quickly as Possible

Math books often begin with long sequences of definitions and theorems, only revealing their purpose and applications at the very end.

So as a first pass, skim the whole book and jump to the final chapters. Find out why the material matters. As a second pass, return to the earlier chapters and work through the details. Everything will feel more alive and connected.

Problem of the week

Can you choose 1983 pairwise distinct positive integers less than 100000, such that no three are in arithmetic progression?

Got a solution to the challenge problem? Submit it here.

New video in the works!

I’m working on a video about sphere packing and the 2022 Fields Medal.

It should be out very soon -- so keep your eyes peeled!

Solution from last week

See here for the solution to last week’s problem. (Shoutout to Rishith from India, whose solution is being featured this week!)

Huge thanks to Hagan Chan (Hong Kong), Anisur Rahaman (India), Valter (Sweden), Jake Sun (Boston), Uddhav Venkatesh (London), Naitik (Switzerland), Ammar Ratnani (Stanford), Valter (Sweden), and Rishith (India) for submitting solutions for this challenge problem.

Thanks for reading and happy learning! See you next week,

Adithya