Wednesday, September 06, 2023

Books to Inspire Math

Two of my colleagues and co-authors from my early days at the University of Chicago have released books over the past few months designed to excite people with math, Howard Karloff's Mathematical Thinking: Why Everyone Should Study Math and Lide Li's Math Outside the Classroom. Karloff was a fellow professor and Li was my PhD student. Neither are currently in academia but both still found the need to inspire young people in mathematics.

Both books aim to make math fun, away from the rote problem solving from high school and early calculus courses to concepts like prime and irrational numbers (Karloff) and sequences and geometric shapes (Li). The books have some overlap, both cover deriving e from interest rates and probability including the Monty Hall problem. Both books have lots of problems to work on. 

Between the two I would suggest Karloff's book for junior high/high school age kids and Li's book for older high school and early college students given the topics covered.

At a time that math plays a larger role in our society, especially dealing with data, finding ways to get more young people interested in mathematics is important. These books fill an important niche for the mathematically curious students to dive in topics they won't likely see in their math classes. Great to see my former colleagues taking the time to reach these students through these books. 


  1. I think this niche is better filled than ever, but not by books but by youtube videos. Numberphile and 3blue1brown's videos are amazing for this purpose, hell even on non-math focused channels like Veritasium, the math videos are pretty good, and are getting millions (!!) of views.

    1. 'Learning' is intrinsically a nonlinear problem and is by definition without a predefined objective and/or outcome (despite the pedagogical fervor to 'improve learning outcomes').
      A book allows me to quickly jump back and forth skip ahead to return back later, etc; this experience is irreplaceable.
      Anything electronic adds a huge amount of distraction for most people, especially more so for children and young adults.

    2. But can you really trust those videos?

  2. Can you trust those videos?
    Yes, I think. A book retains all the typos and thinkos the authors missed until the next edition, but the videos get reviewed immediately in the comments.

    FWIW, the videos vary a lot. Numberphile and Mathlogger are about single, random issues, whereas (some of) both 3blue1brown's and Michael Penn's videos are more organized. I'm currently a Michael Penn fan, because he does courses that I'm currently interested in and then follows them up with serious examples. Today's video, for example, extends his abstract algebra course and is important for comp. sci. types: How the power set forms a ring.

  3. "You don't know what math is until you prove a math theorem by yourself"

    1. Agreed. And that's a good point for books. I'm currently reading "Introduction to Proofs and Proof Strategies" (S. Fuchs) and really liking it. It's part of the (fairly large) literature on moving kids who are good at high-school math into proof-oriented higher math, and as a _textbook_ has lots and lots of problems, some of them of the "Prove that X" variety. Michael Penn's courses alternate between a lecture video and a problem set video, but I think problems on paper are better.

      My current mindset is that grinding a lot of problems has a lot of value, and so I like books that act textbooky by providing lots of problems.

      Still, the math videos show complete proofs or derivations of some seriously painful stuff in gory detail, often demonstrating the use of things you were wondering why the textbook was being so insistent about.

      It's a great time to be reviewing one's math.

  4. "Algorithms to Live By" is also a good book.