Yes, I was going to mention Frederick Mosteller’s Fifty Challenging Problems in Probability; it’s right here on my desk, and I was first introduced to it in childhood. A delightful, challenging little book.

]]>_Godel’s Proof_ by Nagel and Newman

_Interpreting Probability_ by Howie is contending for inclusion too ]]>

Men of Mathematics is a tempting, but to Clifford Truesdell’s quite is worth recalling:

“…[Bell] was admired for his science fiction and his Men of Mathematics. I was shocked when, just a few years later, Walter Pitts told me the latter was nothing but a string of Hollywood scenarios; my own subsequent study of the sources has shown me that Pitts was right, and I now find the contents of that still popular book to be little more than rehashes enlivened by nasty gossip and banal or indecent fancy.”

]]>I suppose it’s true — seeing the 3rd and 4th graders coming out of his classroom chattering excitedly in the pre-covid days, I’ve often wished I could be a third grader in Ilya Zakherevich’s math circle. And I *know* high-performing high school kids today have access to so much online enrichment [and not just in math] that was unimaginable in the late 1970s.

Still, it’s hard to think of oneself as underpriviledged for growing up in suburban DC 40-odd years ago.

]]>Please do write the bok of Statistics Stories. More scholars should do that as they get older. Lots of us collect great stories that we tell in class to illustrate points, and more of us should write them down.

I’m thinking of writing something in the style of William Riker’s The Art of Political Manipulation, with some of my own stories of campus or local politics and some from history. Stories are a good way of getting deep ideas “into the bones” of the listener (things like the Sports Illustrated Effect for Regression to the Mean, or that air force pilots story about it).

]]>+1

]]>https://mathematicalolympiads.files.wordpress.com/2012/08/solved-and-unsolved-problems-in-number-theory-daniel-shanks.pdf ]]>

Yeah that looks great too. Actually, there’s so much really good mathematics content on YouTube that it can be kind of a time sink.

]]>You can call it “That reminds me…”

]]>Speaking of channels, Michael Penn’s videos are great fun. (Mostly math olympiad problems and the like. The problems are hairy enough that they function as good examples of particular techniques, e.g. using modularity to solve number theory problems. If you remember thinking Why did I have to study that in calculus class, you’ll find some answers here.)

]]>Ethan:

That reminds me that I plan to write a book called Statistics Stories where I just tell all the statistics stories I know, in abbreviated form. Not all the stories, I guess. Just all the stories that have happened to me. But maybe for completeness I’ll list the famous stories I know that haven’t happened to me but are still worth mentioning. Between my own stories and all the others, I guess I’d have a few hundred?

]]>This is a fun conversation. It makes me think we should have a blog called Statistical Modeling, Causal Inference, and Social Science where we just talk about fun nerd stuff all year long.

]]>“Sphereland” (which I’ve never read) makes me think of the excellent book “Flatland”, by Edwin Abbott. How has it not been mentioned already? What a great book.

]]>Phil:

Those fortune-teller things were similar to hexaflexagons, but not quite the same thing.

]]>Hexaflexagon! I did not know that word, although I’ve seen examples of them. Indeed, kids (mostly girls, but not exclusively) liked to make them in junior high school.

]]>https://www.amazon.com/Prime-Numbers-Riemann-Hypothesis-Barry-dp-1107101921/dp/1107101921/ref=mt_other?_encoding=UTF8&me=&qid=1613340578

Bob76

]]>Ted:

I looked up that book, and . . . it’s wonderful! I am just now overcome with sadness that nobody did this for *me* when I was four years old. And also this makes me feel like such a bad teacher, as I’ve been finding it so difficult to engage students in this way when everything’s on zoom and we can’t work together face to face.

David:

For sure. But nobody expects comfort food to be nutritious!

]]>It has many inaccuracies as well.

]]>Aah – – yes, I can consider Nelson’s “Proofs without Words” books* as comfort food!

* I’ve got volumes I and II, but I see on the web that there’s a volume III — and his page https://sites.google.com/a/lclark.edu/nelsen/ has some other titles that are enticing; in particular:

Charming Proofs

Math Made Visual

Nuggets of Number Theory: A Visual Approach, and

A Cornucopia of Quadrilaterals

Sphereland – Dionys Burger

The Fourth Dimension – Rudy Rucker

Fifty Challenging Problems in Probability – Frederick Mosteller

]]>I also want to make a plug for Ron Aharoni’s “Mathematics, Poetry, and Beauty” — though I have to qualify it a little as the math examples may be too familiar for a mathematical audience (the usual collatz conjecture, irrationality of sqrt(2), etc), yet his descriptions might be too condensed for someone for whom they are new. But it’s readable and engaging and I really like his approach in trying to convey the beauty of math to a general audience.

I remember really liking “The pleasure of Counting” (Körner) but I can no longer find my copy, it may have been lent to someone.

“Math from Three to Seven” by Alexander Zvonkin is the story of a math circle for pre-schoolers that Zvonkin ran from his apartment in Moscow for his son (Dmitri Zvonkine) and friends in the early 1980s. Very readable, here and there the day-by-day diary aspect may bog down, but there are some beautiful moments, too.:

“…The boys talked about their recent visit to the zoo where they were shown monkeys. I interrupted, telling them that they were not shown monkeys, they were shown *to* monkeys. This naturally provoked a heated protest, but they did not immediately find the right argument.

“We were looking at them.”

“You were looking at them — big deal! They were also looking at you.”

Their second argument was more solid: “We can walk wherever we want to, and the monkeys can’t.”

But I still refuted them with, “No, you can’t go inside the cage. And the monkeys can’t go outside the cage. There are bars separating you, and you walk wherever you want on one side of them and the monkeys do the same on the other side.”

We were arguing this way for some time until Dima exclaimed with delight, as if he had caught me red-handed, “Hey, Dad! We’re doing math again!”

When I was very very young (five? six? seven?) I enjoyed my older siblings telling me what a “google” and a “googleplex” were. We wrote out all the digits of a google on our kitchen blackboard — it look several lines.

At around age 9, I liked writing out Fibonacci and similar sequences. I didn’t know that name at the time. I just liked to write 1, then 2 under I, then add to get 3, then add the 2 and 3 to get 5, etc. –and do the same process starting with two other numbers.

At around age 12, I liked calculating square roots by hand. Then a friend of mine wondered if there was an algorithm for calculating cube roots. Our teacher (who sponsored the math club) didn’t know, but my friend found an algorithm in a very old encyclopedia that had belonged to her grandparents. So we had some fun calculating cube roots.

I think it was in high school that I enjoying making hexaflexagons and other 3-D mathematical models. I also enjoyed geometric proofs and algebraic derivations, and the ideas (e.g. limits, asymptotes, derivatives and their uses) in calculus.

In college, I enjoyed doing proofs, and seeing or reading especially elegant ones. I also enjoyed solving mathematical problems.

In graduate school, I enjoyed doing problems more than listening to lectures, although some lectures were very good. And I enjoyed working on the problems that made up my Ph.D. thesis. I wasn’t just that I worked so much on a particular problem, but that sometimes I generated my own problems to solve.

After getting my Ph.D., I also enjoyed working on conjectures, and sometimes proving them (and sometimes finding counterexamples, and sometimes generating new conjectures). But as I did more and more teaching, I began to enjoy it more and more — especially when a student “got it”, and enjoyed thinking about how to teach in a way that helped students “get it” rather than just “follow rules that were taught”.

]]>Jordan:

Yeah, I was thinking that too, but I checked out a couple Gardner books from the library the other day and flipped through them . . . they were ok but not as fun to read as I was expecting. Maybe just because I read them before, or maybe because I wasn’t ready to put in the effort like I was in the old days, discovering amazing nuggets in back issues of Scientific American, building hexaflexagons out of paper, going to the store and buying a go set so I could try out the Game of Life for myself, and so on. This is comfort reading in a sense, but reading that takes a lot of work to really enjoy. I remember once collecting a bunch of matchboxes and using them to build a tic-tac-toe learning machine that Gardner had described in one of his columns. Just reading the columns passively isn’t as fun as I was imagining.

]]>The Code Book, by Simon Singh, is terrific

]]>Thirty years later it’s still my model of a biography that does justice to both the intellectual and emotional side of its subject.

]]>https://ibaracaldo.files.wordpress.com/2013/06/ogawa-yoko-the-housekeeper-and-the-professor.pdf

]]>I am most certainly NOT a mathematician as anything beyond differential calculus makes my brain hurt.

I do, however, get great pleasure from reading about the application of mathematics to the natural world. And the actions of humanity.

]]>