# Looking for good math stuff to show my son over the summer

June 16, 2023 11:02 AM Subscribe

My son has a really good head for math. He's been taking high school math as an eighth grader. I'm looking for good math stuff to keep his brain stimulated over the summer. I'm looking for stuff they don't shovel at you in school. I want weird stuff that will really push him.

My son has a really good head for math and logic. He just finished up his eighth grade year where he was taking honors algebra II at the high school. But frankly, that's kind of boring math. It's a good foundation if you're going to use math like an engineer, but it's not the sort of math that actual mathematicians do. So I'm wondering if anyone can point me to weird, interesting math stuff that I can feed him. Not an interesting fact or two, I'm looking for a good book, or video series, something he can really sink his teeth into. And it doesn't have to spoon feed it to you, either. He gets stuff. Any suggestions?

My son has a really good head for math and logic. He just finished up his eighth grade year where he was taking honors algebra II at the high school. But frankly, that's kind of boring math. It's a good foundation if you're going to use math like an engineer, but it's not the sort of math that actual mathematicians do. So I'm wondering if anyone can point me to weird, interesting math stuff that I can feed him. Not an interesting fact or two, I'm looking for a good book, or video series, something he can really sink his teeth into. And it doesn't have to spoon feed it to you, either. He gets stuff. Any suggestions?

The Art of Problem Solving has a lot of resources, some free and some paid.

One simple way to start is to go through the past American Mathematics Competitions. For the ones he can't do, there are pretty detailed solutions, so just trying to understand the solution can be a great learning experience. (Start with the grade 8 questions. The first few questions in those are pretty easy, but they get extremely challenging even for very advanced 8th graders.)

posted by Mr.Know-it-some at 11:13 AM on June 16, 2023 [4 favorites]

One simple way to start is to go through the past American Mathematics Competitions. For the ones he can't do, there are pretty detailed solutions, so just trying to understand the solution can be a great learning experience. (Start with the grade 8 questions. The first few questions in those are pretty easy, but they get extremely challenging even for very advanced 8th graders.)

posted by Mr.Know-it-some at 11:13 AM on June 16, 2023 [4 favorites]

Numberphile and Mathologer videos on YouTube, along with 3blue1brown are my rabbitholes.

There's also a course on the History of Mathematics by a prof from Australia, N J Wildberger, that is really good and I learned a lot from.

posted by indianbadger1 at 11:19 AM on June 16, 2023 [1 favorite]

There's also a course on the History of Mathematics by a prof from Australia, N J Wildberger, that is really good and I learned a lot from.

posted by indianbadger1 at 11:19 AM on June 16, 2023 [1 favorite]

When I was a math-obsessed kid, I devoured "recreational mathematics" books. Martin Gardner is the godfather of these, although other people have picked up the torch since then. Doing hundreds of interesting math and logic puzzles as a kid definitely gave me a great grounding for working with math professionally. Raymond Smullyan's books are similarly great on the logic-puzzle side.

posted by dfan at 11:30 AM on June 16, 2023 [12 favorites]

posted by dfan at 11:30 AM on June 16, 2023 [12 favorites]

Eugenia Cheng's

It might read "too easy" at the intro but it goes deep. Or peek at her more advanced

posted by away for regrooving at 11:39 AM on June 16, 2023 [2 favorites]

*How to Bake Pi*might possibly be perfect here. It's an introduction to "mathematician math", getting into category theory, that needs roughly US Algebra I (familiarity with variables and functions) as background.It might read "too easy" at the intro but it goes deep. Or peek at her more advanced

*The Joy of Abstraction*.posted by away for regrooving at 11:39 AM on June 16, 2023 [2 favorites]

For Smullyan,

Old math books that are quite probably sexist if I read them today:

Knuth,

Rucker,

Oh, speaking of Godel, we haven't mentioned Hofstadter yet!

posted by away for regrooving at 11:47 AM on June 16, 2023 [3 favorites]

*To Mock a Mockingbird*is a fun chewy one, on combinators.Old math books that are quite probably sexist if I read them today:

Knuth,

*Surreal Numbers*, on Conway's surreals.Rucker,

*Infinity and the Mind*, Godel and transfinite ordinals.Oh, speaking of Godel, we haven't mentioned Hofstadter yet!

posted by away for regrooving at 11:47 AM on June 16, 2023 [3 favorites]

The Number Devil. He might be a little old for it, but it's a fun read, and full of mathematical insights.

posted by Winnie the Proust at 11:55 AM on June 16, 2023 [2 favorites]

posted by Winnie the Proust at 11:55 AM on June 16, 2023 [2 favorites]

Seconding everything here, as another one who devoured "recreational mathematics" as a kid.

Re: Martin Gardner - here's a list of his Mathematical Games columns. They're collected in fifteen books.

The Hofstadter "Metamagical Themas" from the early eighties is also fun, although more idiosyncratic, and probably less purely mathematical so might not hold up as well. Similarly for Hofstadter's first book,

Mefi's own Jordan Ellenberg has written a couple good books recently - Shape (on geometry, broadly defined) and How Not To Be Wrong. I think a bright almost-high-schooler like your kid could handle them.

posted by madcaptenor at 12:17 PM on June 16, 2023 [4 favorites]

Re: Martin Gardner - here's a list of his Mathematical Games columns. They're collected in fifteen books.

The Hofstadter "Metamagical Themas" from the early eighties is also fun, although more idiosyncratic, and probably less purely mathematical so might not hold up as well. Similarly for Hofstadter's first book,

*Godel, Escher, Bach*.Mefi's own Jordan Ellenberg has written a couple good books recently - Shape (on geometry, broadly defined) and How Not To Be Wrong. I think a bright almost-high-schooler like your kid could handle them.

posted by madcaptenor at 12:17 PM on June 16, 2023 [4 favorites]

E the story of a number, zero, a biography of a dangerous number, and Fermatâ€™s Enigma are all great mathy books that I read in junior high and high school.

posted by rockindata at 12:18 PM on June 16, 2023 [1 favorite]

posted by rockindata at 12:18 PM on June 16, 2023 [1 favorite]

Marilyn Burnsâ€™ I Hate Mathematics Book

posted by wittgenstein at 12:19 PM on June 16, 2023

posted by wittgenstein at 12:19 PM on June 16, 2023

How about some Cliff Pickover? Here's a nitter link to his Twitter stuff: https://nitter.net/pickover

posted by The Half Language Plant at 12:19 PM on June 16, 2023

posted by The Half Language Plant at 12:19 PM on June 16, 2023

I would recommend the very enthusiastic and very energetic teacher at https://www.youtube.com/@misterwootube

For instance what is zero to the zero power: https://youtu.be/r0_mi8ngNnM

Hint: what are the factors of zero?

posted by forthright at 12:54 PM on June 16, 2023

For instance what is zero to the zero power: https://youtu.be/r0_mi8ngNnM

Hint: what are the factors of zero?

posted by forthright at 12:54 PM on June 16, 2023

It's too late for this summer, but you may be interested in Euler Circle, which runs classes year round. The site also links to two books that have been published based on previous classes, which may be a better short term solution.

posted by matildatakesovertheworld at 12:59 PM on June 16, 2023

posted by matildatakesovertheworld at 12:59 PM on June 16, 2023

Vi Hart's videos are always fun.

If they're into history and not afraid of a big book, I read Edna Kramer's

posted by indexy at 1:09 PM on June 16, 2023 [4 favorites]

If they're into history and not afraid of a big book, I read Edna Kramer's

*The Nature and Growth of Modern Mathematics*in high school and really enjoyed it [archive.org link]posted by indexy at 1:09 PM on June 16, 2023 [4 favorites]

If you're anywhere NYC, the Museum of Mathematics is a blast - in fact, I wouldn't be surprised if their website has other resources your kid might enjoy. But if you can make the trip, there were both toddlers having a blast and enough depth to keep us engrossed for a long while (the exhibits let you choose three levels of details). You can ride a bike with square wheels!

posted by itsatextfile at 1:39 PM on June 16, 2023

posted by itsatextfile at 1:39 PM on June 16, 2023

The Nature and Growth of Modern Mathematics (Library of Congress reference; I know it is available on Amazon) contains many short biographies of important mathematicians and concise explanations of many mathematical topics. To quote the Amazon description:

"The book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story - ultimately linked to modern digital computers - the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; erogodic theorems; epsilon-delta arithmetization; integral equations."

posted by TimHare at 2:07 PM on June 16, 2023

"The book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story - ultimately linked to modern digital computers - the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; erogodic theorems; epsilon-delta arithmetization; integral equations."

posted by TimHare at 2:07 PM on June 16, 2023

Maybe Steven Strogatz would have something to offer?

posted by eirias at 4:59 PM on June 16, 2023 [1 favorite]

posted by eirias at 4:59 PM on June 16, 2023 [1 favorite]

A Beginners Guide to Constructing the Universe is one of my lifetime favorite books. I keep acquiring copies and giving them away. There are exercises within, largely geometry, but it marries the numbers to their analogs in art, nature, narrative, architecture... It's easy to read two sentences at a time or gobble front to back. It's a perfect complement to "math" math. (My husband, a middle school math teacher, chimes in, "That's pretty low-key; you could have talked it up a lot more.")

posted by droomoord at 7:21 PM on June 16, 2023

posted by droomoord at 7:21 PM on June 16, 2023

Older, possibly hard to find, but well worth it!:

The Turing Omnibus

The New Turing Omnibus

Many (!) short (2 - 4 pgs) essays on various math related subjects, framed from a computer programming perspective, encouraging experimenting.

posted by cfraenkel at 7:27 PM on June 16, 2023

The Turing Omnibus

The New Turing Omnibus

Many (!) short (2 - 4 pgs) essays on various math related subjects, framed from a computer programming perspective, encouraging experimenting.

posted by cfraenkel at 7:27 PM on June 16, 2023

If he likes solving puzzles and can do some basic programming (and is willing to learn more) he might enjoy Project Euler.

From their "About" page:

From their "About" page:

posted by Nerd of the North at 7:43 PM on June 16, 2023 [1 favorite]What is Project Euler?

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.

Who are the problems aimed at?

The intended audience include students for whom the basic curriculum is not feeding their hunger to learn, adults whose background was not primarily mathematics but had an interest in things mathematical, and professionals who want to keep their problem solving and mathematics on the cutting edge.

My son got seriously involved in math competitions in middle school. (It was great - the problems were hard but the underlying math was in reach - he learned to think like a mathematician without accelerating him through the things he would be doing in school anyway.) Based on his experience, I would recommend the Art of Problem Solving and the materials for AMC Math competitions (both linked to by Mr.Know-it-some.)

I would also strongly suggesting seeing if he can link up with a math buddy or two this summer where they can both try to solve the same problems and share what they come with it before they look at the answers in the back of the book. Most people think of math as a solitary activity but I have seen how motivating it can be to share both the triumphs and frustrations with a buddy.

posted by metahawk at 10:12 PM on June 16, 2023 [2 favorites]

I would also strongly suggesting seeing if he can link up with a math buddy or two this summer where they can both try to solve the same problems and share what they come with it before they look at the answers in the back of the book. Most people think of math as a solitary activity but I have seen how motivating it can be to share both the triumphs and frustrations with a buddy.

posted by metahawk at 10:12 PM on June 16, 2023 [2 favorites]

I don't know where you live, but if there is a math circle in the area, I suggest that you look into having your kid attend. I got a lot out of my experience at one-they teach math outside of typical circular material and going to the Cambridge one is probably part of the reason I ended up majoring in it in college.

posted by Hactar at 5:54 AM on June 17, 2023 [2 favorites]

posted by Hactar at 5:54 AM on June 17, 2023 [2 favorites]

The standard MTV curriculum is arithmetic up to a point, and then a highway - algebra, geometry, trig - to calculus. There is lots of math not on this path, and any of them might be interesting. Probability, topology. Many profs think of linear algebra as the first real math course because its not mostly about calculation.

posted by SemiSalt at 8:48 AM on June 17, 2023 [2 favorites]

posted by SemiSalt at 8:48 AM on June 17, 2023 [2 favorites]

I was your kid when I was younger, so I have to ask: does he

posted by jessica fletcher did it at 11:38 AM on June 17, 2023 [2 favorites]

*want*to spend his summer doing math? Frankly, as someone who pushed themselves hard through the entire school year, I needed to relax during the summer. I needed harder math during the school year, which it sounds like you're already doing. Let him pursue other interests during the summer if he wants.posted by jessica fletcher did it at 11:38 AM on June 17, 2023 [2 favorites]

3blue1brown held a Summer of Math Exposition 2 videos - YouTube contest last year (and is doing another one this year). There are whole bunches of different people doing different types of maths in that long playlist.

posted by zengargoyle at 5:47 AM on June 18, 2023

posted by zengargoyle at 5:47 AM on June 18, 2023

oh boy do I have the book for you! The super weird and wonderful Winning Ways For Your Mathematical Plays. It's written by some high powered mathematicians and introduces the field of combinatorial game theory, but not remotely how a textbook would. It's a fun, conversational exploration through some pencil & paper games, guiding the reader through some observations, conjectures, arguments and proofs that slowly build up an entirely new number system (the surreal numbers) and mathematical theory for analyzing a particular (broad) class of games. It's probably fun for you too! I'd say preview the first chapter and I hope you'll be hooked. I think it would be a *great* introduction to the type of abstraction and careful, logical reasoning that mathematicians engage in.

posted by mathtime! at 8:43 AM on June 18, 2023 [2 favorites]

posted by mathtime! at 8:43 AM on June 18, 2023 [2 favorites]

Don't miss Numberphile2 - YouTube, there are interviews with real world maths people telling their life stories and they are all different. That among other things is why I prefer the British 'maths' (plural) overe the US 'math' (singular). There are so many branches of math stuff beyond the normal high school track. Many could say like work with topological or higher dimensional things but are bad at balancing a checkbook. Maths people are a whole different thing, no two alike.

Like check out this: Matt Parker Reacts to Magic Squares of Squares - Numberphile - YouTube.

And just check out Stand-up Maths - YouTube, Matt is good and like teenage funny.

posted by zengargoyle at 5:40 PM on June 18, 2023

Like check out this: Matt Parker Reacts to Magic Squares of Squares - Numberphile - YouTube.

And just check out Stand-up Maths - YouTube, Matt is good and like teenage funny.

posted by zengargoyle at 5:40 PM on June 18, 2023

Lots of great suggestions in this thread. In particular, although of course I am fond of the books I wrote, I would put Martin Gardner, Winning Ways, Godel Escher Bach, 3blue1brown and Numberphile videos, and Art of Problem Solving courses ahead of my own stuff for your kid's particular situation!

posted by escabeche at 6:24 PM on June 18, 2023

posted by escabeche at 6:24 PM on June 18, 2023

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posted by Alterscape at 11:13 AM on June 16, 2023 [7 favorites]