The bizarre blog that taught everyone math
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- Опубліковано 10 лют 2025
- Learn more from the columns on my Patreon (starting this week with the hexaflexagons article): / tibees
Links to all 15 of the books that compile Mathematical Games articles (check your library first, and some editions are available to borrow for free on archive.org):
1. Hexaflexagons and Other Mathematical Diversions amzn.to/4aMzW4h
2. The Second Scientific American Book of Mathematical Puzzles and Diversions amzn.to/40ZsBer
3. New Mathematical Diversions from Scientific American (alt title Sphere Packing, Lewis Carroll, and Reversi) amzn.to/3Ei1UJ6
4. The numerology of Dr. Matrix amzn.to/3Q9nUsd
5. Knots and Borromean Rings, Rep-Tiles, and Eight Queens (alt title The Unexpected Hanging and Other Mathematical Diversions amzn.to/4jHprDC
6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American amzn.to/3Ep8yxp
7. Mathematical Carnival amzn.to/3Q1DhDa
8. Mathematical Magic Show amzn.to/4b1CEU1
9. Mathematical Circus amzn.to/40HGsVu
10. Wheels, Life, and Other Mathematical Amusements amzn.to/40IUI0b
11. Knotted Doughnuts and Other Mathematical Entertainments amzn.to/4hkqdol
12. Time Travel and Other Mathematical Bewilderments amzn.to/4aRCrTe
13. Penrose Tiles to Trapdoor Ciphers amzn.to/40XGV7p
14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American amzn.to/4gnStVT
15. Last Recreations: Hydras, Eggs, and other Mathematical Mystifications amzn.to/4hKeC1Y
this list has a more detailed view of all the alternative reprintings and titles: en.wikipedia.o...
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Editing by Noor Hanania
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Fun fact: Martin Gardner has a French alter ego! The french edition of the Scientific American is called Pour la Science (i.e., "For Science), and there's an amazing researcher named Jean-Paul Delahaye who writes a monthly column about all sorts of fun topics, from folding games to numerical oddities, Kolmogorov complexity and the intersection between math and computer science. He's been a great source of inspiration and motivation for me and countless others. His articles have also been published in many books.
jean-paul is the king of the number Pi!!!
The German version is probably Albrecht Beutelspacher, who in addition to having a regular math puzzle column also founded the math museum "Mathematikum" in Gießen and had his own educational TV show.
Hearing what Martin says at 2:39 brings to mind Brady Haran of Numberphile!
Bingo. Math PhD here. Age 55. That column is what got me started as a kid.
Incredible line: "Gardner was one of the first ever to talk about fractals, and that's because he happened to be neighbors with Benoir Mandelbrot."
Ylou haave become quite an inspiration yourself covering such a wide spread of topics. Thanx for that!
underrated comment :)
I was a teen in the 1970s, back in the glory days of SciAm, which I read devotedly. I was a regular reader of Martin's column. I once wrote him with a bunch of questions about complex exponentials. He actually wrote back! It was a kind letter, along the lines of: If I took the time to answer all of those questions, I'd have not time to write the column! But he put it very kindly and wished me well. I kept the letter tacked onto the wall of my bedroom as inspiration through my youth. I probably still have it somewhere.... Thanks for providing some biographical info about Martin! -Tom
This was such an incredible deep dive! Martin Gardner’s Mathematical Games column had such an enormous impact on how people engage with math, and your breakdown really captured why he was such a legend. It’s amazing how a single journalist-not even a trained mathematician-managed to ignite curiosity and inspire generations of thinkers. The fact that his work helped introduce fractals, RSA encryption, and even Escher’s art to a wider audience is mind-blowing.
Speaking of Gardner’s influence, did you know that his 1970 article on Conway’s Game of Life was so popular that it supposedly caused a noticeable drop in workplace productivity? Office workers spent so much time programming the game on their computers that companies actually lost money! Just goes to show how captivating his puzzles and ideas were, even before the internet made them widely accessible.
Loved this exploration-now I feel like I need to pick up some of his books myself! Looking forward to more math history content from you!
I have two of his books, Colossal Book of Mathematics and Colossal Book of Short Puzzles and Problems. They're great to dip into when you're needing a mental challenge.
Hexaflexagons, the only time my interest in mathematics crossed over from the theoretical to the practical.
I was a bit too young for Martin Gardner's run, but I started reading A.K. Dewdney's column "Computer Recreations" that followed soon after it in Scientific American. That's what got me into programming, music, and math!
From a young age
"Mathematical Games" - Martin Gardner and "How to Solve It" by George Pólya
Later on were Isaac Asimov science books and the Raymond Smullyan books.
I think Mathmatics youtube is carrying on the legacy of inspiring future mathematicians and scientists.
I think Numberphile is the closest to Martin Gardners blog. And i think, together with the rest of all of mathmatical youtube (Toby, Matt Parker, 3b1b to name a few), they are having a bigger reach and impact than ever. Inspiring the next generation of groundbreakers.
Edit: Typo
I started reading Martin Gardner's articles when I was in my senior year in high school (so about 1967). I then went to university and every month would go to the university library to read his current article. I then started to copy them in the library so I had a permanent copy of each. I graduated with a double degree in Mathematics, and Martin Gardner was a major factor in why I chose to get my degree in Maths. Over the years I have bought many of the books that contain his articles. A real legend!
I've been reading Martin Gardner all my life with a legacy of paper backs from my father going back to the Fifties. Marvelous Man Toby Hendy, wholesome and attractive as ever giving a great contribution.
I’ve never seen the Scientific American articles, though the name rang a bell. I know Martin Gardner as the author of The Annotated Alice, since I’ve long been a Lewis Carroll fan. It’s interesting to learn here that Gardner also helped popularize MC Escher, since I have also long been a fan of his art. I’m not a mathematician, though perhaps I can now say I’ve always been mathematics adjacent?
just yesterday i found a 4 yr old video. it had the bob ross trees in the valley. i had my notbook open to an almost identical drawing. i wasnt necessary looking into logarithms at that moment. i was thinking of weather and wind. but the log infor came at the perfect time to round out my knowledge. i love your enthusiasm for math. i only recently learned it can actually be fun.- i cant believe im saying this. lol
Love your videos and really enjoy your content. Sometimes I am just surprised how common a very US-centric view is. If for example you say, that M. Gardner made MC. Escher famous, who was not widely known before - here in Germany Escher was and is very popular without probably anyone having ever heard of Gardner.
How do you know it wasn't made popular in Germany indirectly through his work? He only became widely around the time of Gardner's work. You could be overcorrecting for US-centricism.
@ I am originated from East Germany and I seriously doubt that an US journalist had much influence on popularity in a communist state.
I thought that was an odd thing for her to say, too, but after thinking about it, I can't decide one way or another. The wikipedia article on Escher also says that he was not widely known until the Mathematical Games column published his work, but it also says he "lectured widely" before that. Perhaps some of the Americans stationed in Germany during this time took Scientific American, and shared Escher's sensational work.
i find it very much plausible that he was known (to some degree) in Central~West Europe. i don't doubt that his work became more popular afterwards.
sometimes there are these weird islands of popularity or lack thereof. like with Rush - most successful band of all time (at least for a time i suppose) but utterly unknown in Germany (i see you who's typing that you know them, guess what, i've known them as well since childhood but we're an odd exception)
Absolutely love ur content tibees❤ as ,seeing you post a new video makes me happy😄
I was a high school student in 1968; my physics teacher had a stash of Scientific American magazines in his closet. I found one that had an array of integers on the cover where those that were prime were highlighted. This was the Ulam Spiral and was the subject of Martin Gardner's column for that month. I spent the next few years exploring this idea and "borrowed" considerable computer time from my college to explore features of this somewhat simple, yet mesmerizing idea. The spiral on the cover had the property that the elements of the main diagonal replecated the values of the Euler polynomial f(x) = x^2 + x + 41 which generates prime values for x = 0, 1, ..., 39. I explored such polynomials on my own and and proved some elementary theorems, certainly well known and could serve as elementary exercises. The Most sigificant result was that any similar polynomial x^2 + x + c has a minimal prime, call it p, which more or less controls the long-term density of primes generated by the polynomial. For example, the Euler polynomial has a minimal prime of 41 - the constant term need not be the minimal value. I hypothesized that if I could find a value k > 41 then a polynomial x^2 + x + c with minimal prime value k would eventually have a greater density of prime values on an interval [0, big number] than the Euler polynomial. I eventually found a very large number (vln) such that x^2 + x ^ vln, with minimal prime value 59, did surpass the Euler polynomial. I burned many, many hours on the campus main frame to produce this result and bound the outputs (132 column sheets at the time) into a large volume which I unfortunately no longer possess. This certainly was not a proof of my conjecture, but was a very exciting result for me.
I met Stan Ulam a few years later and mentioned that the article was an inspiration to me. Before I could launch into any details he mentioned that the article was intended as a joke! That pretty much ended that conversation. Well, that joke brought me many, many hours of pleasure, attempting proofs, learning to make an early mainframe computer produce crude graphic outputs and most importantly, making speculative hypotheses. It also led to a very lengthy and satisfying career of working with engineers to design and optimize computer algorithms. One of those efforts bought me two trips to Munich to present my work. No regrets.
Oddly enough I've pondered returning to the study of mathematics as an older adult. Currently studying on duolingo. It seems being autistic, that when I'm studying music (guitar) on the same day as math class, things fall into place at work & with socializing on a much greater level than ever.
This video has reminded how much joy and freedom there's to be had as a scholar.
Loved Martin Gardners puzzle column, seems a life time ago, thanks for reminding me!
For the years I was subscribed to the print version, I enjoyed Martin Gardner's column.
The device made of stiff tubes connected with flexible sections to form a polyhedron with hexagonal faces reminds me of an invention my stepfather created when I was about twelve.
He called it variously a Xoodle and a Xizix, and tried with indifferent success to market it as a toy. The world wasn't ready for it, but my sister and I used to enjoy playing with them.
I wonder now -- and will have to try to find out -- if this mathemagician was among his inspirations.
I remember reading Martin Gardner's columns in Scientific American, and then later in the collections. The ones on the Game of Life were special standouts, and I later studied cellular automata as part of my physics PhD research.
I read Martin Gardner but was not mathematically adept enough to understand much of it. But in the 1970s, I adored Scientific American and read every issue. Their illustrations were marvelous, both colorful and very informative. I still miss that "version" of Scientific American. It helped keep me thoroughly interested in science and math and enjoy both in my time as a professional pilot.
That and C.L. Stong's 'Amateur Scientist' column, those were the days. Make Scientific American Great Again! ;-)
Felix is very happy to be in the video!
Thanks so much for sharing this wonderful story! :)
Your smile is contagious. Thank you.
Gardner's Hexapawn Educational Robot (HER) article was always in the back of my mind throughout school, and played no small role in inspiring my eventual PhD in AI.
Love the video and also the background too
Bostonians must love your pronunciation of Martin Gardner’s name. I’m not from Boston, but I love it, too.
I had a subscription to Scientific American from the age of 13 to 26
Thanks. I`m using Gardner`s games and ideas to teach Math in high school, expecially to those sleepy students that believe that math is just a boring subject that one has to learn by heart in order to "do" something.
Mathematics is a highly perishable skill set. It is best to keep the set viable though pleasurable activity (i.e., “fun”). A mind in motion tends to stay in motion. QED
A "meebius" strip. Mind blown. I don't know if that is the or a correct pronunciation, but I love it.
Writing about a topic is a great way to learn about said topic :) He seems like my kindred soul
honestly i thought this video was going to be about vihart. her videos were quirky and her counting videos were especially strange, but i learned a lot from her videos and they were very polished and well done. great video nonetheless, but i was sad to find that vihart hid most of her videos. i hope she's doing ok
I find mathematics amazing in that so many things can be explained with it. I mean we landed a probe on a comet using Earth's and Mars's gravity to help propel it out towards where the comet was. Then we used 7.5 hours of an 8-hour rocket burn to catch up with the comet. Now that's mathematics. There's some very intelligent people in the world. I'm not one of them
That column discouraged me for ever learning math.
Thanks Toby. Gardner makes math accessible for many of us.
You look like you are doing well. I remember my Dad bringing Early Scientific Americans with this and his Mensa newsletter.
I was dragged out of my chair, verbally abused and given 6 of the best (all in front of the class) for stumbling across a method of calculating sums. I became highly stressed by doing math's ever since - til about 10 years ago.
I aced all other elements of school.
I don't watch this channel (and other physics/math's channels) because I love math's, but because it's magically interesting.
Thank you Toby for this interesting video
In fact, as an interlated subjects; Physics intersect with Mathmatics in a numberical way. happility, new design can create a new problems out of your brain, and an old problems can get a solution, out of your brain. There is a Mathmatics that looks like a Physics problem problems in the universe.
Thank you so very much Tibees, for this video, and for introducing me to Martin Gardner and mathematical games, it is truly and absolutely appreciated!!!!!!!💙🙏🙏🙏🙏🙏🙏🙏💙.
He also edited a great edition of Thompson's Calculus Made Easy.
I was a fan of Martin Gardner's column.
This reminds me of a German book in the same veins as Martin Garnder's work I read when I was a young teen: "Aus eins mach zehn und zehn ist keins. Glanz und Elend der Mathematik. " published way before I even existed in 1960 by Helmu Kracke on ro ro ro.
I have a number of Martin Gardner's books; I adore them!
Inspiring stuff, as always. 🤔🤗
As soon as I saw this, I thought, could you be talking about Martin Gardner? 😊 As a 57-year-old erstwhile mathematician (well, PhD dropout!), I was certainly inspired by Mathematical Recreations.
I've made a hexaflexagon. Good fun.
Love your vids thanks! take care.
Mathematical Games was a monthly goto reading Scientific American
Wow so many things I have heard of, from one book (well 15 ) books
Martin Gardner's column was always something to look forward to. I wouldn't call it bizarre, though.
Gracias, en español también he leído algunos libros de Martin Gadner!..que bueno que le des este video!
have most of his books
I read _Scientific American_ every month, and the first page I turned to was Mathematical Games. Its successor, Metamagical Themas, by Douglas Hofstadter, was a worthy replacement.
Thanks for sharing
❤❤❤ This plastered a level 32 smile on my face for the entire video. He influenced me, too. Not just in my math, but in my writing, as well. TYVM - the future author of Endo’s Deity. He’s in my book.
It’s great that you’re into math.
Hexagons are the bestagons.
Mathematical cheesecake. Abe Books sells his out of print books.
Great video!
I follow u from egypt i am 14 i really like Ur Channel zu viel please keep going
what is your favorite math joke in The Simpsons?
Splendid Toby maybe on a good day i ll tell you some
best love story of the week.
not all heroes wear capes
Wow ,so fascinating
So he was kind of a carl sagan of math.
I started reading Martin Gardner’s columns and books in the 1960’s. I would usually read his column in Scientific American before all the other articles. Unfortunately, in the last decade or so, Scientific American has become too politically biased to be worth the subscription price or the time to dump it straight into the recycling bin.
Very cool
i dont like math but im here for your asmr lol
I could listen to your voice all day.. ❤
I am math-deficient. So I wonder... how can you have limits on infinity?
Good Video
I watched your video, even though i didn't have a cmue what you were talking about 😮.
3954 in two hours =
wait what happened to the vihart channel?
Math mommy has returned
Martin Gardner never had a math degree , but was a genius at igniting the passion for maths in others. Toby Hendy is following in Martin Gardners footsteps.
As he said in the video, he never considered his self as a mathematician. Watching the video first, could answer some question in the first place.
@@IPMan-me6lo I think you misinterpreted the comment above. They weren't correcting her, just agreeing.
At least, that's how I read it.
Martin gardner's a genius 💯
was*
I love your videos lol
Estou apaixonado por vc
Thank you for this video 💐 Have you thought about recording audio books in your voice? I think you'll be great 👍😎
That is amazing
First
And the way you explain is really good and easy to understand
Hi Felix!
I think I love you.❤
Never was a fan of Scientific American. I liked National Geographic and Car & Driver instead.
His name sounds very German to me.
❤🤯
Mom, I’m here 🙋♂️🙋♂️🙋♂️
So late.
💚
🎉❤ followed her since my 13th ,now I'm 18.
I have followed her since I was 29th, now I am 34😂
🌞
🤩🤩🤩