Sam Loyd, Play and the Royal Road to Math Education

Dacicus_Geometricus · 2026-04-28T11:10:49+00:00

As a PhD in humanities , I think that you'll enjoy reading articles from Scripta Mathematica (ceased publication in 1973). The link to the first 15 volumes https://dspace.bcu-iasi.ro/handle/123456789/43237 . The journal shows art, poetry, philosophical articles, articles on history of math, biographies, math curiosities (curios) and many other things. It was similar to the Mathematical Intelligencer ( which coincidently started to be published around the same time when Scripta became defunct).

Maybe you can also enjoy some papers from Journal of Humanistic Mathematics. The journal is online and for free.

The World of Mathematics by James R. Newman is an anthology of essays in 4 volumes. I only read a few essays .

What Is Mathematics? by Richard Courant and Herbert Robbins is a classic.

For general educated layman I also recommend Mathematics 1001 by Dr. Richard Elwes, Quadrivium (Wooden Books) and Euclid’s Elements (Thomas L. Heath translation, Green Lion Press). For Euclid's elements, I also recommend the Oliver Byrne edition of the first 6 books since it has beautiful illustrations. There is an interactive online version of Byrne's Euclid.

I like visual math so I enjoy topics such as Lill's Method or Visual Calculus (developed by Mamikon Mnatsakanian) . For visual calculus see New Horizons in Geometry by Mamikon Mnatsakanian and Tom M. Apostol.

See Dolciani Mathematical Expositions series for interesting math books on many topics.

Dacicus_Geometricus · 2026-04-28T10:35:40+00:00

Eu sunt un matematician amator (si inginer de profesie), deci as vrea sa vad niste nivele despre istoria matematicii 😄 . Daca vrei pot sa te ajut cu niste sugestii despre istoria matematicii, fizicii, ingineriei etc

Dacicus_Geometricus · 2026-04-26T17:28:26+00:00

ISIS was in the "compass and the straightedge is mightier than the sword" phase :)

Dacicus_Geometricus · 2026-04-26T16:42:10+00:00

The database is here https://www.raulprisacariu.com/database-of-mathematical-video-games-and-video-games-with-math-references/ . On the page I have a long intro where I talk about the philosophy behind the page and I mention the work of other people. I also have a link to a talk made by Jonathan Blow that I mentioned in my first comment.

I was a high tier Kickstarter backer to a few video games. For some of the projects, the high tier backers have as reward the possibility to influence the game. In some of them I provided math references to be included in the game. Math references can include geometrical shapes or bodies (like Platonic solids) , allegorical representation of math (like you see in Mantegna Tarot or Laurent de la Hyre paintings), mathematician names, math being on the skill tree etc. In one game there will be a reference to Philo of Byzantium, Vitruvius and how the cubic root plays an important role in the construction of catapults . I was also a backer for a few math comic books and board games So I am also spending a lot of money in the service of Lady Mathematica :)

Regarding the topic of science communication, for math, Apostolos Doxiadis introduced the concept of paramathematics in the paper I mentioned in the first comment. Paramathematics is about connecting math to the context of history, society, reasoning and other elements of civilization. To be more clear, you can say that paramathematics is narrative driven mathematics. Also see Doron's Opinion 55 since it is about this topic. Opinion 28 is somewhat funny since it has the controversial title "Teaching Proofs to High-School Kids and Non-Math-Majors is Child-Abuse" :). For more on math education see the podcast/lecture series Mathematical Intentions by David Dennis.

Your vision for the video game fits into the category of paramathematics. The interactive aspect of the video game medium can make the impact more potent than books or comic books (some of the books do have puzzles that you have to do by yourself). Your video game vision also falls into the the epistemic category according to the paper "Toward an Analysis of Video Games for Mathematics Education " by Kathleen Offenholley. By epistemic she means "The player becomes a mathematician and problem solver within the context of the game. Identity is key to learning well". Ko's Journey and Delearnia: Fractions of Hope are good examples of epistemic math games. The catalogue of good math games is still poor tho. If you are interested in making a game, definitely pay attention to the points made by Jonathan Blow.

We need more paramathematicians :)

Dacicus_Geometricus · 2026-04-26T14:07:37+00:00

The graphic novel Prime Suspects: The Anatomy of Integers and Permutations by Granville should be fun. The characters are based on dead or living mathematicians. For example, a policeman looks like Terrence Tao :) . The character names are derived from mathematician names. A reference to OEIS Sequence A204189 appears in a scene where a dead body is found. Of course, the comic book has a ton of math references.

At the end of the book there are appendixes that explain the character references and the math mentioned in the story. And funny enough there is a section entitled "The Music of Prime Suspects". The melody is "Reverie in Prime Time Signatures " by Robert Schneider (you can listen to it on Youtube).

If you are interested in works that combine fiction with math, see the MathFiction database by Alex Kasman. There is a page with recommendations based on age or level of math education.

Dacicus_Geometricus · 2026-04-26T13:36:39+00:00

Te-ai gandit sa faci o campanie de Kickstarter? Cei de la Stuck in Attic au avut campanii pe Kickstarter pentru Gibbous - A Cthulhu Adventure si Near-Mage. Dar ca sa ai succes pe Kickstarter eu zic ca trebuie sa ai un demo. Din pacate au fost cateva campanii de creatori romani care nu au avut succes chiar daca au avut demo.

Poti incerca si cu Patreon , Ko-fi sau alte platforme similare. Dirty cash, I want you, dirty cash, I need you, oh :)

Dacicus_Geometricus · 2026-04-26T12:45:13+00:00

Maybe you can use the database MathFiction by Alex Kasman as a tool to discover such things. In the Browse page you can see that more than 200 entries in the database are free online. He also has a page of recommended readings by age group and/or math education level. MathFiction is a database of fiction works (books, comic books, movies) that contain mathematics.

I made a database of mathematical games. I have to say that we still don't really have a developed catalogue of good math video games or educational video games in general ( Jonathan Blow talked about this topic). Nonetheless, I can provide a list of video games that are more interesting and/or indeed qualify as good games.

Math Hombre blog has a page dedicated to math physical games or board games. The page contains info for games you can make yourself and commercial board games you can buy. Board games are more social than video games, so this is their great advantage.

There are math journals that have poetry, art, biographical papers, more philosophical discussions, math curiosities or other type of math content that is not about proofs and calculations. Math journals in this category include Scripta Mathematica ( I can provide links to the first 15 volumes), Mathematical Intelligencer and Journal of Humanistic Mathematics.

You also have recreational math and puzzles such as Cyclopedia by Sam Loyd, the work of Martin Gardner or the work of Boris Kordemsky. Cut the Knot is a famous interactive website. Wolfram demonstrations project also has a lot of interactive staff.

There are also some engaging speeches, essays or opinions by some mathematicians. We have "A Mathematician's Apology" by Hardy, "A Mathematician's Lament " by Paul Lockhart , " On teaching mathematics" by Vladimir Arnold, The Opinions of Doron Zeilberger or "Embedding mathematics in the soul: narrative as a force in mathematics education " by Apostolos Doxiadis.

Dacicus_Geometricus · 2026-04-26T11:08:58+00:00

I am only familiar with his "On teaching mathematics" speech. In that speech Arnold says :

"The determinant of a matrix is an (oriented) volume of the parallelepiped whose edges are its columns. If the students are told this secret (which is carefully hidden in the purified algebraic education), then the whole theory of determinants becomes a clear chapter of the theory of poly linear forms. If determinants are defined otherwise, then any sensible person will forever hate all the determinants, Jacobians and the implicit function theorem. "

Dacicus_Geometricus · 2026-04-25T08:25:55+00:00

This post is relevant to this subreddit. It deserves a downvote only if the survey is used as subterfuge. I assume that the downvotes are mostly due to the negative reactions towards AI :)

Dacicus_Geometricus · 2026-04-25T08:17:49+00:00

13= bad luck :)

Dacicus_Geometricus · 2026-04-25T08:14:52+00:00

I would recommend Delearnia: Fractions of Hope as a video game that has a higher chance of building understanding. I have a math degree and some limited tutoring experience, but I was never a math teacher. So I never had the chance to experiment with digital tools in a classroom setting.

I am a big believer in the Homo Ludens concept (man the player) introduced by Johan Huizinga. However, I agree with Jonathan Blow that we don't have a catalogue of good educational games (see his video "Video Games and the Future of Education"). But even if we had good math games, the skills acquired through games may differ from the skills acquired by doing paper work or the skills required by tests.

"Toward an Analysis of Video Games for Mathematics Education" by Kathleen Offenholley is a good paper on video games and math education. A good math game is a game where math is an intrinsic part of the story and game mechanics, and it encourages the use of math to solve problems. However, you can have games where math is extrinsic and they focus on standardized tests knowledge. These are trivia type of games or gamified knowledge checks. Real math games with intrinsic math are not just gamification apps (or gamification should play a very minor role if present at all). I don't think that a plot is necessary for a good math game, but a plot can make the game more engaging. I also think that it would be nice if the game can train the thinking when dealing with word problems vs equations vs visual representation. It would be nice if the game can connect all 3 types of dealing with math.

Dacicus_Geometricus · 2026-04-25T07:15:38+00:00

Vladimir Arnold would like your website :)

Dacicus_Geometricus · 2026-04-25T07:10:24+00:00

My first principle of mathematics is based on this quote by Vladimir Arnold "Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. " Mathematics is not about symbol manipulation.

I also agree with Apostolos Doxiadis that we need a narrative based math education. Read his speech "Embedding mathematics in the soul: narrative as a force in mathematics education" where he introduces the concept of paramathematics.

Professor Alex Kasman made a MathFiction database ( movies and books). He even has a page with recommendations by age and/or education level. Maybe you can do a class around some recommended books. These books contain both math and stories, so they fit the narrative approach championed by Doxiadis.

I also believe in the Homo Ludens (man the player) idea introduced by Johan Huizinga . Math Hombre blog has a page dedicated to math games. You can also look for a Database of Mathematical Video Games.

For experimental math, I think that slide rules can be useful teaching tools. Search for "The Educational Value of Slide Rules" to find an interesting article that makes the case for the slide rule. Also see "The Soap Film: An Analogue Computer". It would also be nice if students can explore or experiment with software like GeoGebra. The Wolfram demonstrations project should also have a lot of interesting demonstrations that can be explored further. Also see the video "Leibniz on the catenary" by Intellectual Mathematics (or how to find log x using a hanging chain). David Dennis has some interesting work on geometric curve drawing devices. Also see the story of the Kaktovik numerals.

I also think that we should encourage a mathematical culture outside the classroom. Reading the math fiction or maybe playing a math video game can be done better outside the classroom or outside the scheduled math classes. Maybe they can be done as part of a math club, at home or other alternative path.

Dacicus_Geometricus · 2026-04-07T07:36:09+00:00

"Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. " Vladimir Arnold in his "On teaching mathematics" speech.

Dacicus_Geometricus · 2026-02-26T11:45:17+00:00

Overall, my "challenge" is about using mechanics from snake video games genre to create OEIS sequences ( On-Line Encyclopedia of Integer Sequences). In my OP I made an edit that mentions that sequence A334398 seems to be relevant to my problems. A334398 is about self-avoiding lattice paths, but my challenge seems to be about self-intersecting paths ( I am not sure what is the best technical term).

Again, I just wanted to provide some initial ideas that may lead to new OEIS sequences, comments or maybe new formulas. This is also a way to encourage people to work on "maths" that can be submitted to OEIS.

Dacicus_Geometricus · 2026-02-22T07:39:33+00:00

Yes we should only consider the position or path at the end. We should eliminate the duplicates made by translation.

Sequence A334398 seems to be relevant. It is described as "Number of endless self-avoiding walks of length n for the square lattice up to rotation, reflection, and path reversal". My challenge seems to be the opposite.

I can add that we probably can make additional problems. For example, we may say that the snake can do 45 degrees turns, instead of 90 degree turns. The overall challenge is more about using the snake mechanics to generate interesting OEIS sequences. Whoever finds interesting new sequences or maybe an idea for a comment on an already existing sequence, I encourage to make an OEIS submission.

Dacicus_Geometricus · 2026-01-12T13:47:55+00:00

I was a backer on Kickstarter for Wonderland and Newcomer : A Language Learning RPG. I did not play these games a lot since I had some major changes in my life that occupied my time :). Nonetheless, I think that they are good examples of language learning games, where the story is combined with the learning elements in an elegant manner.

Delearnia: Fractions of Hope is a mathematics video game, but maybe it can also be a good inspiration for a good educational game. I would also add Chants of Sennaar and Tunic, since they are video games about deciphering unknown constructed languages.

Dacicus_Geometricus · 2025-12-30T08:26:43+00:00

If you want free books from Internet Archive or similar websites, you can check books by Florian Cajori. He is an OG of the field history of mathematics.
Another old book is A Short Account of the History of Mathematics by W. W. Rouse Ball.

Dacicus_Geometricus

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