Martin Gardner's Mathematical Games

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1. memetomancerDec 2021
   Maybe this won't be a popular opinion, but there are some non-CS-specific works that really helped cement some underlying principles.

   Namely, the fun stuff like "Martin Gardner's Mathematical Games" articles, "Gödel, Escher, Bach" by Hofstadter, and "The Cyberiad" by Stanislaw Lem.

   These require a bit of thoughtfulness applied to relate to CS. And it was specifically worthwhile to actually work through the number theory stuff in GEB.

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2. todd8Dec 2017
   I grew up in an inner city Detroit neighborhood. The junior high school that I attended was pretty rough so, to avoid the gangs that formed after school, I quickly ran over to the near by public library and stayed there until it was safe to walk home around dinner time.

   A friend showed me a magazine at the library; it was Scientific American and it completely hooked me. This was 1963 and SA was then a great magazine. I read every current issue and then read the bound volumes of past issues. My favorite monthly columns were Martin Gardner's Mathematical Games and the Amateur Scientist. I read every one of those two columns ever published.

   The schools I attended were not very good, but I learned a lot of math and science during those years at the library. I went on to score very high in math and science, got into great colleges and ended up with a very successful career.

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3. JtsummersMay 2016
   Practice, and read about similar puzzles/problems. Track down reprints/scans of Martin Gardner's Mathematical Games and similar publications.

   In general, for identifying if something is a graph problem:

   1) Through some mapping, (almost?) everything can be transformed into a graph problem of some sort. Now, that's a bit too big a set and ignores the real question.

   2) How do I identify that a problem is practically solved with graphs?

   Some heuristics (note, these are heuristics, particularly useful for getting started, but not at all absolutes):

   Is it discrete? In the given problem from the link we have a finite number of extreme points (ends of each line segment), but an infinite number of points between. Fortunately, thanks to the problem constraint, there are only a few non-endpoints that we are concerned with. So we can safely ignore the infinity of possibilities by only examining this finite set.

   Are there transitions between these states that are easily modeled as edges? In the given puzzle, absolutely. And its symmetric so an undirected graph is suitable (sometimes directed graphs would be more suitable or the only applicable solution).

   After this, proving various things (like that the generalized statement that all properly constructed puzzles have a solution) will require learning some of the basic properties of graphs, and how to restate the premises (such as constraints on altitude and movement) in a graph-theoretic form. It's easy to intuit the proof now that you have a simplified, but complete, model of the problem, but harder to state it with mathematical certitude. That part really will just require more practice and exposure.

   At some point you'll develop sufficient vocabulary in the field that you may not be able to prove it straight off, but you'll know what and where to look for the elements you need to construct a proof like they have.

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4. tzsMay 2016
   > Practice, and read about similar puzzles/problems. Track down reprints/scans of Martin Gardner's Mathematical Games and similar publications.

   The entire set of the 15 books that collected his "Mathematical Games" columns from Scientific American are available in PDF form on a CD-ROM:

   http://www.amazon.com/Martin-Gardners-Mathematical-Games-Gar...

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5. lioetersJun 2026
   > John Baez's This Week's Finds posts

   As an aspiring amateur of recreational mathematics, it gives me joy to find this recommendation and start reading the series. It reminds me of Martin Gardner's "Mathematical Games" column, and its successor, Douglas Hofstadter's "Metamagical Themas".

   For a while now I've been chewing on Baez's paper, "Physics, Topology, Logic and Computation: A Rosetta Stone". I'm intrigued by it. At first baffled, then continued studying related topics, coming back to re-read and appreciate what it's saying. I'm exploring what it means from the computation angle, in the context of Haskell Curry, combinators, lambda calculus, cellular automata, rewriting systems. And more far-fetched thoughts, like Stephen Wolfram, Max Tegmark, or how it may relate to biology such as Michael Levin's research.

   On the role of AI in mathematics, it brings up more questions about the use of computers in experimental/exploratory mathematics. Part of the concensus emerging, it seems, is the formalization of programs as proofs, in particular the Lean language ecosystem. It's like the field of software engineering is rediscovering its roots.

   The deeper I go the more I want to participate, write and talk about the fun things I'm discovering. Maybe one day write a paper of my own, if I can manage to do it in a respectable rigorous manner. For that I know I still have a lot of basics to learn, cultural etiquette too, and probably lean on something like Lean to be able to demonstrate that the ideas are sound.

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6. glimsheOct 2024
   What is this CD? I like old compilations.

   Edit: found it, it's called "Martin Gardner s Mathematical Games: The Entire Collection of His Scientific American Columns"

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