It stretched my brain in ways that my day job doesn't. I've since continued to take all of the courses in the series, which are always about "interesting" mathematics. The professor (Dr. Michael Miller) has been teaching these graduate-level extension courses for something like 20+ years. If you are in the area of UCLA, I highly recommend attending. Sadly, there's no online option, so you'll have to be a local.
Unfortunately, I don't live near UCLA (Does anyone know of a similar program in the Boston area?).
However, I have found that it is not too hard to learn advanced math without the help of an instructor. A couple math-inclined co-workers and I have been reading Topology by Munkres. Since it is such a popular textbook, there are plenty of solutions to exercises online. Working with other people makes it easier to ask questions if you are confused, and also helps me stay motivated.
My favorite books by Gardner, and these are great introductions to his lighthearted approach to math, are the pair Aha! Insight [1] and Aha! Gotcha. These are probably the least rigorous works he made, but extremely fun and still tackle interesting subjects (in other words, great for kids). If you want something longer form or less approachable, he was a very prolific author so any of his other dozens of books are great too.
This is a little narrow-minded. The process of doing mathematics is mostly diligence and hard work, and the higher up you go the more work you have to put in to reach those moments of insight and clarity that make the struggle worth it.
If your argument is that there is a blurry line between recreation and work when you love your job, then sure. Maybe the average person will believe that in some abstract intellectual sort of way. But I don't think you'll convince any mathematicians that their entire job is recreation. By analogy, I don't think you'd convince any world-class musicians that their entire job is recreation when they're doing music drills and rehearsing for ten hours a day.
puzzles = the best, most significant part of math.
is always true. Sometimes, sure but the entire math terrain is complex and shouldn't be reduced to pure puzzles, pure progressions of abstraction or any other simplistic view.
... but there is a certain amount of joy and amusement to such endeavors, isn't there? Why else suffer the rote exercises? For the money?
It is a recreation, of a kind, that shouldn't be taken for granted even after doing rote derivations for ten hours a day. If you enjoy it that ten hours is rarely enough.
I have to disagree with that kind of absolutist statement.
I become interested in mathematics at a young age. While puzzles and such have sort-of interested me, the truly amazing part of math has always been it's ability to open up more abstract ways of thinking - new and exciting ways to unify ideas. (I read Gardner as a kid and got rather little of him. His puzzles go so quickly from simple games to really hard math that it's easy to get lost. I honestly would see him as a terrible introduction to math for kids since a kid reading him will hit quickly "why can't I solve this even slightly" moments, which isn't a way to encourage someone).
A lot of puzzles to my mind seem to have "trick" solutions. They're nice for increasing one's ability to manipulate symbols but they aren't really introducing new worlds into one's thinking.
I enjoy abstract algebra, functional analysis and differential geometry more than number theory, which is the branch of math closest to ordinary puzzle solving. On the other hand, category theory seems more like accounting to me but clearly category theory has yielded results that have advanced many parts of math and computer science.
I can certainly acknowledge that others might have different tastes and the development of math has certainly has come through different people developing their particular interests rather than there being a simple "fun"/"not-fun" division.
How so? There is math beyond arithmetic. A great deal of math, in fact. Non-recreational math goes by many, many other terms beyond accounting, such as engineering, particle physics, astrophysics, physical chemistry, etc.
Hint for the coin puzzle (rot13): As mentioned in the article, gur fbyhgvba trarenyvmrf gb nal cbjre bs guerr, gubhtu gur ahzore bs jrvtuvatf jvyy bs pbhefr inel.
Solution (rot13): Fcyvg gur pbvaf vagb guerr tebhcf bs guerr. Chg gjb tebhcf ba gur gjb fvqrf bs gur fpnyr, yrnivat gur guveq bss. Vs gurl ner rdhny va jrvtug, gur snxr pbva vf va gur guveq tebhc. Bgurejvfr vg vf va gur yvtugre bs gur gjb.
Qvfpneq gur tebhcf gur snxr vfa'g va. Chg gjb bs gur erznvavat pbvaf ba gur gjb fvqrf bs gur fpnyr. Ntnva, vs gurl ner rdhny va jrvtug, gur snxr vf gur guveq; bgurejvfr vg vf gur yvtugre bs gur gjb.
Guvf vf n grkgobbx qvivqr-naq-pbadhre nytbevguz. Gur xrl vafvtug vf gung lbh pna qvivqr ol n snpgbe bs guerr, abg whfg gjb.
The insight for size of groups can be shown by constructing the weighing that maximizes entropy.
With lg(9) bits of information needed to identify the odd coin, and a scale with only three possible outcomes (< > =), we can show the best sequence of weighings must reveal lg(3) + lg(3) bits of information by yielding a uniform distribution on the outcomes.
It stretched my brain in ways that my day job doesn't. I've since continued to take all of the courses in the series, which are always about "interesting" mathematics. The professor (Dr. Michael Miller) has been teaching these graduate-level extension courses for something like 20+ years. If you are in the area of UCLA, I highly recommend attending. Sadly, there's no online option, so you'll have to be a local.
More info on the course from another student (and clear fan): http://boffosocko.com/2015/09/22/dr-michael-miller-math-clas...