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Most read Wikipedia articles about mathematical theorems last month:
1 Pythagorean theorem 53294
2 Central limit theorem 32590
3 Binomial theorem 22297
4 Law of large numbers 16510
5 Chain rule 16142
6 Fundamental theorem of calculus 13694
7 Law of cosines 13061
8 Gaussian integral 12078
9 Divergence theorem 11077
10 Chinese remainder theorem 9984
@MichaelHale, yep, looks exactly like a top ten list of theorems people might look up. I count four calculus/analysis results and only one number theory result; interesting skew.
@Guesswhoitis. I removed minimax from the list because I figured the article was more focused on an algorithm than a theorem. Perhaps a similar argument could be made for Chinese remainder, but it had theorem in the article title.
If we removed CRT though, next on the list is mean value theorem.
@Guesswhoitis. I'm trying to list the order in which I encountered them in my life, but there are some difficulties. Like, I never explicitly worked out a Gaussian integral. I just saw Sqrt[Pi] in some formulas. I think the order in which I encountered them in my life is: Middle school - 1, 3, 7; High school - 6, 5, 4, 2, 8; College - 10; Reading after college - 9
@bel, now here, but I'm glad you reckoned it out. :)
@MichaelHale, interesting. I'd say the only bits in your list that I ever picked up in a classroom were 1, 2, 3, 5, and 7. The rest I wouldn't have ever known if I didn't bother leafing through the appropriate literature.
The lesson I picked up from this is that sometimes one just has to pick up a book or paper well outside your comfort zone. Surprisingly, it can often give you new insights into stuff you thought you knew forwards and backwards.
And a more humbling lesson: there's always something that's not yet even in your wildest imagination.
@Guesswhoitis. I didn't really have any math teachers that really stood out to me (other than my dad helping me when I was very young) until I got to college. Like for the fundamental theorem of calculus, the high school teacher just showed us the steps to solve the required problems for the test in the book. But I remember that was the first math book I really looked through on my own and it had nice pictures inside the cover.
Showing "with geometry you can do area of a polygon, with calculus you can do area under curves, etc".
Then in college I started reading the using Wikipedia for math studying. In high school I only used it for biographical and historical type things, although I liked the principles of the site.
I probably wouldn't have ever heard of abstract algebra, etc if I hadn't looked at the Wikipedia article for mathematics. That really helped set up a framework in my mind for where to place future knowledge.
I couldn't understand a lot of Wikipedia though, so I got some books about math history from Amazon.
@Guesswhoitis. Actually, no! Although it looks like that could have saved me a lot of time if I had known about it sooner. I think I somehow saw on Wikipedia that there was a popular book about the history of pi. So I read that, and then Amazon linked me to Symmetry by Sautoy and other modern math books for general audiences.
I didn't even know about The Story of Civilization volumes until about a month ago. They are so much better than the high school history books we used. I never read the high school history books. But a few pages into those volumes and they are giving all sorts of colorful details about Aborigines hunting ducks by swimming under them and drowning them by their legs.
Ah, you should get a copy when you can. Marvelously covers "classical" math history. Alas, I know of no comparable book for 20th-century math, probably on account of being already too broad to fit in a single manageable book.
I think it's true everywhere that history textbooks for children are often crap.
The lot of them make it look so dry that people don't see that it's supposed to be a narrative from which we can hopefully pick up something useful.
But back to math: I am forever thankful to the unusually permissive libraries I've been to, and the Internet, without which I would not know at least 80 % of what I now know.
@Guesswhoitis. Beckmann's History of Pi was definitely my first exposure to reading about mathematicians themselves. Even college classes never talked about them. So many were so quirky and had interesting stories that I really think they should sprinkle more of that into grade school. Or just taking a moment to think about how the Egyptians, etc would try to calculate pi just helped me a lot. Having some anchor images to start interpolating a historical trajectory for math.
@Guesswhoitis. I guess the purpose of grade school doesn't seem to be to instill enthusiasm about the subjects though. That's probably becoming worse and worse as the importance of lifelong learning to keep up with changes increases.
But yes, any serious student of subject X can and should know the history of subject X. This is missing in most curricula. Certainly, there was no "History of Chemistry" in my time; that would have greatly enriched the other courses that went like: "here's the concept/formula, here's where you might see it, now take out your quiz book…" *rolls eyes*
@Guesswhoitis. Yes, I think chemistry is a particularly interesting case. On the one hand, you can efficiently teach someone our current models without any history. Then if they ask why is probabilistic or something then you point to a couple of experiments. On the other hand, if you want to develop a good sense of how to make a better metal for bridge making or buildings, then understanding the whole messy history can be very valuable.
"you can efficiently teach someone our current models without any history." - that's true, and yet the flip side is that most kids come out of this treating the lessons like the Ten Commandments, not subject to challenge.
Also, if they see that it was not quite that cut and dried before their time, maybe they won't take the knowledge for granted.
@Guesswhoitis. Well, yes. I definitely think it's extremely important to point out where the gaps are, or even hint where to go for more detail. Or to say, if you can find a way to explain the twin slit experiment without probabilities that would change everything, etc.
@Guesswhoitis. True. An example I always give is that I think high school teachers should always point out that friction is an emergent property, and that the formula they teach in early physics classes is just a simple model that is a good approximation for many scales. That helps tie it all together and point curious students where to go for more. Otherwise it is just a random, isolated formula that is easily forgotten.
@Guesswhoitis. I guess a simple thing I would have appreciated at a young age was a list of books titled "If we had a lot of time to teach each subject, we would be reading a fair bit from these". And it would have Feynman's lectures, the math history book you mention, The Story of Civilization volumes, etc.
I was surprised by the content of the A-level in Physics I did a few years ago. There was no maths in it at all. We "found the area under a graph" by "counting the squares on the graph paper".
Asked this question quite innocently, but have since come across this
which indicates there may be a problem downloading larger image sizes. Should I take down the question / apply to moderators to do so? I am loathe to do this, since @belisaurius has put in much time and effort into answerin...
