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Daniel Geisler (Jul 19 2020 at 18:50):CT makes the cut.
The burn it down and start again mathematics curriculum
John Baez (Jul 19 2020 at 20:51):Oldridge advocates visualizing mathematics "wherever and whenever" possible. That would be good for me, but it's good to remember that some people really don't like visualization and don't feel good at it.
John Baez (Jul 19 2020 at 20:54):He raises a question mark about teaching more set theory, given some people's bad experiences with the "New Math." I think set theory is essential, and the main lesson from the New Math is that it's almost impossible for teachers to teach well what they don't understand. To teach category theory, we need people who understand category theory.
John Baez (Jul 19 2020 at 21:13):I'm hoping Eugenia Cheng's forthcoming book on category theory will help jump-start this process.
Ellis D. Cooper (Jul 19 2020 at 21:27):@Daniel Geisler Some little kids ask questions. A "teacher" for little kids ought to learn how to help all little kids ask questions. Then, pretty much all questions have some mathematical aspect, and a "teacher" ought to know how to make the connection between a little kid's question(s) to some little bits of mathematics. To me, that means *every * "teacher" should be a perpetual student of mathematics. And, of course, everyone ought to be a perpetual student of everything. Life is short.
Daniel Geisler (Jul 19 2020 at 22:00):@Ellis D. Cooper I believe in a holistic approach to math education - set theory and CT, human and computer instruction. While people have different opinions about the significance of different branches of mathematics, few debate the importance of mathematics itself.
In third grade I began asking my teachers about the patterns I was seeing in multiplication tables. I developed a good chunk of mathematics before I realized that I had reinvented discrete calculus during an IQ test and was using simultaneous equations to solve chemistry problems.
While I love mathematics, it is only a hobby, as I work as a computer developer. It is my hope that soon we will develop AI systems for analysing in detail people's mathematical problem solving ability.
Ellis D. Cooper (Jul 19 2020 at 22:06):@Daniel Geisler When I was in 6th grade in the early 1950s at PS139 in Brooklyn, NY my wonderful teacher Miss Keit had a guest who asked if anyone could spell "infinitesimal." I did, and (a lot) later I learned Abraham Robinson's explanation.
David Michael Roberts (Jul 20 2020 at 11:18):John Baez said:
I'm hoping Eugenia Cheng's forthcoming book on category theory will help jump-start this process.
Another one on category theory? I know she had another book just come out, but that is not on CT per se, as far as I can tell (though I gather it is probably filled with ideas informed by CT).
John Baez (Jul 20 2020 at 20:55):Yes, I believe this new book by Eugenia will be a textbook on category theory suitable for high school and college students.
Robert Seely (Jul 21 2020 at 23:53):John Baez said:
Yes, I believe this new book by Eugenia will be a textbook on category theory suitable for high school and college students.
Eugenia's next book:
x + y
A Mathematician’s Manifesto for Rethinking Gender
"Why are men in charge? After years in the male-dominated field of mathematics and in the female-dominated field of art, Eugenia Cheng has heard the question many times. In x + y, Cheng argues that her mathematical specialty — category theory — reveals why. Category theory deals more with context, relationships, and nuanced versions of equality than with intrinsic characteristics. Category theory also emphasizes dimensionality: much as a cube can cast a square or diamond shadow, depending on your perspective, so too do gender politics appear to change with how we examine them. Because society often rewards traits that it associates with males, such as competitiveness, we treat the problems those traits can create as male. But putting competitive women in charge will leave many unjust relationships in place. If we want real change, we need to transform the contexts in which we all exist, and not simply who we think we are."
(From her webpage)
David Michael Roberts (Jul 22 2020 at 00:02):@Robert Seely this book is out now (it was what I was alluding to), and seems to be different to the one @John Baez was mentioning.
Robert Seely (Jul 22 2020 at 03:07):David Michael Roberts said:
Robert Seely this book is out now (it was what I was alluding to), and seems to be different to the one John Baez was mentioning.
Ok - my e-book "shop" (Kobo) has it to appear August 25th - I'll wait for that version, I guess.
Robert Seely (Jul 22 2020 at 03:09):Robert Seely said:
David Michael Roberts said:
Robert Seely this book is out now (it was what I was alluding to), and seems to be different to the one John Baez was mentioning.
Ok - my e-book "shop" (Kobo) has it to appear August 25th - I'll wait for that version, I guess.
Oh - I see - UK vs US release dates!! (And I guess Canada is in the "US area" for this purpose ... )
Robert Seely (Jul 22 2020 at 03:30):In the meantime, there's always her "Cakes, Custard, and Category Theory", as well as her 2002 Category Theory Lecture Notes (DPMMS) - though those are rather "brief" in scope. Unfinished I guess ...
John Baez (Jul 22 2020 at 21:54):I was talking about the book she's writing now. She calls it her "very explanatory category theory book".
David Michael Roberts (Jul 23 2020 at 05:28):@John Baez cool. Where did she talk about it?
John Baez (Jul 24 2020 at 01:41):In email to me. We're friends.
David Michael Roberts (Jul 24 2020 at 02:45):OK, secret project then. I look forward to it.
John Baez (Jul 24 2020 at 14:41):Well, not exactly "secret". This is her second year running a summer camp for high school students, and she's teaching them category theory. (It's online this year due to coronavirus.)
David Michael Roberts (Jul 25 2020 at 03:00):I mean more like as opposed to people who write their books in a public GH repo or hosted on the nLab for all the world to see :-)