[math-fun] Who has written a clear summary of what research mathematicians do?
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why? I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians. The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices.
i think polya's how to solve it is a pretty good source for this. On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
Davis and Hersch had a collection of essays called "The Mathematical Experience" that was good too. On Sun, Aug 11, 2019 at 2:08 PM Thane Plambeck <tplambeck@gmail.com> wrote:
i think polya's how to solve it is a pretty good source for this.
On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 2019-08-11 11:09, Allan Wechsler wrote:
Davis and Hersch had a collection of essays called "The Mathematical Experience" that was good too.
Although this is not directly what you asked for, in the interviews and profiles of working mathematicians collected in "Mathematical People", there are examples and explanations of what research mathematicians do, and why.
On Sun, Aug 11, 2019 at 2:08 PM Thane Plambeck <tplambeck@gmail.com> wrote:
i think polya's how to solve it is a pretty good source for this.
On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Maybe slightly tangential, but excellent insight from an inspirational teacher (despite being --- technically speaking --- an amiably abysmal lecturer) : WILLIAM P. THURSTON (1994) ON PROOF AND PROGRESS IN MATHEMATICS https://arxiv.org/pdf/math/9404236.pdf WFL On 8/11/19, Allan Wechsler <acwacw@gmail.com> wrote:
Davis and Hersch had a collection of essays called "The Mathematical Experience" that was good too.
On Sun, Aug 11, 2019 at 2:08 PM Thane Plambeck <tplambeck@gmail.com> wrote:
i think polya's how to solve it is a pretty good source for this.
On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Maybe someone should get a bunch of non-mathematician spouses of mathematicians to collaborate on an essay about “Ten Things I Learned about Mathematicians by Being Married to One”. :-) Jim Propp On Sun, Aug 11, 2019 at 2:44 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Maybe slightly tangential, but excellent insight from an inspirational teacher (despite being --- technically speaking --- an amiably abysmal lecturer) :
WILLIAM P. THURSTON (1994) ON PROOF AND PROGRESS IN MATHEMATICS https://arxiv.org/pdf/math/9404236.pdf
WFL
On 8/11/19, Allan Wechsler <acwacw@gmail.com> wrote:
Davis and Hersch had a collection of essays called "The Mathematical Experience" that was good too.
On Sun, Aug 11, 2019 at 2:08 PM Thane Plambeck <tplambeck@gmail.com> wrote:
i think polya's how to solve it is a pretty good source for this.
On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Hi Scott, There really is no definition that adequately explains science at the level of its practitioners, and attempts to do so usually turn out looking bad on the author. It’s much more common to hear arguments about what science is not (think of all the rejection letters), but this still turns out laughable at times. I liked reading R. Dawkin’s “Oxford Book of Modern Science Writing” and F. Dyson “Scientist as a Rebel”. Both do an adequate job of incorporating diversity, and some of the content is mathematical. However, both of these references have elitist leanings, so may be more useful as a template to success or as competitor works, rather than as supporting citations. Cheers —brad
On Aug 11, 2019, at 11:07 AM, Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Thanks everyone for your ideas. I'm familiar with some of the references — they are good reminders — and look forward to reading Thurston's paper, and the science writings. I think it's an occupational hazard of being an expert in any field, not just math, that it can be hard to explain what you do to an outsider. Nonetheless I think it's important to do, and not just for outsiders, but also for people inside the field. At least it's important to me — the dearth of mathematicians talking about what mathematics is I find intolerable, and makes me distrustful of mathematics as a field. Well then I'll write something up and post it. On Sun, Aug 11, 2019 at 4:48 PM <bradklee@gmail.com> wrote:
Hi Scott,
There really is no definition that adequately explains science at the level of its practitioners, and attempts to do so usually turn out looking bad on the author.
It’s much more common to hear arguments about what science is not (think of all the rejection letters), but this still turns out laughable at times.
I liked reading R. Dawkin’s “Oxford Book of Modern Science Writing” and F. Dyson “Scientist as a Rebel”. Both do an adequate job of incorporating diversity, and some of the content is mathematical.
However, both of these references have elitist leanings, so may be more useful as a template to success or as competitor works, rather than as supporting citations.
Cheers —brad
On Aug 11, 2019, at 11:07 AM, Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Good question. Here's why I think mathematicians don't write about the process of doing math more often. *1. Lack of motivation. *The simple reason is that there is no driving need to explain mathematical research to people not doing it. That might be wrong however; anyone seeking funding for research needs to explain the importance of their work to outsiders. In science there are two drivers for visualizing scientific data: allowing researchers to discover/confirm patterns, and explaining their work to funders, which result in two very different types of research. You would think that training young mathematicians would be a good motivation to write about how math is done; it's why Keith Devlin wrote Introduction to Mathematical Thinking. But there's a vicious circle at work here — the people who enter math tend to be the ones who already get it. *2. Lack of skill. *Mathematicians are of course not trained to be writers/teachers. In addition, the common practice among mathematicians of hiding messiness and only reporting polished results interferes with writing to outsiders. I see similar biases in other fields shaped by the values of the field itself — artists speak through images, so are distrustful of artists who write about art, while writers, who practice exposing internal mental processes, can be quite articulate talking about their craft. *3. Lack of support*. A common attitude in academia is to look down on "popularization" of mathematics, though in this group that is probably not the rule. Marcus du Sautoy is a professor for the public understanding of math — what is remarkable here is not his position, but the fact that it is so incredibly rare. And on the flip side is that many science journalists who write about math for the public often don't understand math deeply enough (fortunately many do). *4. Resistance in the audience. *Institutionalized misunderstanding in the general public about what mathematics is, perpetuated by math education that perpetuates the myth that mathematics is no deeper than mindless calculation techniques. That means that any good explanation needs first to overcome misunderstanding. Personally I find the topic of how math is done to be really interesting, so I am eager to work on it more. On Mon, Aug 12, 2019 at 12:03 AM Andres Valloud < avalloud@smalltalk.comcastbiz.net> wrote:
Why do you think this is?
On 8/11/19 20:58 , Scott Kim wrote:
the dearth of mathematicians talking about what mathematics is I find intolerable
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Hi Scott. I would love to hear your thoughts on how to design puzzles. An intern of mine designed a wooden puzzle this Summer, and she was hoping to find readings about the art of puzzle design. In particular, we felt that “hard” and “tricky” are different things, that some puzzle designs are deceptive and others are not, and that a “good” puzzle involves some interesting balance of these things. - Cris
On Aug 12, 2019, at 8:43 AM, Scott Kim <scott@scottkim.com> wrote:
Good question. Here's why I think mathematicians don't write about the process of doing math more often.
*1. Lack of motivation. *The simple reason is that there is no driving need to explain mathematical research to people not doing it. That might be wrong however; anyone seeking funding for research needs to explain the importance of their work to outsiders. In science there are two drivers for visualizing scientific data: allowing researchers to discover/confirm patterns, and explaining their work to funders, which result in two very different types of research. You would think that training young mathematicians would be a good motivation to write about how math is done; it's why Keith Devlin wrote Introduction to Mathematical Thinking. But there's a vicious circle at work here — the people who enter math tend to be the ones who already get it.
*2. Lack of skill. *Mathematicians are of course not trained to be writers/teachers. In addition, the common practice among mathematicians of hiding messiness and only reporting polished results interferes with writing to outsiders. I see similar biases in other fields shaped by the values of the field itself — artists speak through images, so are distrustful of artists who write about art, while writers, who practice exposing internal mental processes, can be quite articulate talking about their craft.
*3. Lack of support*. A common attitude in academia is to look down on "popularization" of mathematics, though in this group that is probably not the rule. Marcus du Sautoy is a professor for the public understanding of math — what is remarkable here is not his position, but the fact that it is so incredibly rare. And on the flip side is that many science journalists who write about math for the public often don't understand math deeply enough (fortunately many do).
*4. Resistance in the audience. *Institutionalized misunderstanding in the general public about what mathematics is, perpetuated by math education that perpetuates the myth that mathematics is no deeper than mindless calculation techniques. That means that any good explanation needs first to overcome misunderstanding.
Personally I find the topic of how math is done to be really interesting, so I am eager to work on it more.
On Mon, Aug 12, 2019 at 12:03 AM Andres Valloud < avalloud@smalltalk.comcastbiz.net> wrote:
Why do you think this is?
On 8/11/19 20:58 , Scott Kim wrote:
the dearth of mathematicians talking about what mathematics is I find intolerable
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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When my son was creating his role-playing computer game, Homesick, I helped him develop puzzles to be solved in the game. First, it's quite challenging to create puzzles that will have no explanations or clues, so that part of the problem is to make sure they are recognized as puzzles to be solved. Second, the puzzles need to be solvable in some reasonable amount of time (you don't want your player stuck for hours and hours) and yet be challenging and not susceptible to solution by just trying everything. After the game was published I was surprised by the range of feedback on the puzzles: from "impossible" to "too easy". Of course his is not the only computer game incorporating puzzles, so there are a lot of them out there. I'm not a game player, but it would be interesting to catalogue and categorize the different game puzzles. Brent On 8/12/2019 8:12 AM, Cris Moore via math-fun wrote:
Hi Scott. I would love to hear your thoughts on how to design puzzles. An intern of mine designed a wooden puzzle this Summer, and she was hoping to find readings about the art of puzzle design. In particular, we felt that “hard” and “tricky” are different things, that some puzzle designs are deceptive and others are not, and that a “good” puzzle involves some interesting balance of these things.
- Cris
On Aug 12, 2019, at 8:43 AM, Scott Kim <scott@scottkim.com> wrote:
Good question. Here's why I think mathematicians don't write about the process of doing math more often.
*1. Lack of motivation. *The simple reason is that there is no driving need to explain mathematical research to people not doing it. That might be wrong however; anyone seeking funding for research needs to explain the importance of their work to outsiders. In science there are two drivers for visualizing scientific data: allowing researchers to discover/confirm patterns, and explaining their work to funders, which result in two very different types of research. You would think that training young mathematicians would be a good motivation to write about how math is done; it's why Keith Devlin wrote Introduction to Mathematical Thinking. But there's a vicious circle at work here — the people who enter math tend to be the ones who already get it.
*2. Lack of skill. *Mathematicians are of course not trained to be writers/teachers. In addition, the common practice among mathematicians of hiding messiness and only reporting polished results interferes with writing to outsiders. I see similar biases in other fields shaped by the values of the field itself — artists speak through images, so are distrustful of artists who write about art, while writers, who practice exposing internal mental processes, can be quite articulate talking about their craft.
*3. Lack of support*. A common attitude in academia is to look down on "popularization" of mathematics, though in this group that is probably not the rule. Marcus du Sautoy is a professor for the public understanding of math — what is remarkable here is not his position, but the fact that it is so incredibly rare. And on the flip side is that many science journalists who write about math for the public often don't understand math deeply enough (fortunately many do).
*4. Resistance in the audience. *Institutionalized misunderstanding in the general public about what mathematics is, perpetuated by math education that perpetuates the myth that mathematics is no deeper than mindless calculation techniques. That means that any good explanation needs first to overcome misunderstanding.
Personally I find the topic of how math is done to be really interesting, so I am eager to work on it more.
On Mon, Aug 12, 2019 at 12:03 AM Andres Valloud < avalloud@smalltalk.comcastbiz.net> wrote:
Why do you think this is?
On 8/11/19 20:58 , Scott Kim wrote:
the dearth of mathematicians talking about what mathematics is I find intolerable
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You might want to look at Seymour Papert's Mindstorms. On 8/11/19 9:07 , Scott Kim wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun .
Stewart Coffin’s writings, such as his recent “Compendium”, have some comments from the puzzle invention side looking toward mathematics. And he writes (p. 11) that “Mathematical Snapshots” by Hugo Steinhaus captured his imagination long ago. His comments on “incongruous solutions” (p. 193) pose a mathematical challenge. (But I bet you’re aware of all that.)
On Aug 11, 2019, at 12:07 PM, Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Two books by Jacques Hadamard; “The Mathematician’s Mind” and “An Essay on the psychology of invention in The Mathematical Field” On Mon, Aug 12, 2019 at 18:24 Mike Beeler <mikebeeler2@gmail.com> wrote:
Stewart Coffin’s writings, such as his recent “Compendium”, have some comments from the puzzle invention side looking toward mathematics. And he writes (p. 11) that “Mathematical Snapshots” by Hugo Steinhaus captured his imagination long ago. His comments on “incongruous solutions” (p. 193) pose a mathematical challenge. (But I bet you’re aware of all that.)
On Aug 11, 2019, at 12:07 PM, Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Hardy's "A Mathematician's Apology". http://www.math.ualberta.ca/~mss/misc/A%20Mathematician's%20Apology.pdf Hilarie
A book I've appreciated:
Cédric Villani: "Birth of a Theorem: A Mathematical Adventure"
Presentation (in English, one hour) here: https://www.youtube.com/watch?v=nD6UvYrNoXI Best, É.
Éric — Thanks for the reference. I don't know this one, and it looks very interesting. I'll look into it. — Scott On Tue, Aug 13, 2019 at 7:06 AM Éric Angelini <bk263401@skynet.be> wrote:
A book I've appreciated:
Cédric Villani: "Birth of a Theorem: A Mathematical Adventure"
Presentation (in English, one hour) here: https://www.youtube.com/watch?v=nD6UvYrNoXI
Best, É.
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Thanks everyone for your thoughts. My conclusion is that the best work on explaining math to nonmathematicians is happening not in books and papers, but in short videos on YouTube. Not only do sound and animation greatly improve the accessibility of the presentation, being on YouTube means these little gems can be found by mere mortals, instead of being buried away in academic journals. And there is something about the evolving conventions of YouTube videos that encourages personal, emotionally honest writing that is easy to relate to. The Math YouTubers well known in this community include Numberphile and Vi Hart. I'm finding there are other gems: *3blue1brown* has a huge library of lucid videos that edge into higher math. The following video analyzes an elegant International Math Olympiad problem that requires no higher math at all, but is nonetheless difficult, and serves as an excellent example of how research mathematicians think — the moral is that to simplify a complex problem, search for an invariant. https://www.youtube.com/watch?v=M64HUIJFTZM&t=95s *The Domain of Science* has produced an outstanding series of videos that give 10-15 minute overviews of the history of entire fields of science, and yes one of mathematics...also available as a poster. https://www.youtube.com/watch?v=OmJ-4B-mS-Y And what's really remarkable about these two videos is that they have 2 and 5 million views, respectively. The hunger is out there! For the last year I've been shooting, editing and animating weekly videos for my own Game Thinking business ( https://www.youtube.com/channel/UC9jS5pCo5v8MoF6GjpGiXBw?view_as=subscriber). I'm looking forward to making short math videos in the future. Any of you interested in getting into making short math videos? It'd be fun to compare notes. — Scott On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices.
I’ve stuck my toes in with my Barefoot Math videos, but I haven’t found the time to make many of them. Jim Propp On Thu, Sep 5, 2019 at 11:14 AM Scott Kim <scottekim1@gmail.com> wrote:
Thanks everyone for your thoughts. My conclusion is that the best work on explaining math to nonmathematicians is happening not in books and papers, but in short videos on YouTube.
Not only do sound and animation greatly improve the accessibility of the presentation, being on YouTube means these little gems can be found by mere mortals, instead of being buried away in academic journals. And there is something about the evolving conventions of YouTube videos that encourages personal, emotionally honest writing that is easy to relate to.
The Math YouTubers well known in this community include Numberphile and Vi Hart. I'm finding there are other gems:
*3blue1brown* has a huge library of lucid videos that edge into higher math. The following video analyzes an elegant International Math Olympiad problem that requires no higher math at all, but is nonetheless difficult, and serves as an excellent example of how research mathematicians think — the moral is that to simplify a complex problem, search for an invariant. https://www.youtube.com/watch?v=M64HUIJFTZM&t=95s
*The Domain of Science* has produced an outstanding series of videos that give 10-15 minute overviews of the history of entire fields of science, and yes one of mathematics...also available as a poster. https://www.youtube.com/watch?v=OmJ-4B-mS-Y
And what's really remarkable about these two videos is that they have 2 and 5 million views, respectively. The hunger is out there!
For the last year I've been shooting, editing and animating weekly videos for my own Game Thinking business ( https://www.youtube.com/channel/UC9jS5pCo5v8MoF6GjpGiXBw?view_as=subscriber ). I'm looking forward to making short math videos in the future.
Any of you interested in getting into making short math videos? It'd be fun to compare notes.
— Scott
On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices.
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What's your vision of a positive outcome? How do you plan to measure? On 9/5/19 8:13 , Scott Kim wrote:
Thanks everyone for your thoughts. My conclusion is that the best work on explaining math to nonmathematicians is happening not in books and papers, but in short videos on YouTube.
Not only do sound and animation greatly improve the accessibility of the presentation, being on YouTube means these little gems can be found by mere mortals, instead of being buried away in academic journals. And there is something about the evolving conventions of YouTube videos that encourages personal, emotionally honest writing that is easy to relate to.
The Math YouTubers well known in this community include Numberphile and Vi Hart. I'm finding there are other gems:
*3blue1brown* has a huge library of lucid videos that edge into higher math. The following video analyzes an elegant International Math Olympiad problem that requires no higher math at all, but is nonetheless difficult, and serves as an excellent example of how research mathematicians think — the moral is that to simplify a complex problem, search for an invariant. https://www.youtube.com/watch?v=M64HUIJFTZM&t=95s
*The Domain of Science* has produced an outstanding series of videos that give 10-15 minute overviews of the history of entire fields of science, and yes one of mathematics...also available as a poster. https://www.youtube.com/watch?v=OmJ-4B-mS-Y
And what's really remarkable about these two videos is that they have 2 and 5 million views, respectively. The hunger is out there!
For the last year I've been shooting, editing and animating weekly videos for my own Game Thinking business ( https://www.youtube.com/channel/UC9jS5pCo5v8MoF6GjpGiXBw?view_as=subscriber). I'm looking forward to making short math videos in the future.
Any of you interested in getting into making short math videos? It'd be fun to compare notes.
— Scott
On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Good question. My visions: 1. Cultural shift. When you go to a party and introduce yourself as a mathematicians, people will be interested and have a sense of what that means through positive ersonal experiences, rather than feeling embarrassed and saying something like "I was never good at math". It is not that everyone will be good at math, any more than everyone is good at writing, but it will be less mysterious. The children's book author who has done this the best is Mitsumasa Anno, whose work is now continued by his soon. His beautiful illustrations and charming stories jump deep into mathematical thinking in a way that a young child can understand. 2. Cultural value. Math literacy will be a culturally supported value, the same way reading is supported by libraries, reading programs, and reading to your child at night. I'm working on this issue now by starting the math game enrichment program http://mathmonday.net 3. Anyone who wants to understand parts of mathematics can easily find ways to do that...YouTube is starting to do that now. 4. For me personally, I'll have a satisfactory answer to the classic question "what is mathematics" in plain English that is practical and insightful, and easily shared with others. This is the question that has kept me up at night for the last 50+ years. I'm very close to resolving this for myself. On Sat, Sep 7, 2019 at 1:45 AM Andres Valloud < avalloud@smalltalk.comcastbiz.net> wrote:
What's your vision of a positive outcome? How do you plan to measure?
On 9/5/19 8:13 , Scott Kim wrote:
Thanks everyone for your thoughts. My conclusion is that the best work on explaining math to nonmathematicians is happening not in books and papers, but in short videos on YouTube.
Not only do sound and animation greatly improve the accessibility of the presentation, being on YouTube means these little gems can be found by mere mortals, instead of being buried away in academic journals. And there is something about the evolving conventions of YouTube videos that encourages personal, emotionally honest writing that is easy to relate to.
The Math YouTubers well known in this community include Numberphile and Vi Hart. I'm finding there are other gems:
*3blue1brown* has a huge library of lucid videos that edge into higher math. The following video analyzes an elegant International Math Olympiad problem that requires no higher math at all, but is nonetheless difficult, and serves as an excellent example of how research mathematicians think — the moral is that to simplify a complex problem, search for an invariant. https://www.youtube.com/watch?v=M64HUIJFTZM&t=95s
*The Domain of Science* has produced an outstanding series of videos that give 10-15 minute overviews of the history of entire fields of science, and yes one of mathematics...also available as a poster. https://www.youtube.com/watch?v=OmJ-4B-mS-Y
And what's really remarkable about these two videos is that they have 2 and 5 million views, respectively. The hunger is out there!
For the last year I've been shooting, editing and animating weekly videos for my own Game Thinking business (
https://www.youtube.com/channel/UC9jS5pCo5v8MoF6GjpGiXBw?view_as=subscriber ).
I'm looking forward to making short math videos in the future.
Any of you interested in getting into making short math videos? It'd be fun to compare notes.
— Scott
On Sun, Aug 11, 2019 at 9:07 AM Scott Kim <scottekim1@gmail.com> wrote:
Does anyone know of a clear explanation written for nonmathematicians of the fundamental types of things research mathematicians do, and why?
I'm planning to write about how the process of inventing puzzles is similar to the process fo doing mathematical research, and how we can teach kids about mathematical research by having them invent puzzles. I'd like to reference other authors, and wonder what has been written that isn't just mathematicians talking to mathematicians.
The authors I know who have attempted this are Keith Devlin in Introduction to Mathematical Thinking, written to tell math grad students how "real" mathematics differs from how math is conventionally taught in K-12, and Eugenia Cheng in many of her books, starting with How to Bake Pi. These are good, but there's room for more voices.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (15)
-
Allan Wechsler -
Andres Valloud -
bradklee＠gmail.com -
Brent Meeker -
Cris Moore -
Fred Lunnon -
Hilarie Orman -
James Propp -
Michael Greenwald -
Mike Beeler -
Scott Kim -
Scott Kim -
Thane Plambeck -
Victor Miller -
Éric Angelini