First, as a Swiftie, I can't pass up the bait you offered.
I won't try to claim that Taylor Swift is a scientific innovator. But she is an innovator in a lot of other ways, including being an amazing storyteller. Maybe she belongs in the section for "teaching ideas through stories"? I'm happy to drown you in examples... ;-)
On a different note, when you list the related patterns, can you add hyperlinks for the ones that have already been written? I think that would make these much easier to browse later.
Ha! I think "Swiftie-baiting" needs to become a common term...
(If it means anything, though I'm wouldn't claim to be part of the social phenomenon that is Taylor Swift fandom, I really like her music, agree with everything you said about her, and think how she handled her exit from Big Machine makes her one of the most baller entrepreneurs ever. Also, I just put "Folklore" on.)
Can I add hyperlinks? Yes, and I must! Will I? Oh gosh, I'm definitely incapable of staying on top of stuff like that! I should look into paying someone a little bit of money to (1) hunt for typos and fix 'em, and (2) do exactly that. If anyone reading this would ENJOY this task, and can show a history of being trusted with such things, lemme know.
Actually, I probably would enjoy a task like that. Professionally, I'm a software engineer, so staying on top of fiddly computer things is kind of my area of expertise.
Denise Gaskins has a lot of math book suggestions that would fall under the history/biography category (the books are organized by topic when you click on one of the age categories): https://denisegaskins.com/living-math-books/
There have been a lot of great math history videos on Veritasium in the past couple of years...it's a bummer he doesn't have them organized into a playlist. I'd say these are advanced middle school/high school level and up, though he is really great at making complex concepts understandable. https://www.youtube.com/@veritasium
Steven Strogratz's books (The Joy of X and Infinite Powers) are both really good and have a lot of history in them...Middle School and up (well, a middle schooler should be able to do all of Joy of X and at least understand about half of Infinite Powers...LOL... I think every high schooler about to take Calc should listen to Infinite Powers, because then they will understand what Calc is REALLY about, rather than just all the techniques and formulas you learn in class).
Out of print but an old favorite of mine is Asimov on Numbers by Isaac Asimov. Not all the essays are historical, but a lot of them are.
I have a couple of vintage series I like for science biographies... The Immortals of Science series and the Messner Shelf of Biographies (Messner isn't all science books - it's all kinds of bios).
This is probably the best list of the Messners: https://www.biblioguides.com/pub/series/messner-biographies (I have a personal list I've made of all the ones that are about scientists, which I can give to anyone who wants it, but I've only read about 3 of them so far).
So far in my experience, Immortals is the slightly drier of the two series, but can still be pretty good. Alessandro Volta and the Electric Battery was a great jumping off point for studying the topic of electricity.
We just finished reading Copernicus by Henry Thomas (Messner Shelf of Biographies) and it was really fascinating. I think we'll do a bio of Kepler after Christmas break. The Messners are very readable, but are a bit more in the "lightly fictionalized" style of biography with dialog.
Any readers ok with a religious perspective should check out the "Exploring the World of..." series by John Hudson Tiner. They are more textbooky but still a good resource, and I like that they are organized by topic (chemistry, biology, math, etc). They are very much in the vein of looking at the history of various discoveries.
Those of you who haven't been part of the homeschooling community may be forgiven for wondering if we're a bunch of kooks. All communities have their share, and probably ours punches above its weight! (I'M surely not the least kooky person on my block.)
But what we ALSO have is a small number of moms (and who knows, maybe some dads?) who have cultivated a connoisseur's taste for older, high-quality nonfiction books. A member of this group can recommend, for any subject you name, a half-dozen books you and your kid would LOVE, worthy to be read aloud — books you'll never find on a bestseller list, which rarely pop up on a first page of Amazon results, written in a time when authors defaulted toward a more straightforward style.
Kirsten is one of these people. And holy CRAP are we lucky to have her (and, let me say, at least one more such person I can name) as a regular commenter here.
Which is all to say: when you see a comment where Kirsten recommends things, follow the links.
At the undergraduate level, David Bressoud has been a big proponent of storytelling in math education; his wonderful book _A Radical Approach to Real Analysis_ takes you through the historical development of the subject in a very proof-oriented but still storytelling style. He used to teach a seminar on "The Life and Mathematics of Srinivasa Ramanujan" which definitely used the crazy stories of Ramanujan's life to motivate the mathematical material, and a similar but broader course on "Newton's Principia and the Scientific Revolution".
I think that focusing on the originators/saints is great, but not enough. More than that, I reckon the focus should be on the problem that needed to be solved. Of course, it all becomes more colourful as you include the person, their quirks, their facts. But when we talk about, say, infinity, more than talking about Cantor, we probably want to express how the obvious idea of infinity was so tantalizing to generations of Mathematicians, how they struggled to define it, how they failed! Yes, we should not only show successes on our classrooms, but also failure, shortcomings, misunderstandings!
Poincarè got all the Maths for Relativity, but he did not dare! This genius polymath, the man who knew so much Mathematics that he invented new fields just to keep going, he saw the whole of his work and he shied away from going in a particular direction, as it felt wrong! And it was actually right!
Gosh, I just got sidetracked, but I think this is important - as students, I think it would be worthwhile to understand that thinking about stuff involves lots of going back and forth, of missing opportunities, of going back to review something half-forgotten, of talking to friends! Yes, talking to friends, extremely important, just in that example you gave of Tesla! Just like what you're doing in the Substack!
We want to impart to other humans these experiences, how we get somewhere, and they are all important - getting some time alone to reflect on the ideas, working on several problems at once, talking to friends, being part of this special group/space where you get to discuss interesting things, getting exposed to different points of view!
Let me reiterate the point from this that I most appreciate:
> "focusing on the originators/saints is great, but not enough. More than that, I reckon the focus should be on the problem that needed to be solved. Of course, it all becomes more colourful as you include the person, their quirks, their facts. But..."
Hard agree! Let me put this forcefully: in science or math, the purpose of telling origin stories is to help students get into the questions, hypotheses, and solutions.
There really is a danger — I run into this sometimes in my science lessons — where the biographical details become detached from the ideas. THAT said, quirky stories can be useful in making a person stick into a student's memory.
I think you're raising, too, a separate idea: that a lot of progress in math & science comes NOT from individuals, but from groups. Again, hard agree! We can use stories to capture this, too — and since we want to paint an accurate picture of where good ideas come from (and see Steven Johnson's wondrous book of that title: amazon.com/dp/1594485380), we very much SHOULD do that.
No need to make this shorter - you organized it so well into sections that it's easy to chunk up mentally. As long as the formats you choose accomplish similar things, you're golden. Thanks again for the great read.
If she's anything like my girlfriend, she probably constantly tells you to keep it brief cuz you both have things to do. But you're doing something great, and I just hope you keep doing it. You're giving me so so so many tools to educate my kids.
This is one of my main tools for motivating or providing context in computer science education. Thankfully we have so many real, wacky characters! I do feel like I have a lower success rate with historical storytelling though than I have with other hooks (e.g. demo with surprising result, personal rant about the state of things) but it's basically always there as an option.
More recently I've been trying to use more historical context with math for my kids, and confronted the same open questions that you raise. Even when we do have a historical record, faithfulness can be boring for preschoolers as there can be a lot of missing context: "well you see, the Egyptians taxation system was based on land area, and this was complicated due to the Nile flooding... oh what is the Nile? ... Well you see...". So, I've embraced the storytelling aspect of it, and we simply have fun "imagining" people "a long time ago" who had some problem to solve. For this, the history of mathematics ends up mostly as inspiration for motivating problems, whether supported by the historical record or not. At the very least, it reminds me what is most fundamentally useful and interesting about the field, for instance with geometry we find problems that involve land measurement. Oh and as you and I discussed the other day, starting with a phrase like "there's an old story that..." or similar seems to appease the spirits of our historiographer elders.
Separately, are you familiar with David Pengelley? He taught undergraduate mathematics from primary sources, for instance here's a number theory textbook for a course he taught based around Sophie Germain's correspondence with Gauss attempting to prove Fermat's last theorem https://bookstore.ams.org/view?ProductCode=CLRM/70 ... I really love this stuff and particularly enjoyed a book he co-authored called Mathematical Expeditions. However I have not yet had the courage to teach entire courses in this style :)
When we don’t know the full story, I love the invocation of posing it as a mystery to be solved. A lot of economics (where I am training now) is like detective work, but maybe it’s even more obvious in linguistics. Starting from some assumptions about how humans operate, asking things like “what problems were they trying to solve,” or “what kinds of tools were available to them” lets us make sense of the mystery, and allows analogies form for when we would use the ideas ourselves. Of course we have to be careful about *wrong* ex post rationalization, which you allude to when talking about the myths. But even this can be a bridge: “why is that particular myth so salient? What value does it give our current culture?”
Finally, I’m (finally) reading Joesph Henrich’s The Secret of our Success about cultural evolution. Surely, you are aware of him (I think Scott did a SSC review a while ago), but I keep thinking how much your work (and from what I know of Egan from you) makes total sense in light of Henrich.
First, as a Swiftie, I can't pass up the bait you offered.
I won't try to claim that Taylor Swift is a scientific innovator. But she is an innovator in a lot of other ways, including being an amazing storyteller. Maybe she belongs in the section for "teaching ideas through stories"? I'm happy to drown you in examples... ;-)
On a different note, when you list the related patterns, can you add hyperlinks for the ones that have already been written? I think that would make these much easier to browse later.
Ha! I think "Swiftie-baiting" needs to become a common term...
(If it means anything, though I'm wouldn't claim to be part of the social phenomenon that is Taylor Swift fandom, I really like her music, agree with everything you said about her, and think how she handled her exit from Big Machine makes her one of the most baller entrepreneurs ever. Also, I just put "Folklore" on.)
Can I add hyperlinks? Yes, and I must! Will I? Oh gosh, I'm definitely incapable of staying on top of stuff like that! I should look into paying someone a little bit of money to (1) hunt for typos and fix 'em, and (2) do exactly that. If anyone reading this would ENJOY this task, and can show a history of being trusted with such things, lemme know.
♫♩In my defense, I have none... ♪♬
Actually, I probably would enjoy a task like that. Professionally, I'm a software engineer, so staying on top of fiddly computer things is kind of my area of expertise.
Email me and we can chat more?
timjohnson314 (at) gmail.com
Denise Gaskins has a lot of math book suggestions that would fall under the history/biography category (the books are organized by topic when you click on one of the age categories): https://denisegaskins.com/living-math-books/
There have been a lot of great math history videos on Veritasium in the past couple of years...it's a bummer he doesn't have them organized into a playlist. I'd say these are advanced middle school/high school level and up, though he is really great at making complex concepts understandable. https://www.youtube.com/@veritasium
Steven Strogratz's books (The Joy of X and Infinite Powers) are both really good and have a lot of history in them...Middle School and up (well, a middle schooler should be able to do all of Joy of X and at least understand about half of Infinite Powers...LOL... I think every high schooler about to take Calc should listen to Infinite Powers, because then they will understand what Calc is REALLY about, rather than just all the techniques and formulas you learn in class).
Out of print but an old favorite of mine is Asimov on Numbers by Isaac Asimov. Not all the essays are historical, but a lot of them are.
I have a couple of vintage series I like for science biographies... The Immortals of Science series and the Messner Shelf of Biographies (Messner isn't all science books - it's all kinds of bios).
Immortals of Science on LibraryThing: https://www.librarything.com/nseries/24675/Immortals-of-Science
This is probably the best list of the Messners: https://www.biblioguides.com/pub/series/messner-biographies (I have a personal list I've made of all the ones that are about scientists, which I can give to anyone who wants it, but I've only read about 3 of them so far).
So far in my experience, Immortals is the slightly drier of the two series, but can still be pretty good. Alessandro Volta and the Electric Battery was a great jumping off point for studying the topic of electricity.
We just finished reading Copernicus by Henry Thomas (Messner Shelf of Biographies) and it was really fascinating. I think we'll do a bio of Kepler after Christmas break. The Messners are very readable, but are a bit more in the "lightly fictionalized" style of biography with dialog.
Any readers ok with a religious perspective should check out the "Exploring the World of..." series by John Hudson Tiner. They are more textbooky but still a good resource, and I like that they are organized by topic (chemistry, biology, math, etc). They are very much in the vein of looking at the history of various discoveries.
WOW. How do I say this?
Those of you who haven't been part of the homeschooling community may be forgiven for wondering if we're a bunch of kooks. All communities have their share, and probably ours punches above its weight! (I'M surely not the least kooky person on my block.)
But what we ALSO have is a small number of moms (and who knows, maybe some dads?) who have cultivated a connoisseur's taste for older, high-quality nonfiction books. A member of this group can recommend, for any subject you name, a half-dozen books you and your kid would LOVE, worthy to be read aloud — books you'll never find on a bestseller list, which rarely pop up on a first page of Amazon results, written in a time when authors defaulted toward a more straightforward style.
Kirsten is one of these people. And holy CRAP are we lucky to have her (and, let me say, at least one more such person I can name) as a regular commenter here.
Which is all to say: when you see a comment where Kirsten recommends things, follow the links.
At the undergraduate level, David Bressoud has been a big proponent of storytelling in math education; his wonderful book _A Radical Approach to Real Analysis_ takes you through the historical development of the subject in a very proof-oriented but still storytelling style. He used to teach a seminar on "The Life and Mathematics of Srinivasa Ramanujan" which definitely used the crazy stories of Ramanujan's life to motivate the mathematical material, and a similar but broader course on "Newton's Principia and the Scientific Revolution".
I think that focusing on the originators/saints is great, but not enough. More than that, I reckon the focus should be on the problem that needed to be solved. Of course, it all becomes more colourful as you include the person, their quirks, their facts. But when we talk about, say, infinity, more than talking about Cantor, we probably want to express how the obvious idea of infinity was so tantalizing to generations of Mathematicians, how they struggled to define it, how they failed! Yes, we should not only show successes on our classrooms, but also failure, shortcomings, misunderstandings!
Poincarè got all the Maths for Relativity, but he did not dare! This genius polymath, the man who knew so much Mathematics that he invented new fields just to keep going, he saw the whole of his work and he shied away from going in a particular direction, as it felt wrong! And it was actually right!
Gosh, I just got sidetracked, but I think this is important - as students, I think it would be worthwhile to understand that thinking about stuff involves lots of going back and forth, of missing opportunities, of going back to review something half-forgotten, of talking to friends! Yes, talking to friends, extremely important, just in that example you gave of Tesla! Just like what you're doing in the Substack!
We want to impart to other humans these experiences, how we get somewhere, and they are all important - getting some time alone to reflect on the ideas, working on several problems at once, talking to friends, being part of this special group/space where you get to discuss interesting things, getting exposed to different points of view!
Let me reiterate the point from this that I most appreciate:
> "focusing on the originators/saints is great, but not enough. More than that, I reckon the focus should be on the problem that needed to be solved. Of course, it all becomes more colourful as you include the person, their quirks, their facts. But..."
Hard agree! Let me put this forcefully: in science or math, the purpose of telling origin stories is to help students get into the questions, hypotheses, and solutions.
There really is a danger — I run into this sometimes in my science lessons — where the biographical details become detached from the ideas. THAT said, quirky stories can be useful in making a person stick into a student's memory.
I think you're raising, too, a separate idea: that a lot of progress in math & science comes NOT from individuals, but from groups. Again, hard agree! We can use stories to capture this, too — and since we want to paint an accurate picture of where good ideas come from (and see Steven Johnson's wondrous book of that title: amazon.com/dp/1594485380), we very much SHOULD do that.
No need to make this shorter - you organized it so well into sections that it's easy to chunk up mentally. As long as the formats you choose accomplish similar things, you're golden. Thanks again for the great read.
Oh man, my wife is not going to be happy to read this... ;)
If she's anything like my girlfriend, she probably constantly tells you to keep it brief cuz you both have things to do. But you're doing something great, and I just hope you keep doing it. You're giving me so so so many tools to educate my kids.
This is one of my main tools for motivating or providing context in computer science education. Thankfully we have so many real, wacky characters! I do feel like I have a lower success rate with historical storytelling though than I have with other hooks (e.g. demo with surprising result, personal rant about the state of things) but it's basically always there as an option.
More recently I've been trying to use more historical context with math for my kids, and confronted the same open questions that you raise. Even when we do have a historical record, faithfulness can be boring for preschoolers as there can be a lot of missing context: "well you see, the Egyptians taxation system was based on land area, and this was complicated due to the Nile flooding... oh what is the Nile? ... Well you see...". So, I've embraced the storytelling aspect of it, and we simply have fun "imagining" people "a long time ago" who had some problem to solve. For this, the history of mathematics ends up mostly as inspiration for motivating problems, whether supported by the historical record or not. At the very least, it reminds me what is most fundamentally useful and interesting about the field, for instance with geometry we find problems that involve land measurement. Oh and as you and I discussed the other day, starting with a phrase like "there's an old story that..." or similar seems to appease the spirits of our historiographer elders.
Separately, are you familiar with David Pengelley? He taught undergraduate mathematics from primary sources, for instance here's a number theory textbook for a course he taught based around Sophie Germain's correspondence with Gauss attempting to prove Fermat's last theorem https://bookstore.ams.org/view?ProductCode=CLRM/70 ... I really love this stuff and particularly enjoyed a book he co-authored called Mathematical Expeditions. However I have not yet had the courage to teach entire courses in this style :)
When reading Wikipedia articles, I’m almost always clicking through the names and reading the personal stories.
As for a title--yeah Saints might be too much :)
Originators, Pioneers (my fav), Discoverers, Groundbreakers, and yes (Content) Creators, maybe?
When we don’t know the full story, I love the invocation of posing it as a mystery to be solved. A lot of economics (where I am training now) is like detective work, but maybe it’s even more obvious in linguistics. Starting from some assumptions about how humans operate, asking things like “what problems were they trying to solve,” or “what kinds of tools were available to them” lets us make sense of the mystery, and allows analogies form for when we would use the ideas ourselves. Of course we have to be careful about *wrong* ex post rationalization, which you allude to when talking about the myths. But even this can be a bridge: “why is that particular myth so salient? What value does it give our current culture?”
Finally, I’m (finally) reading Joesph Henrich’s The Secret of our Success about cultural evolution. Surely, you are aware of him (I think Scott did a SSC review a while ago), but I keep thinking how much your work (and from what I know of Egan from you) makes total sense in light of Henrich.