History of Math

[Jackie]

Wasn’t quite sure what subforum to try this question in, but this seemed most likely for the question.

My middle school kid is asking for a History of Mathematics course. She is a strong reader, and has had a sustained interest in math, so materials that would be considered accessible to a high schooler are probably the right level, but nothing really dense.

A couple things I have found while searching:

New York Times Book of Mathematics: https://smile.amazon.com/dp/1402793227/?coliid=I3GSWU3IXM1309&colid=3TRA5MVMURXMZ&psc=1&ref_=lv_ov_lig_dp_it

Math Through the Ages: https://smile.amazon.com/dp/0486832848/?coliid=I3OS8M5I4M27RY&colid=3TRA5MVMURXMZ&psc=1&ref_=lv_ov_lig_dp_it

Any feedback on these? Other options I might want to consider? Books, videos, MOOCs, etc, would all be possibilities.

[Not_a_Number]

How modern do you want the math?

[UHP]

There's a famous book from the 1930s called "Men of Mathematics," which is extremely fun but should be read skeptically.

As a teenager I enjoyed one by Carl Moyer and Uta Merzbach, I think it's just called "History of Mathematics."

Edited May 27, 2021 by UHP

[theelfqueen]

BBC The Story of Maths documentary 

[Caroline]

The Crest of the Peacock: Non-European Roots of Mathematics by George Gheverghese Joseph  is a fascinating book, but it is pretty dense. I’ve used it in a college history of math course. 

Edited May 28, 2021 by Caroline

[LAS in LA]

Mathematicians are People, Too is a two-book series of short biographies.

[stripe]

Lukeion has a (one hour per day for four days) workshop in June called “Bizarre Ancient Mathematics & Numbers “ that is open to middle schoolers 

https://www.lukeion.org/courses.html

They also have a class this fall for students who are at least in pre-algebra, that uses “Math Through the Ages, A Gentle History for Teachers and Others” by Berlinghoff and Gouvea

https://www.lukeion.org/math.html

Another BBC video, if you can find it, include Magic Numbers (currently showing on Acorn TV). I liked Marcus du Sautoy’s Story of Math too.

I also highly recommend books by Simon Singh. 

And definitely watch Donald in Mathmagic Land (yep, that’s Donald Duck), and read and watch The Phantom Tollbooth.

Edited May 27, 2021 by stripe

[Not_a_Number]

Well, assuming you don't mind the math being modern... I've been rereading this one: 

https://www.amazon.com/Honors-Class-Hilberts-Problems-Solvers/dp/1568811411/ref=sr_1_3?dchild=1&keywords=the+honors+class&qid=1622161256&sr=8-3

It's 20th century mathematics, following the mathematicians who solved Hilbert's problems. It's also fascinating in that it intersects with 20th century history in general. In the late 19th century, Germany was the center of the mathematical world. You can imagine how that went from 1900 to 1940, especially since there were many Jewish mathematicians. 

I remember learning more history from that book as a teen than I learned from anything else, mostly because I was actually interested in the subject 😉 . It's not beautifully written or anything, but I remember finding it fascinating. (But then I was a teen who wanted to be a mathematician when she grew up...) 

[Jackie]

Modern, ancient, stuff in between. It’s all good.

This has been an ongoing interest, so she’s read most the stuff accessible to elementary kids, such as Mathematicians Are People Too and the Murderous Maths series and a variety of storybooks. She’s also read a bunch of general interest math books like the Simon Singh stuff, Math With Bad Drawings, some stuff by John Conway, and probably a bunch of other stuff that I’m either forgetting or don’t even know she has read. 

Really, she already knows more math history than I ever did. She clearly wants something more, but definitely still gets scared away by dense text, so mass market books are an easier sell than textbooks. 

[daijobu]

I really enjoyed this book.  The author has a thesis, which I can't say I agree or disagree with.  But he includes so many interesting tidbits of math history, it's worth it just for that.  (Don't skip the appendices...they have the juiciest bits!)

My favorite part is he reproduces a copy of a letter written from one monk to another in the middle ages.  This monk was complaining because his teacher gave him some crazy wrong formula for the area of a triangle.  (I think it included the number 7.)  Anyway, he's complaining because this wrong formula is, not surprisingly, giving him the wrong answer, which demonstrates by drawing a triangle over a grid of squares.  It's fairly hilarious, and I love that all these formulas that, frankly, are not all that intuitive, we so take for granted these days.  It wasn't that long ago when people in the sticks didn't get the memo about triangle area.  

 

[stripe]

She’s got to read Men of Mathematics. It reads a bit like gossip, and forms the basis for for my long and very imaginary friendship with a fellow named Evariste.

 

Also there’s a thin Dover publishers book by Struik about the history of math. 

Edited May 28, 2021 by stripe

[MamaSprout]

Did anyone mention Numberphile yet? Numberphile

There is a certain amount of talking about doing math with friends in pubs. And given my track-record this week for allowing inappropriate reading for my kiddo... preread/ preview. These are graduate students making these videos. I haven't seen anything alarming, but I'm not easily alarmed. Dd is the youngest kiddo. You know how that goes.

ETA Beware. My dd has something of a Klein Bottle obsession (that replaced her mobius strip obsession) in middle school thanks to these videos. At least I didn't end up buying any Klein Bottles. ETA2... oh yeah. I forgot about the hexaflexagon obsession in between.

One of the Numberphile guys, Matt Parker, has a couple of books. Humble Pi is probably more historical, but in a "when math went wrong" kind of way:

Amazon.com: Matt Parker: Books, Biography, Blog, Audiobooks, Kindle

Edited May 28, 2021 by MamaSprout

[stripe]

1 hour ago, MamaSprout said:

ETA Beware. My dd has something of a Klein Bottle obsession (that replaced her mobius strip obsession) in middle school thanks to these videos. At least I didn't end up buying an Klein Bottles.

Just FYI, MEP has a Klein cube you can make at home. It’s kind of fiddly, but doable.

https://www.cimt.org.uk/projects/mepres/book8/y8s6act.pdf

[kirstenhill]

3 hours ago, MamaSprout said:

Did anyone mention Numberphile yet? Numberphile

There is a certain amount of talking about doing math with friends in pubs. And given my track-record this week for allowing inappropriate reading for my kiddo... preread/ preview. These are graduate students making these videos. I haven't seen anything alarming, but I'm not easily alarmed. Dd is the youngest kiddo. You know how that goes.

ETA Beware. My dd has something of a Klein Bottle obsession (that replaced her mobius strip obsession) in middle school thanks to these videos. At least I didn't end up buying any Klein Bottles. ETA2... oh yeah. I forgot about the hexaflexagon obsession in between.

One of the Numberphile guys, Matt Parker, has a couple of books. Humble Pi is probably more historical, but in a "when math went wrong" kind of way:

Amazon.com: Matt Parker: Books, Biography, Blog, Audiobooks, Kindle

I was about to suggest this channel too...so many great things there! Veritasium just did a really interesting history-of-math related video too if you haven't seen it yet.  

We checked out The Math Book by Pickover from the library and 14 year old DS and I both really enjoyed it. 

[kirstenhill]

A couple more titles for you --

Asimov on Numbers by Isaac Asimov (out of print, but available with reasonably priced used copies) has many historical tidbits and was one of my favorite books in middle school (I was a bit of a weird kid!).  My DS14 has not found the same love unfortunately even though I did purchase him a copy!

Mage Merlin's Unsolved Mathematical Mysteries - a bit lighthearted and fun.  All my DS's like this one.  It uses a fictional story to tell about real unsolved problems in math.

An Imaginary Tale: The Story of the Square Root of -1 - DS14 has been slowly working his way through this one.  He says he can only read small chunks at a time because he really has to think about it

The Great Mathematicians: Unraveling the Mysteries of the Universe - DS14 picked this one out at a bookstore but hasn't started reading it yet.

Edited May 28, 2021 by kirstenhill

[Jackie]

Oh, she has definitely found Numberphile! And Vi Hart, which inspired her hexaflexagon stage. She and I are currently working our way through Art Benjamin’s Math and Magic from Great Courses, learning the magic tricks and working our way through the math behind them.

Talking to her more, she loves the interesting tidbits of mathematician’s lives (basically, the gossipy stuff). She likes the stories of both rivalries and collaborations. She likes hearing about how theories were proven or disproven, especially if it happened in any unusual manner.

I am bookmarking resources and sitting down to request a stack of books from the library to go over!

[Jackie]

It would be a bonus if any of the resources included female mathematicians. She is definitely aware of the gender disparity in all of her most-loved subjects.

[Not_a_Number]

26 minutes ago, Jackie said:

It would be a bonus if any of the resources included female mathematicians. She is definitely aware of the gender disparity in all of her most-loved subjects.

There are a couple in the book I linked. But it's heavily male, because the field is. 

Edited May 28, 2021 by Not_a_Number

[stripe]

Emmy Noether and Ada Byron Lovelace, and (modern) Maryam Mirzakhani are interesting figures who were very, very smart. Also Hedy Lamarr! And definitely read and watch Hidden Figures.

[Jackie]

11 minutes ago, stripe said:

Emmy Noether and Ada Byron Lovelace, and (modern) Maryam Mirzakhani are interesting figures who were very, very smart. Also Hedy Lamarr! And definitely read and watch Hidden Figures.

We’ve read and watched Hidden Figures. Also just listened to Code Girls on a road trip last weekend.

I’m definitely aware that a History of Math will be almost exclusively men. She’s very much a STEM kid, but has been dismayed by seeing the gender disparities in math camps, math circles, and science programs that she has participated in. Up until the last couple years when she started being parts of these groups, I think she thought the disparities were only historical and is frustrated to learn that they still exist so strongly.

[Jackie]

45 minutes ago, stripe said:

Emmy Noether and Ada Byron Lovelace, and (modern) Maryam Mirzakhani are interesting figures who were very, very smart. Also Hedy Lamarr! And definitely read and watch Hidden Figures.

Oh, she'd probably love to learn more about Mirzakhani! The Epsilon Camp groups are all named for mathematicians, and that was the only one she wasn't familiar with.

And I had no idea about Hedy Lamarr. Looks like there are a couple of fictionalized novel versions about her life, so I reserved one to preread and see if it might work.

DH is a mathy computer guy, so she is very well versed in who Ada Lovelace and Grace Hopper were.

[kiana]

What about Lynn Osen's "Women in Mathematics" book from 1975? I felt it was pretty similar to "Men of Mathematics"; it's a little dated on the "where we are today" section but good short biographies.

[mathprof99]

I have taught History of math regularly at my university. I recommend "Math Through the Ages" as well as the BBC documentary "Story of Maths". The following are good supplements:

1) Man of Numbers by Keith Devlin, about Fibonacci , who introduced Hindu-Arabic numerals to the West to replace the Roman numeral system, and revolutionized Western mathematics

2) The Mathematical Universe by William Dunham; (Description from amazon.com) The Mathematical Universe is a solid collection of short essays, with each addressing a particular mathematical topic. Titles range from "Isoperimetric Problem" to "Where Are the Women?" Author Dunham manages to maintain a conversational tone while referencing diagrams, equations, and rigorous arguments throughout the book.

3) "Fermat's Last Theorem" documentary by Simon Singh, as well as his book "Fermat's Enigma"

Re: women in math - I am one of the few women in my subfield of mathematics.  It is still rare to find women at the top of the profession even though roughly 35-40% of all PhD's in math are awarded to women. Many women. like myself, find careers at teaching universities. Doing theoretical math at the top research level is highly competitive. There are  a few "superstars", and many math PhD's , both male and female, drop out of the research stream at a higher rate than other disciplines. I would encourage your daughter to research current women mathematicians like Ingrid Daubechies and Eugenia Cheng.