A Tribute to Euler - William Dunham
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange answerers point people to it for an accessible, entertaining account of Euler's work, including his partition arguments and as a companion to Dunham's books.
Recommended by 2 people across 2 different months, 2013 to 2019.
What it is
A public lecture by historian of mathematics William Dunham at Harvard's Clay Public Lecture series. He sketches Euler's life and contributions to number theory and algebra, then walks through Euler's proof that partitions into distinct parts equal partitions into odd parts.
Cited in 2 Wikipedia articles, including Leonhard Euler, William Dunham (mathematician).
What people said
Recommends peter a g · 2017-11 · Mathematics Stack Exchange · on “Use of the fact that $e^{i\pi}=-1$?”
@MichaelStern While we're advertising Durnham / Euler, you and your son might enjoy the following entertaining 55 minute video: [this video]
Recommends Dabed · 2019-07 · Mathematics Stack Exchange · on “Partitions in a generating function $(1-x)(1-x^2)(1-x^3)(1-x^4)...(1-x^{1000})$”
I think what you need is the Euler's pentagonal theorem [LINK] There is an interesting video [this video] about how Euler solved the problem of the partitions, linked the particular part but I recommend the entire video. Added: $\prod_{i=1}^\infty (1-x^i) = \sum_{i=0}^\infty a_ix^i,$ $a_i := \begin{cases}1 & \mbox{ if } i = \frac{1}{2}(3k^2 \pm k) \mbox{ and } k \mbox{ is even}\\ -1 & \mbox{ if } i = \frac{1}{2}(3k^2 \pm k) \mbox{ and } k \mbox{ is odd }\\ 0 & \mbox{ otherwise }\end{cases}$ $P_{even}-P_{odd}=\sum_{i \mathrm{\ even}} p(n{-}g_i)-\sum_{i \mathrm{\ odd}} p(n{-}g_i)=\sum_{i=0}^n p(n{-}i) a_i=0\ $ ( $g_k$ the k th generalized pentagonal number)
Cites Xodarap · 2013-05 · Mathematics Stack Exchange · on “"Great Theorems" references”
I've since found some other books that I thought I should include for others' reference: Dunham is the master of this niche; his other books include: The Calculus Gallery [LINK] , The Mathematical Universe [LINK] and Euler: Master of us All [LINK] . (See also Dunham's Clay Lecture [this video] on Euler) The MAA has several books in this line, the only one of which I've read so far is Charming Proofs: A Journey into Elegant Mathematics [LINK] Benson's The Moment of Proof: Mathematical Epiphanies [LINK] had some good stuff, but it also had a lot of introductory material which I didn't like as much.