Ask HN: Books that made you fascinated to learn more mathematics?
27 comments
Reading a battered old second-hand copy of "Calculus Made Easy" by Silvanus P Thompson as a teenager was the first step on a path that eventually lead to me getting a degree in mathematics. Until then, I always thought calculus and other higher-level maths topics were out of reach for someone like me, but the explanations in that book were so careful and encouraging that it made me realise that anyone could study these topics with just a bit of effort. I believe the latest edition of the book has been updated to replace the slightly handwavy description of "infinitesimals" with a more rigorous limit-based foundation, but I don't know if the book's magic was lost as a result.
As an undergraduate, I purchased a cheap Dover reprint of "Ordinary Differential Equations" by Tenenbaum and Pollard to supplement an ODE course I was taking, mostly because it had lots of exercises in it. However, I found that book hugely inspiring, and it's become one of my favourite maths books ever. Amongst other things, it essentially has a complete course in Newtonian physics in it, just tossed off in the examples! Highly recommended. I eventually went on to study ODEs and PDEs at Masters level, partly as a result of enjoying that book so much.
As an undergraduate, I purchased a cheap Dover reprint of "Ordinary Differential Equations" by Tenenbaum and Pollard to supplement an ODE course I was taking, mostly because it had lots of exercises in it. However, I found that book hugely inspiring, and it's become one of my favourite maths books ever. Amongst other things, it essentially has a complete course in Newtonian physics in it, just tossed off in the examples! Highly recommended. I eventually went on to study ODEs and PDEs at Masters level, partly as a result of enjoying that book so much.
Some "pop"-sci books that have inspired me:
1."Uncle Petros & Goldback's Conjecture" & "Logicomix" (both by Apostolos Doxiadis),
2."Chaos" by James Gleick,
3. "The Man Who Loved Only Numbers" by Paul Hoffman
4. "A Mathematician's Apology" by G.H. Hardy
5. "The Indian Clerk" (fiction) by David Leavitt (about GH Hardy & Ramanujan)
6. "Genius at Play" by Siobhan Roberts (about John Conway). Normally I stay away from pop-math books with the words "The mind of..." or "Genius" in the title but this is a delightful book.
Some "actual" math books: 1. Nonlinear Dynamics & Chaos (Strogatz)
2. the Way of Analysis (Strichartz) -- note, this one is controversial as to its quality as a math book but I really like the presentation style
3. The Nature of Computation (Moore & Mertens)
1."Uncle Petros & Goldback's Conjecture" & "Logicomix" (both by Apostolos Doxiadis),
2."Chaos" by James Gleick,
3. "The Man Who Loved Only Numbers" by Paul Hoffman
4. "A Mathematician's Apology" by G.H. Hardy
5. "The Indian Clerk" (fiction) by David Leavitt (about GH Hardy & Ramanujan)
6. "Genius at Play" by Siobhan Roberts (about John Conway). Normally I stay away from pop-math books with the words "The mind of..." or "Genius" in the title but this is a delightful book.
Some "actual" math books: 1. Nonlinear Dynamics & Chaos (Strogatz)
2. the Way of Analysis (Strichartz) -- note, this one is controversial as to its quality as a math book but I really like the presentation style
3. The Nature of Computation (Moore & Mertens)
I was a Physics guy, a significant portion of my personality was centered around Physics.
When I started my Physics major, I had to complete two advanced Maths courses titled- Mathematical Methods I, II.
My love for Math took off from there. If you ask for books, then I would mention the MP book by Arfken, Weber, Harris. So minimal, yet straight to the point. Consistent and edifying.
I read a different Maths book in HS than what everyone else read. It was a local book, but very well written by prominent Mathematical intellectuals- the kind that write Math columns or act as mentors of syllabus advisory committee. This made a huge difference.
I liked Statistical Mechanics in college. I read Blundell and Blundell for it along with an unusual book as a reference- https://www.amazon.com/Thermal-Physics-Thermodynamics-Statis... .
How Math explains the physical world so prominently blew my mind. I loved it.
I also watched Calculus video from MIT-OCW when in HS.
I switched to Deep Learning after college. How I could actually use Math to build something extremely practical made me love Math even more. This was the true turning point.
I now want to spend three years- part-time, studying higher math by myself. I think it is worth it, and I want to do original, basic research in the Deep Learning space.
While I keep my eye out for resources, I follow these lists-
* https://www.susanrigetti.com/math
* https://marksaroufim.medium.com/technical-books-i-%EF%B8%8F-...
I can recommend this book for you to read right now-
1. The Joy of X: A Guided Tour of Mathematics from Zero Infinity by Steven Strogatz. A truly remarkable book.
2. How Not to Be Wrong: The Hidden Maths of Everyday Life by Jordan Ellenberg.
YouTube videos from 3blue1brown and Numberphile also increased my love for Maths.
Edit: I read some chapters from Alex Bello's Alex's Adventures in The Numberland. It was fantastic. I can recommend it.
When I started my Physics major, I had to complete two advanced Maths courses titled- Mathematical Methods I, II.
My love for Math took off from there. If you ask for books, then I would mention the MP book by Arfken, Weber, Harris. So minimal, yet straight to the point. Consistent and edifying.
I read a different Maths book in HS than what everyone else read. It was a local book, but very well written by prominent Mathematical intellectuals- the kind that write Math columns or act as mentors of syllabus advisory committee. This made a huge difference.
I liked Statistical Mechanics in college. I read Blundell and Blundell for it along with an unusual book as a reference- https://www.amazon.com/Thermal-Physics-Thermodynamics-Statis... .
How Math explains the physical world so prominently blew my mind. I loved it.
I also watched Calculus video from MIT-OCW when in HS.
I switched to Deep Learning after college. How I could actually use Math to build something extremely practical made me love Math even more. This was the true turning point.
I now want to spend three years- part-time, studying higher math by myself. I think it is worth it, and I want to do original, basic research in the Deep Learning space.
While I keep my eye out for resources, I follow these lists-
* https://www.susanrigetti.com/math
* https://marksaroufim.medium.com/technical-books-i-%EF%B8%8F-...
I can recommend this book for you to read right now-
1. The Joy of X: A Guided Tour of Mathematics from Zero Infinity by Steven Strogatz. A truly remarkable book.
2. How Not to Be Wrong: The Hidden Maths of Everyday Life by Jordan Ellenberg.
YouTube videos from 3blue1brown and Numberphile also increased my love for Maths.
Edit: I read some chapters from Alex Bello's Alex's Adventures in The Numberland. It was fantastic. I can recommend it.
Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré
Reading about the personalities of mathematics really widened my perspective of the motivations behind the math and the wide range of people involved in pushing it forward. It’s what inspired me to learn math for fun in my free time
https://en.m.wikipedia.org/wiki/Men_of_Mathematics
Reading about the personalities of mathematics really widened my perspective of the motivations behind the math and the wide range of people involved in pushing it forward. It’s what inspired me to learn math for fun in my free time
https://en.m.wikipedia.org/wiki/Men_of_Mathematics
What Is Mathematics? by Richard Courant and Herbert Robbins
https://en.wikipedia.org/wiki/What_Is_Mathematics%3F
https://en.wikipedia.org/wiki/What_Is_Mathematics%3F
1. Physics for Entertainment (aka Physics for Fun), Mathematics can be Fun, Arithmetic for Fun, Algebra for Fun etc. all by Yakov Perelman (aka Y.I.Perelman) and published by Mir Publishers in the erstwhile USSR. These were absolutely fantastic and kindled interest in Science/Maths for a whole generation of people across the World. Beg, Borrow or Steal these and make every kid read them. None of the "Modern" popular science books can hold a candle to these books.
- https://archive.org/search.php?query=creator%3A%22YAKOV+PERE...
2. Men of Mathematics and Mathematics: Queen and Servant of Science both by E.T.Bell
- https://archive.org/search.php?query=creator%3A%22Bell%2C+Er...
3. More recently, i found Who Is Fourier?: A Mathematical Adventure excellent. It is written in "manga" style but the contents are great! Every student should read this.
- https://archive.org/search.php?query=creator%3A%22YAKOV+PERE...
2. Men of Mathematics and Mathematics: Queen and Servant of Science both by E.T.Bell
- https://archive.org/search.php?query=creator%3A%22Bell%2C+Er...
3. More recently, i found Who Is Fourier?: A Mathematical Adventure excellent. It is written in "manga" style but the contents are great! Every student should read this.
I discovered Martin Gardner's Scientific American column collections in the local (UK) library as a schoolboy in the early 80s. This got me thinking about topological ideas, and hypercubes for instance, almost without realising it was maths.
My family weren't particularly science-focussed, so the fact that the (fairly small) library had several books like this was a real godsend.
My family weren't particularly science-focussed, so the fact that the (fairly small) library had several books like this was a real godsend.
I can recommend the following:
John Derbyshire's Unknown Quantity - A real and imaginary history of algebra
David Well's The Penguin Dictionary of Curious and Interesting Numbers
William Dunham's The Mathematical Universe - An Alphabetical Journey Through the Great Proofs, Problems and Personalities
Alex Bello's Alex's Adventures in The Numberland - Dispatches from the wonderful world of mathematics
John Derbyshire's Unknown Quantity - A real and imaginary history of algebra
David Well's The Penguin Dictionary of Curious and Interesting Numbers
William Dunham's The Mathematical Universe - An Alphabetical Journey Through the Great Proofs, Problems and Personalities
Alex Bello's Alex's Adventures in The Numberland - Dispatches from the wonderful world of mathematics
The Man Who Counted, first read when I was about 13.
https://www.theguardian.com/science/alexs-adventures-in-numb...
https://www.theguardian.com/science/alexs-adventures-in-numb...
Lockhart “Measurement” https://www.hup.harvard.edu/catalog.php?isbn=9780674284388 Mathematics is about curiosity, exploration and imagination, asking questions, and looking for answers.
Stanley Farlow's "Partial Differential Equations for Scientists and Engineers" is a great introduction to partial differential equations. That book was at exactly the right level for me when I was 19 to be introduced to a wide variety of things in differential equations in general.
Understanding Digital Signal Processing, by Richard G Lyons. I read it in my first couple months of college. I had no idea how to understand the differential equations, but the content was interesting enough to motivate me to study Applied Math.
The Lore of Large Numbers by Philip J. Davis. Out of print, but used copies available.
The construction of the real numbers in Pugh's Real Mathematical Analysis.
As a dad to a 7 year old (and another one on the way :)) , I find the following books wonderful. They evoke wonder in me and hopefully I will be able to transmit some of this to the kids .
1. Euclid's Window
2. Music of the primes
1. Euclid's Window
2. Music of the primes
The Phantom Tollbooth. I knew what a dodecahedron is years before the other kids, many of whom still don’t know.
The Little Typer by Daniel P. Friedman and David Thrane Christianse. It's basically one long book of examples building on each other to show the semantics of a dependently typed programming language. It inspired me to learn some type theory and made me interested in mathematical logic more generally.
Against the Gods: The Remarkable Story of Risk
The book talks and tells stories about the history of statistics, probability and risk. I came first from a poker background before I did my BA then MSc in Math & Stats. It reignited some of my dwindling passion.
The book talks and tells stories about the history of statistics, probability and risk. I came first from a poker background before I did my BA then MSc in Math & Stats. It reignited some of my dwindling passion.
The Man Who Loved Only Numbers
William Dunham's "The Mathematical Universe" was already mentioned but I actually came to suggest his earlier work "Journey Through Genius".
"The Music of the Primes" by Marcus du Sautoy
Gödel, Escher, Bach: An Eternal Golden Braid
Douglas Hofstadter
Douglas Hofstadter
Sitting on my shelf. Haven't had the courage to start it.
I’m the same with several books that I’ve bought over the years.
For a classic book dealing with “big” topics like math, music, and philosophy, it’s surprisingly accessible because Hofstadter is able explain complex things in the simplest way possible, which is a hallmark of great writing (not to mention great intellect).
My aptitude in math is slightly above average at best (and way below among my fellow geeks, who tend to be good at stuff like that), so I think you’ll be fine when you do decide to crack it open.
For a classic book dealing with “big” topics like math, music, and philosophy, it’s surprisingly accessible because Hofstadter is able explain complex things in the simplest way possible, which is a hallmark of great writing (not to mention great intellect).
My aptitude in math is slightly above average at best (and way below among my fellow geeks, who tend to be good at stuff like that), so I think you’ll be fine when you do decide to crack it open.
[deleted]
The books got you from understanding mathematics as rote arithmetic calculations to what mathematics really is about. Of course the books were themselves good teachers due to their excellent exposition and carefully set exercise problems (maybe with solutions).
Btw, I am not talking only about pure mathematics.
Do you have a few such books?