12
$\begingroup$

Some students of an High School asked me some books from famous mathematicians that they can read (so advanced high school level focused mainly on real-analysis). They were asking things like Cauchy, Fermat... but I think the language would be technical in an akward ancient way for them so that probably will not be suitable. I thought that maybe Riemann dissertation could do but maybe it's too advanced. I then thought Galois, but again the original papers are quite difficult to understand if you don't already have the right picture in your mind.

I'm not sure there's effectively a book from an historically famous mathematician that could fit the request. They didn't specifically requested that the argument should be mathematical even if I think they implied this, otherwise I could suggest something of Poincaré which rather philosophical but at least readable.

They didin't specify the period (even if I think they might want to already know the name of the writer). In modern period maybe I would suggest Mumford the Indra's Pearls. But I'm quite sure they don't know Mumford...

I'm now thinking that maybe some kind of physicist would be better. But they were asking mathematicians.

I really don't have a clue of what to suggest. Please help me!

Edit. Someone correctly asked me why I'm "limiting to Mathematicians they've heard of". I totally agree with who's asking. Old mathematics would be kind of akward I think. The problem is not that "I'm limiting", the problem is that "this is what they asked". It's something like "We have seen their theorems, heard a lot about them, we would like to read something written by them". As pointed out is that probably this request cannot be fulfilled entirely or is not a good idea to fulfill their request. So any suggestion will be take into account. If it was physics Schroedinger "What is Life" and some Heisenberg essays would be in order... in mathematics I've no clue if exists something similar... I think maybe Poincaré is the only one...

$\endgroup$
  • $\begingroup$ See whether this helps you: mathoverflow.net/questions/28158/… $\endgroup$ – Rohan Feb 10 '17 at 17:21
  • 1
    $\begingroup$ The "philosophy of science" books by Henri Poincaré. "Science and Hypothesis" and "The Value of Science". $\endgroup$ – Jean Marie Feb 10 '17 at 17:21
  • $\begingroup$ Unfortunately it doesn't... I more or less would know how to prepare them for Undergraduate Mathematics. The problem is they were for curiosity sake interested in books written by famous mathematicians $\endgroup$ – Dac0 Feb 10 '17 at 17:24
  • $\begingroup$ @JeanMarie thank you. "The Value of Science" was exactly the one I had in mind when I wrote. Unfortunately it's not mathematical (in the sense they would appreciate) $\endgroup$ – Dac0 Feb 10 '17 at 17:25
  • 1
    $\begingroup$ I've only read a little bit of it, but from what I read, I think the Feynman Lectures on Physics might suit your needs. $\endgroup$ – Echan Feb 10 '17 at 20:42

10 Answers 10

2
$\begingroup$

I would personally recommend "God created the Integers" by Stephen Hawking.

From the introduction:

Showcasing excerpts from thirty-one of the most important works in the history of mathematics, this book is a celebration of the mathematicians who helped us move forward in our understanding of the world and who paved the way for our current age of science and technology .

I thoroughly enjoyed reading this book, though it has received mixed reviews. Hope it helps.

$\endgroup$
  • $\begingroup$ I think that this might very well be the right answer for what I was looking for $\endgroup$ – Dac0 Feb 11 '17 at 23:11
6
$\begingroup$

It's quite difficult to find maths books written by famous mathematicians of the past that even contemporary mathematicians would find worth reading from a mathematical point of view, since mathematicians write for their peers, who have both different knowledge and different interests from people of today. On the other hand, presumably mathematicians writing about stuff that isn't mathematics is not quite what you have in mind.

  • Hardy, A Course in Pure Mathematics. Yes, it's an analysis textbook, but it's written by one of the English mathematicians of the twentieth century.

  • Littlewood, A Mathematician's Miscellany. This is one of those books that you either really enjoy, or don't connect with, but a lot of mathematicians praise it highly.

  • Hilbert and Cohn-Vossen, Geometry and the Imagination. I wish more mathematicians wrote books like this: it's a nice classical bridge from Euclidean to advanced geometry, with plenty of illustrations.

$\endgroup$
5
$\begingroup$
  • An introduction to the theory of numbers by G.H. Hardy and E.M. Wright
  • Number theory. An approach through history and Number theory for beginners by André Weil
  • Solving mathematical problems. A personal perspective, Terence Tao
  • Calcul des probabilités by Henri Poincaré (in french)
$\endgroup$
  • $\begingroup$ Also Dickson's history of number theory is free on archive.org $\endgroup$ – Joel Feb 10 '17 at 18:15
3
$\begingroup$

I recommend a classic from one of our greatest, published in 1748, with accessible content and wonderful to read

Introduction to the Analysis of the Infinite

by Leonhard Euler.

$\endgroup$
2
$\begingroup$

Mathematics: The Music of Reason by Jean Dieudonné (translation of Pour l'honneur de l'esprit humain).

Discourses on Algebra by Shafarevich

$\endgroup$
  • $\begingroup$ I doubt high school students would consider these famous mathematicians. $\endgroup$ – Aweygan Feb 10 '17 at 17:28
  • 1
    $\begingroup$ @user414098 True, But that makes it a learning opportunity. $\endgroup$ – Ethan Bolker Feb 10 '17 at 17:30
  • $\begingroup$ I doubt that they ever heard of Shafarevich. I'm not even sure they heard about Dieudonné but I'll give a try anyway... Thank you $\endgroup$ – Dac0 Feb 10 '17 at 17:30
  • 1
    $\begingroup$ @Dac0 Why restrict to books authored by "famous mathematicians that students have heard about?" Doing so imposes so severe a constraint that the results will be far from optimal. Most famous mathematicians have little time to write expository surveys accessible to high school students. Rather, this is more commonly done by less famous mathematicians, who both have the time to do so, and also frequently have much better expository skills. $\endgroup$ – Bill Dubuque Feb 10 '17 at 23:08
  • $\begingroup$ @Dac0: I agree with Bill. If nothing else, if you limit it to mathematicians they've heard of, then you're limiting yourself to things written before, say, 1900. The text is going to be so old-fashioned as to be unreadable. Even Hardy's Pure Mathematics is almost inaccessible to modern high school students (including myself a few years ago). If they're going to read mathematics then they should read some modern books; that way, they at least learn how to properly write mathematics. $\endgroup$ – Will R Feb 10 '17 at 23:14
2
$\begingroup$

Vladimir I. Arnold (who may not be known to high school students, but is certainly a famous mathematician) wrote some books directed specifically towards high school students. Of course, Arnold was very clever and was intending to teach the material directly to students, and I can't vouch for how accessible these books would actually be without some guidance. They don't limit themselves to real analysis, but they're certainly very interesting!

One mathematician who they might be more likely to have heard of is Waclaw Sierpinski - as in Sierpinksi's triangle and other fractals. Although this book has nothing (to my knowledge) to do with fractals, it is probably accessible enough and contains lots of interesting tidbits.

$\endgroup$
  • $\begingroup$ Two great authors! And really great books! $\endgroup$ – Dac0 Feb 11 '17 at 6:04
2
$\begingroup$

Dedekind's essays on the theory of numbers are quite accessible, in particular the first one on the construction of the real numbers by Dedekind cuts.

Disquisitiones arithmeticae by Gauss is not about real analysis, but it's written by one of the best known mathematicians of all time, and and it is possible to read quite far in it without any prior exposure to number theory.

$\endgroup$
  • $\begingroup$ I was thinking somethign about Gauss! I'll have it a look! Thank you! $\endgroup$ – Dac0 Feb 11 '17 at 5:57
1
$\begingroup$

Not exactly what you're asking for, but worth thinking about recommending:

Timothy Gowers Mathematics: A Very Short Introduction

https://global.oup.com/academic/product/mathematics-a-very-short-introduction-9780192853615?cc=us&lang=en&

https://www.amazon.com/Mathematics-Short-Introduction-Timothy-Gowers/dp/0192853619

Hugo Steinhaus Mathematical Snapshots:

What was the book that opened your mind to the beauty of mathematics?

and other recommendations at that question.

$\endgroup$
1
$\begingroup$

John Nash, "Non-cooperative Games" enter image description here

http://lcm.csa.iisc.ernet.in/gametheory/Classics/NCG.pdf

$\endgroup$
  • $\begingroup$ That's brilliant since they might have seen Beautiful mind. I'll suggest to them to have a look $\endgroup$ – Dac0 Feb 11 '17 at 5:59
0
$\begingroup$

This might be (i.e. probably is) a bit too advanced, in the sense that it requires a good amount of prerequisites, but I find Milnor's Topology from the differentiable viewpoint very nice. In particular, I find it mainly focuses on intuition without getting lost in too many technical details. Also, the results presented there are really interesting.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.