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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!

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See whether this helps you: mathoverflow.net/questions/28158/… – Rohan 8 hours ago
    
The "philosophy of science" books by Henri Poincaré. "Science and Hypothesis" and "The Value of Science". – JeanMarie 8 hours ago
    
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 – Dac0 8 hours ago
    
@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) – Dac0 8 hours ago
1  
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. – Echan 4 hours ago
up vote 3 down vote
  • 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)
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Also Dickson's history of number theory is free on archive.org – Joel 7 hours ago
up vote 2 down vote

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

Discourses on Algebra by Shafarevich

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I doubt high school students would consider these famous mathematicians. – Aweygan 8 hours ago
1  
@user414098 True, But that makes it a learning opportunity. – Ethan Bolker 8 hours ago
    
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 – Dac0 8 hours ago
1  
@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. – Bill Dubuque 2 hours ago
    
@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. – Will R 2 hours ago
up vote 1 down vote

It's quite difficult to find maths books written by famous mathematicians of the past that even contemporary mathematicians, 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.

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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.

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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.

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up vote 0 down vote

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.

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