Name: Letters to a young mathematician
ISBN: 9780465008414

Letters to a young mathematician

"Letters to a Young Mathematician tells readers what Ian Stewart wishes he had known when he was a student. He takes up subjects from the philosophical to the practical - what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others - in a style that combines subtle, easygoing humor with a talent for cutting to the heart of the matter"--Jacket.

What Hacker News says

wdutchJul 2020

Maths tutor here. At that age I was very inspired by Fermat's Last Theorem by Simon Singh. It's not a technical book but gave me my first idea of what mathematicians actually do and how the process works. This book motivated me to major in maths.

Anything by Ian Stewart would also be good, 'Letters to a Young Mathematician' springs to mind.

Given that you use the word 'maths' with an s I'm guessing you're not American. If you're British like me, I would recommend avoiding American books for high schoolers because they will assume quite different prerequisites.

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billybatsonDec 2018

A Mind for Numbers by Barbara Oakley: Decent. I think this book would best be read in conjunction while working through a textbook. I will admit that it did do quite a bit to help relieve math anxiety, but the nature of the book is practicality.

Brave New World by Aldous Huxley: A reread. A bit depressing considering the state of the world today. I found myself wondering which reality would be preferable.

Letters to a Young Mathematician by Ian Stewart: Easy, but fruitful read. I've struggled a lot with math confidence, and this helped alleviate a lot of that.

How to Speak, How to Listen by Mortimer J. Adler: A lot of practical advice. My biggest takeaway was this: if it's worth talking about, even if the conversation sucks or the other person doesn't understand, any bit of advancement and understanding is worth the effort. Really helped me increase my patience when talking to people.

Quack This Way by David Foster Wallace and Bryan Garner: Super useful and practical discussion between two lovers of language. I keep a copy with me at all times.

The Autobiography of Gucci Mane: Just a fun read while on vacation. "If Gucci can do it, you can do it".

Jesus' Son by Denis Johnson: A nice if brutal read. It was my first foray in DJ. I felt Cormac McCarthyish vibes.

Blood Meridian by Cormac McCarthy: A classic. The Judge.

Thinking About Mathematics by Stuart Shapiro: Highly recommended for anyone interested in the philosophical questions of mathematics. Shapiro writes clearly, concisely, and in a manner that is easy to read.

The Liars' Club by Mary Karr: Pretty great but brutal.

The Broom of the System by David Foster Wallace: I really enjoyed it. It's ode to Wittgenstein and it helped me cope with a lot of questions that I felt after studying LW.

The Sorrows of Young Werther by Johann Wolfgang von Goethe: I think we've all been in Werther's shoes. Though I hope that nobody comes to the same conclusion he came to.

Manage Your Day-To-Day: Build Your Routine, Find Your Focus, & Sharpen Your Creative Mind: A pretty great book. I find myself writing a book report on it to make sure I internalize a lot of the lessons. If you're having trouble doing creative work while working, read this.

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derangedHorseDec 2018

How was The Autobiography of Gucci Mane? Was it interesting, inspiring, funny, etc? It seems like a huge change of pace from the other books haha. I’ve also read Letters to a Young Mathematician and it honestly one of the reasons I was able to survive my math classes (mentally) when I was in school.

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janshoAug 2017

I recommend Ian Stewart's Letters to a Young Mathematician. He addresses your question (Platonism vs formalism) pretty succinctly, in my opinion as a noob.

Accordingly "the working philosophy of most mathematicians is a mostly unexamined Platonist-Formalist hybrid ... Math is a product of human minds but not bendable to human will. Exploring it is like exploring a new tract of country ... but the mathematical countryside does not come into existence until you explore it."

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imranqMar 2017

I guess you are referring to Yitang Zhang who created the first bound on the twin-prime conjecture. These days mathematics has become so specialized that its rather difficult to come up with anything new that is noteworthy and not already discovered. Just browsing through the graduate math library the other day and the stacks and stacks of journals dating from the 1700's and from various parts of the globe made me realize just how much math is out there.

Still, like Ian Stewart said in his "Letters to a Young Mathematician", math is an inverted pyramid - when a problem is solved, it leads to more branches to be solved. So maybe breakthroughs are possible from a determined amateur.

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lkrubnerDec 2015

Some of this overlaps with what Ian Stewart has written about the profession of mathematicians. Ian Stewart has written a bunch awesome books about math, and he writes in a classic 20th Century style of science/math popularizer, believing that there is a "general" public out there that might find math interesting. More about him here:

https://en.wikipedia.org/wiki/Ian_Stewart_(mathematician)

From the essay itself, this part struck me:

"What I called the transitional generation, those born around 1920, entered the universities, often late in their careers and without Ph.D.s. The Irving Howes and Daniel Bells became professors but retained their allegiance to a world of readable essays and small periodicals. The next generation — my generation — came of age in the universities and never left them. The world became specialized journals, monographs, and grant applications. This generation wrote for colleagues. If they were intellectuals, they no longer were "public" intellectuals; rather, they were academic or professional intellectuals oriented toward one another and microfields. In the 1880s, political science could claim one journal; now more than 40 populate the discipline. The American Political Science Association recognizes more than 30 subfields. The larger culture, I believe, suffers when intellectuals turn inward."

This is very much what Ian Stewart has lamented about the field of math. In one of his books (I think "Letters to a Young Mathematician") he mentions that there are now a vast multitude of journals that publish work about math, but that the field now consists of narrow specialists who are unable to understand each others work.

Considering that the whole field of science depends on math, and progress in science often depends on progress in math, the breakdown in math is especially worrisome.

I have the impression that what is needed is more people, within each field, who are willing to play the role of cross - pollinator. These people would not be "popularizers" in the old sense, since they would not be reaching out to the "general" public, but they would be reaching out to various specialities, and trying to unlock the knowledge in each sub-field. Sadly, there are not many incentives for this. I have friends who work in academia, and they would love to see more cross-pollination of ideas, but there is no reward to them for doing so, and there are large penalties if they fail to make progress in their narrow speciality.

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