Terence Tao: Just a brief announcement that I have been working with Quanta Books to publish a short book in popular mathematics entitled “Six Math Essentials“, which will cover six of the fundamental concepts in mathematics.
It should be according to Tao's own comment at the bottom of the blog:
"This book is for a general audience, without necessarily having a college-level math education. It is aimed more at adults than at children, but some children with an interest in mathematics may be able to get something of it."
I don't think a popular audience is buying a book on mathematics.
But, the world is huge. Even if this is kind of niche (people who didn't really get into maths in school or college, but now have a strange impulse to pick it up for shits and giggles) the audience is still thousands of people. Or just, people who want to see how Tao connects everything up, because the way he sees and explains stuff is amazing.
There are levels to what's worth publishing or working on in general. Hardly anyone is going to be the next Steven Hawking but this obsession with the most popular or successful celebrity creators ultimately leads to this highly homogenised global media landscape. The most exciting thing about the internet for me was always accessing the long tail of truly unusual shit that you wouldn't find in book/record stores, tv, etc.
It has one chapter each for Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, Logic.
He positioned it as a sort of a modern update to Felix Klein's Elementary Mathematics from an Advanced Standpoint series of books.
From the preface;
This book grew from an article I wrote in 2008 for the centenary of Felix Klein’s Elementary Mathematics from an Advanced Standpoint. The article reflected on Klein’s view of elementary mathematics, which I found to be surprisingly modern, and made some comments on how his view might change in the light of today’s mathematics. With further reflection I realized that a discussion of elementary mathematics today should include not only some topics that are elementary from the twenty-first-century viewpoint, but also a more precise explanation of the term “elementary” than was possible in Klein’s day.
So, the first goal of the book is to give a bird’s eye view of elementary mathematics and its treasures. This view will sometimes be “from an advanced standpoint,” but nevertheless as elementary as possible. Readers with a good high school training in mathematics should be able to understand most of the book, though no doubt everyone will experience some difficulties, due to the wide range of topics...
The second goal of the book is to explain what “elementary” means, or at least to explain why certain pieces of mathematics seem to be “more elementary” than others. It might be thought that the concept of “elementary” changes continually as mathematics advances. Indeed, some topics now considered part of elementary mathematics are there because some great advance made them elementary...
a brief tour of six core ideas—numbers, algebra, geometry, probability, analysis, and dynamics—that capture the beauty and power of mathematical thinking for everyone.
In Six Math Essentials, the renowned mathematician and Fields Medalist Terence Tao introduces readers to six central concepts that have guided mathematicians from antiquity to the frontiers of what we know today and now help us make sense of our complex world. This slim, elegant volume explores
numbers as the gateway to quantitative thinking;
algebra as the gateway to abstraction;
geometry as a way to calculate beyond what we can see;
probability as a tool to navigate uncertainty with rigorous thinking;
analysis as a means to tame the very large or the very small; and
dynamics as the mathematics of change.
Six Math Essentials—Tao’s first popular math book
Terence Tao's comment :- This book is for a general audience, without necessarily having a college-level math education. It is aimed more at adults than at children, but some children with an interest in mathematics may be able to get something out of it.
It is just 160 pages so must be information dense with no fluff. I am sold !
I am atrocious at mathematics and held much contempt for the field until I was in college and 'saw the light,' if you will. Since college, I have absolutely fallen in love with mathematics. I learned it was not mathematics I always hated, but the U.S. public education system's method of teaching mathematics.
While I am still quite weak in the matter, I do believe that I will be preordering a copy of this book. Thank you for sharing this.
Genuinely, what is it that you get from studying mathematics?
I get that it's a hobby, but what do you even do with the knowledge you acquire?
I don't exactly fear math (even though I'm complete shit at it) but the time investment required is absolutely massive for something with questionable utility, even just for playing around with. You need a super strong base to even attempt bashing basic problems, so that's easily four or five years of study just to play around a bit.
For me, math was a way to study structure. I find this sort of thing tremendously beautiful on its own, but as it happens "finding the structure in things" turns out to be quite lucrative in the professional world as well, and I often use various ideas and strategies I chanced upon as a student of mathematics.
I do, yes. I won't call it a hobby because I don’t create anything, I'm just a mindless rabid stupid cunt of a consoomer who doesn't know how to differentiate his ass from a hole on the fucking ground, but I do spend a lot of time listening to music. I've spent a lot of money on audio equipment.
Even so, if you wanted to bring up time signatures, microtonality or something like math rock… I'm aware of those, but I still think the only thing that matters is that they're tools meant to allow you to express a certain message in the most appropriate ways, not so much an end in themselves.
Both of them give a nice tour of various domains within modern mathematics and their inter-relationships which is what i believe is most important to understand for a general reader.
Absolutely! Any person willing to study and think can understand the above books. As i mentioned, they cover a broad swath of mathematics and are meant for the general reader. You can checkout reviews on Amazon and elsewhere on the web.
Mathematics can be approached in two ways; 1) For understanding 2) For techniques of usage.
The above books help with (1). Textbooks focus on (2). A very good succinct (< 150 pages!) introductory text for (2) is George Simmons' Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry. It is available at https://github.com/enilsen16/The-Math-Group
One word of advice; most people's phobia of mathematics arises from not knowing/understanding the notation. It is just a shorthand language which you need to get familiar with. When you come across a formula, just expand and read it out aloud in your own version of easy English. You will understand better and lose your fear of mathematics. A book like Mathematical Notation: A Guide for Engineers and Scientists by Edward Scheinerman is of great help here. There are of course lots of free resources for this on the web starting with https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo... and https://mathvault.ca/hub/higher-math/math-symbols/
I find good popular books on higher mathematics difficult to come by. A nice exception is the trilogy written by Avner Ash and Robert Groß:
Elliptic Tales, Fearless Symmetry and Summing it up (in my order of preference)
It should be according to Tao's own comment at the bottom of the blog:
"This book is for a general audience, without necessarily having a college-level math education. It is aimed more at adults than at children, but some children with an interest in mathematics may be able to get something of it."
But for a book intended for a popular audience, it sure does have a bore-you-to-death cover.
But, the world is huge. Even if this is kind of niche (people who didn't really get into maths in school or college, but now have a strange impulse to pick it up for shits and giggles) the audience is still thousands of people. Or just, people who want to see how Tao connects everything up, because the way he sees and explains stuff is amazing.
There are levels to what's worth publishing or working on in general. Hardly anyone is going to be the next Steven Hawking but this obsession with the most popular or successful celebrity creators ultimately leads to this highly homogenised global media landscape. The most exciting thing about the internet for me was always accessing the long tail of truly unusual shit that you wouldn't find in book/record stores, tv, etc.
It has one chapter each for Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, Logic.
He positioned it as a sort of a modern update to Felix Klein's Elementary Mathematics from an Advanced Standpoint series of books.
From the preface;
This book grew from an article I wrote in 2008 for the centenary of Felix Klein’s Elementary Mathematics from an Advanced Standpoint. The article reflected on Klein’s view of elementary mathematics, which I found to be surprisingly modern, and made some comments on how his view might change in the light of today’s mathematics. With further reflection I realized that a discussion of elementary mathematics today should include not only some topics that are elementary from the twenty-first-century viewpoint, but also a more precise explanation of the term “elementary” than was possible in Klein’s day.
So, the first goal of the book is to give a bird’s eye view of elementary mathematics and its treasures. This view will sometimes be “from an advanced standpoint,” but nevertheless as elementary as possible. Readers with a good high school training in mathematics should be able to understand most of the book, though no doubt everyone will experience some difficulties, due to the wide range of topics...
The second goal of the book is to explain what “elementary” means, or at least to explain why certain pieces of mathematics seem to be “more elementary” than others. It might be thought that the concept of “elementary” changes continually as mathematics advances. Indeed, some topics now considered part of elementary mathematics are there because some great advance made them elementary...
Note: "Elementary" here does not mean Easy.
It will be interesting to see if Tao's writings are as clear, though possibly he is targetting a different audience.
a brief tour of six core ideas—numbers, algebra, geometry, probability, analysis, and dynamics—that capture the beauty and power of mathematical thinking for everyone.
In Six Math Essentials, the renowned mathematician and Fields Medalist Terence Tao introduces readers to six central concepts that have guided mathematicians from antiquity to the frontiers of what we know today and now help us make sense of our complex world. This slim, elegant volume explores
numbers as the gateway to quantitative thinking;
algebra as the gateway to abstraction;
geometry as a way to calculate beyond what we can see;
probability as a tool to navigate uncertainty with rigorous thinking;
analysis as a means to tame the very large or the very small; and
dynamics as the mathematics of change.
Six Math Essentials—Tao’s first popular math book
Terence Tao's comment :- This book is for a general audience, without necessarily having a college-level math education. It is aimed more at adults than at children, but some children with an interest in mathematics may be able to get something out of it.
It is just 160 pages so must be information dense with no fluff. I am sold !
PS: Another book in the same (but easier) vein would be Ian Stewart's classic Concepts of Modern Mathematics - https://store.doverpublications.com/products/9780486284248
I am atrocious at mathematics and held much contempt for the field until I was in college and 'saw the light,' if you will. Since college, I have absolutely fallen in love with mathematics. I learned it was not mathematics I always hated, but the U.S. public education system's method of teaching mathematics.
While I am still quite weak in the matter, I do believe that I will be preordering a copy of this book. Thank you for sharing this.
I get that it's a hobby, but what do you even do with the knowledge you acquire?
I don't exactly fear math (even though I'm complete shit at it) but the time investment required is absolutely massive for something with questionable utility, even just for playing around with. You need a super strong base to even attempt bashing basic problems, so that's easily four or five years of study just to play around a bit.
Even so, if you wanted to bring up time signatures, microtonality or something like math rock… I'm aware of those, but I still think the only thing that matters is that they're tools meant to allow you to express a certain message in the most appropriate ways, not so much an end in themselves.
Concepts of Modern Mathematics by Ian Stewart - https://store.doverpublications.com/products/9780486284248
Elements of Mathematics: From Euclid to Gödel by John Stillwell - https://press.princeton.edu/books/hardcover/9780691171685/el...
Both of them give a nice tour of various domains within modern mathematics and their inter-relationships which is what i believe is most important to understand for a general reader.
Mathematics can be approached in two ways; 1) For understanding 2) For techniques of usage.
The above books help with (1). Textbooks focus on (2). A very good succinct (< 150 pages!) introductory text for (2) is George Simmons' Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry. It is available at https://github.com/enilsen16/The-Math-Group
One word of advice; most people's phobia of mathematics arises from not knowing/understanding the notation. It is just a shorthand language which you need to get familiar with. When you come across a formula, just expand and read it out aloud in your own version of easy English. You will understand better and lose your fear of mathematics. A book like Mathematical Notation: A Guide for Engineers and Scientists by Edward Scheinerman is of great help here. There are of course lots of free resources for this on the web starting with https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo... and https://mathvault.ca/hub/higher-math/math-symbols/