Six Math Essentials

This is an interesting profile of Terence Tao as an ~8 year old: https://gwern.net/doc/iq/high/smpy/1984-clements.pdf, written by somebody who seems to have been well-versed in working with mathematically precocious children. It's interesting less for how good at math Tao already is but a peek into how he went about learning and doing math at a time when the subject matter was still accessible to, say, most users here. Among other things, what might be called his "openness to math experience" and independence are both remarkable.

> ... six of the fundamental concepts in mathematics ... and how they connect with our real-world intuition

While the connections are interesting, I would be as interested in the disconnects, as there's a bunch of cases where our human intuitions can fail us in subtle ways. This is actually one of the lessons I treasure from mathematics: it has helped me grow a healthy set of alarm bells for those unintuitive cases. Especially for probability and statistics.

I'm sure it's a great book :).

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)

Jeremy Kun's A Programmer's Introduction to Mathematics is also a good one.

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.

Looks like an inspiration from Richard Feynman's "Six Easy Pieces"

Hopefully we shall get a Feynman type math book from a true Master.

Six Math Essentials as a title reminds me of Six Easy Pieces. I wonder if that's intentional.

Dynamics? What branch of mathematics does it refer to? Is he talking about differential equations?

I greatly admire Tao's work.

But for a book intended for a popular audience, it sure does have a bore-you-to-death cover.

Seems similar to John Stillwell's classic Elements of Mathematics: From Euclid to Gödel - https://press.princeton.edu/books/hardcover/9780691171685/el...

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.

Which ebook provider should I use to get an actual epub file?

Is this Terry's 17th book?

This is a highly interesting comment from user "thoughtfullyd4c9a86b93" on the above site:

>"My two cents worth — Logic is fundamental. Most of mathematics does not treat infinities nor singularities as first class citizens. Yet, there are a lot of problem classes in which you can actually reason with a set that includes those limits. My preference is a strict axiomatic hierarchy where you can not blend “levels”. Each level is a gatekeeper for the next tier.

The idea that mathematics is a language of its own does not work until you completely disambiguate mathematics in your language of choice — and logic is a language that facilitates complete understanding.

* ⟨T⟩0: ZFC (The Material). The box that contains the idea of a box. If you aren’t starting here, you aren’t even playing the game.

* ⟨T⟩1: Topology (The Stage). This defines “nearness” before you own a ruler. It’s the rubber floor where a donut is a coffee cup—and where singularities (like the zero-point or the absolute) are perfectly admissible inhabitants.

* ⟨T⟩2: Geometry (The Ruler). Adding distance and angles. It’s just Topology after it’s been forced to commit to a specific measurement.

* ⟨T⟩3: Algebra (The Syntax). The ledger for people who trust the ruler more than the stage. It tracks the symmetries the geometry allows.

* ⟨T⟩4: Analysis (The Measure). Measuring the vibration of a string to prove the violin is real. Great for change, but “blind” to the structural admissibility of the stage itself."

the only math essential is Hessians

How exciting!

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.

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