The book is quite basic. Don't expect to get much out of it if you have a STEM degree.

> The book is quite basic.

Perplexing how it's on the front page then given the background of the median HN user (presumably technical with some STEM background in general, some pure VC bros peppered in etc).

The Tao love conquers all, as it were.

I enjoy reading less technical books even on technical topics I know about. They serve a different purpose.

Eh, I just like reading new books on mathematics, even if they're covering well trod ground. I think a lot of people in math are like this. I'm not endlessly grinding through introductory textbooks, but there is something nice about seeing someone brilliant give their take on something fundamental. And the cultural differences you get in reading different texts from different periods or from different authors is really stimulating, for me at least.

He’s the Michio Kaki for AI bros who want to adopt the veneer of associating with an expert.

im not pro-ai-bro but i gotta say some of the maths involved is pretty cool

That math isn't being discussed here, it's barely even discussed in the book! Frankly how often do you open an HN thread on the front page and see any significant technical discussion of anything other than coding? I find the times I see someone writing out equations and discussing fundamentals so rare and welcome as to be memorable.

Most conversation here is profoundly non-technical and never touches anything like "the math".

HN guidelines:

> Be kind. Don't be snarky.

I'm not talking to another member or referring to a particular comment, I'm making a brief comment by analogy regarding a pair of public figures who profit from their notoriety.

Moreover I was accurate, unless your idea of kindness is to imply that comparison to a success physicist is "unkind".

Basic knowledge resources are very common in HN in front page. And such resource from someone known to write very well will be helpful for newbies even from lesser known personalities. Shared here all the time so why pretend its not common. Its dishonesty not perplexing.

1) Not everyone, and 2) some of us regularly find ourselves recommending books to others, or for kids.

It is still good as a book on philosophy of mathematics. Not the best, perhaps, but a solid introduction.

Like, the epistemology and metaphysics of mathematics? That kind of philosophy? Realism, idealism and all that jazz?

Nothing so esoteric — it’s written for the popular audience. But there’s a lot of “what is mathematics?” or “how do we do mathematics?” Some random highlights:

> A big part of mathematical training is becoming acquainted with different concepts and recognizing how they’re cousins to each other.

> I encourage everyone to fool around with numbers—some enthusiasts discover important patterns that way, and some famous mathematicians, like the late John Conway, made a career of it.

> When we give word problems in school, we tend to cherry-pick perfect models that have one correct answer. Rather than teach a preordained procedure, we could encourage exploration by asking students to fix more realistic models where things are slightly noisy or slightly incorrect.

I'm hoping my kids will get a lot out of it as they grow up :)

I heard he was writing a book about the Cosmic Distance Ladder. I was looking forward to that, I hope this isn't what it evolved into.

It is listed as 'in preparation' when you click on |> Books and scroll to the bottom of the list at: https://teorth.github.io/tao-web/index.html

You could link directly: https://teorth.github.io/tao-web/climbing-the-cosmic-distanc...

He did a great collaboration with 3Blue1Brown on it: https://youtu.be/YdOXS_9_P4U . Didn't realize there a book coming, cool!

I quite liked this interview:

Terence Tao explains 6 essential mathematical concepts: https://www.youtube.com/watch?v=OOMx2BHHWtE

Received my copy today via Amazon.

What do you think?

[delayed]

Despite the downvoting I agreed with this comment completely

The amazon preview [1] does not even show the contents page. How am I supposed to check if I might be interested in this book?

[1] https://www.amazon.com/dp/0374621799?tag=macmillan-20

The above page has the ToC:

1. numbers as the gateway to quantitative thinking

2. algebra as the gateway to abstraction

3. geometry as a way to calculate beyond what we can see

4. probability as a tool to navigate uncertainty with rigorous thinking

5. analysis as a means to tame the very large or the very small

6. dynamics as the mathematics of change

> numbers as the gateway to quantitative thinking

That's a historical artifcat, not an innate property. (Math was first invented in the Bronze Age for accounting and architecture.)

There's a theoretical parallel universe with a mathematics where numbers aren't first on the ladder but down there around number five. (Ironically computers are an example of that. Figuring out how to do numbers when all you have is finite sequences from an alphabet is advanced CS.)

Firstly are you so very sure he claimed that is an innate property? That Numbers are a gateway to quantitative reasoning seems a perfectly reasonable claim either way.

Secondly there are lots of mathematical objects that significantly predate the bronze age (eg https://en.wikipedia.org/wiki/Ishango_bone but there are others) and because these objects are so old we have no idea why math was first invented.

Thirdly I have no idea what relevance the theoretical “late numbers “ parallel universe but Tthis thread is about a book in this one.

> That Numbers are a gateway to quantitative reasoning seems a perfectly reasonable claim either way

This isn't true though. It's not supported by anything except Bronze Age tradition.

I.e., when teaching kids advanced math at an early age it's often better to skip numbers altogether and start with set theory or logic. Many kids find that a much easier gateway.

> I.e., when teaching kids advanced math at an early age it's often better to skip numbers altogether and start with set theory or logic.

What do you mean by "often better". Has it even ever been tried out?

I belive this is what was attemped in France (they taught set teory in an abstract way in elementary school), but with poor results and abandoned this approach after some time.

> Has it even ever been tried out?

Of course, and it's standard practice in some places.

P.S. I'm talking about extracurricular math clubs/circles. School curriculum is a separate thing that's divorced from actual math.

Math club for set theory before 1st grade and numbers? Do you have a link?

Set theory and logic stay below numbers, but they do not belong to quantitative thinking.

By definition, quantities, either discrete or continuous, as already classified by Aristotle, are the properties that can be expressed by numeric values, as a result of counting for discrete quantities, or as a result of measuring for continuous quantities.

Properties that are not quantities, but which can be compared, to determine which is greater or less, or if they are equal, are qualities.

The simplest numbers, i.e. cardinal numbers a.k.a. natural numbers, are equivalence classes of sets, so indeed the theory of numbers is built upon that of sets (a.k.a. multitudes in older language), but this does not contradict in any way the title from the book, because quantitative thinking refers to only a part of mathematics, not to all of ite.

Super interesting that geometry is about going beyond what we can see since in my limited world view it is more specifically that which we can see..

That's where geometry starts -- in the same way as numbers start by counting on fingers. When you run out of fingers, numbers keep going. When you run out of visible dimensions, geometry keeps going too.

The paperback is 89 pages, the hardcover is 128. That's the only info Amazon shows me. And there's an audiobook, which is odd for a maths book.

Amazon isn't even trying these days. They seem to no longer care about the shopping experience, especially for media.

That said, you can switch to the Kindle version and request a sample. The kindle samples usually have a ToC.

From a previous discussion - https://news.ycombinator.com/item?id=47116851

Click on the kindle option. They click the 'Download sample' button.

Or click on the link to a sample chapter, listed on the submission:

https://www.sciencefriday.com/articles/six-math-essentials-b...

I read the sample chapter: it's surprisingly bad! (He's a good writer normally.)

It's boring, and badly-written (the Greeks didn't use symbols like x, instead they used x), with poorly-chosen examples (curtains not a good example of abstraction; correlated risks a good example of correlation, which is off-topic here, but a bad example for algebra), and lacking pictures that would help (the wine barrel).

Your quotation is taken out of context, so it has become completely meaningless, but the original text is not so bad as your weird quotation implies.

It is true that the author failed to express himself very clearly, but what he says is that the ancients did not use an abstract unknown denoted by an arbitrary symbol like "x", but they used instead of it the length of some line segment, instead of the squared value of the unknown, the area of some square constructed on that segment, instead of the cubed value of the unknown, the volume of a cube constructed on that segment, transforming thus an abstract algebra problem into a concrete geometry problem, which then they solved.

Click through to the UK Publisher and there's a "look inside" with the TOC.

This listing does have the TOC

https://www.amazon.co.uk/Six-Maths-Essentials-Model-World/dp...

Beats Math Essentials by Terrence Howard.

What age range or skill level is this targeting?

It is very manageable, if not overly basic. Standard, general secondary school education is good enough.

I pre-ordered some time ago, and received a copy this morning. I love it.

It's direct and well-written; a high-level overview of mathematics from numbers to analysis and dynamics. I think it's well organized, if brief at ~100pp.

This would be a great read for laypeople as well as a potential gap-filler for anyone in STEM.

Books should be brief, technical ones at least. I cannot stand the filler pages where the same concept is repeated again and again.

I got this book today, as I had it on pre-order. It's a bit disappointing because, on a quick count, there are only five pages with pictures. And I think I saw just a few equations. It's a bit strange to leave out two essential mechanisms for how mathematicians work and think in a book named Six Math Essentials.

Tao's essentials are, "... 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."*

Does Tao intend that as the 100,000 ft view of all mathematics, a way to categorize (almost) all of it, the roots of the mathematics tree? Are these the essentials or just some valuable ones.

For comparison, Gowers begins a much larger book with, "there is a crude division that undoubtedly works well as a first approximation, namely the division of mathematics into algebra, geometry, and analysis." [0]

There must be other schemes out there?

[0] Timothy Gowers, ed. The Princeton Companion to Mathematics. p.1 (2008)

Gowers' division misses probability, though, which really is its own thing. Similarly, counting is the foundation for the axiomatization of mathematics and probably deserves its own category. They all bleed into one another (analysis uses counting for its formalization, probability uses both counting and analysis), but they can each stand on their own informally (and did, in some cases for centuries).

[delayed]

How does it compare to Basic Mathematics by Serge Lang?

I haven't read Tao's book yet, but Lang's very ... schooly kinda book. From what I gather of the Tao's ToC it's more approachable as a non-fiction type of book.

Probability is where I always get it wrong. Experiments and AI are my saviors.

The link: https://www.quantabooks.org/books/six-math-essentials/

Why waste money on the book when you can just ask Claude about this?

Bought the book yesterday! Seems nice :)