A reminder: Second Breakfast is on hiatus until the new year. Well, sort of, as here's a Second Breakfast email in your inbox. There are a couple of weeks' worth of news articles to link to, to be sure – the usual Friday stuff. But I've got a few other things to say, more in general, about the state of "AI" and education technology, about their utter indignity.

A few weeks ago, I attended a conference at Duquesne University – the 2025 Tech Ethics Symposium – where I spoke on a couple of panels about the future (of the "AI" industry, of higher education). It was a remarkable event – the first time in my 15+ years as an education writer (and 25+ years working in and adjacent to ed-tech) that I've been to a technology event where "No" was presented as a viable (indeed, perhaps even the moral) response to computing.

Typically, instead of encouraging statements (and subsequently, practices) of refusal, these events channel any and all resistance into a reframing, into acquiescence: these technologies might be dangerous and damaging – inextricable from (as we can see with "AI") fascism, eugenics, environmental destruction, war, imperialism, and growing wealth inequality – but somehow, somehow we can still bend them "for good." (????????)

Many people so desperately want to believe that they have a relationship with technology that is, at the very least, symbiotic. "Bicycle for the mind" cliches galore. But computing technologies, built by the most powerful companies in the world, run by the richest men in the world (the richest the world has ever seen) are all fundamentally committed to something else altogether: not to symbiosis but to extraction, exploitation, and domination.

This all plays out in "markets." And this plays out on bodies. It has already taken a massive toll on life, on work, on school, on knowledge. On human dignity.

Whose bodies? Whose autonomy? Whose dignity?

The House Oversight Committee's release of some of the documents from Jeffrey Epstein's estate should serve to remind us of this: the ways in which the elite move through the world with such thoughtlessness and with such impunity. That Larry Summers even still had a job teaching at Harvard – my god.

(Among the positions Summers has stepped down from this week: his role on the board of OpenAI.)

There is a real rot at the core of many of our institutions – and certainly at the core of those powerful players operating within and adjacent to them. "Artificial intelligence" emerges from this rot. It cannot be a bulwark against it. Among Epstein's friends (correspondents, visitors to his island) were luminaries in the field of "AI," including Marvin Minsky and Roger Schank. Luminaries in the field of technology and education.

Epstein, if you'll recall, was personally interested in all sorts of scientific research, but particularly in eugenics (he hoped, according to a 2019 NY Times article, to "seed the human race with his DNA") as well as in artificial intelligence. I feel like I'm losing my mind sometimes having to repeat this: "AI" and eugenics are inextricable.

Whatever belief that some folks have that they can "do good" with this technology, the technology itself bends in other directions (bends with a cc to jeevacation@gmail.com, I dare say). It bends towards the automation of everything. It bends towards indignity. It bends towards the end of education (certainly towards the end of the Department of Education), the reduction of school to "workforce prep," and the elimination altogether of a profession called "teaching" (in no small part because these folks have always viewed girls and women for other "uses" altogether).

Just a few more stories on ed-tech, "AI," and authoritarianism:

• "'Antivirus for libraries’: How a Texas startup is capitalizing on school book bans" – The San Antonio Express News on a company called Bookmarked that will identify "problematic material" for schools
• "'They Dragged Her Out in Front of the Kids': Inside Chicago’s ICE Raid at a Bilingual Daycare" – via Mother Jones
• 404 Media reports on how "DHS Is Deploying a Powerful Surveillance Tool at College Football Games"
• Speaking of school surveillance, a little bit of good news, for once – an update from Ian Linkletter on his legal battle with Proctorio
• "Stop AI in Malden Schools"

Stop it everywhere.

Today's bird is the bearded vulture, which according to Wikipedia, is "the only known vertebrate whose diet consists of 70-90% bone." Although primarily a scavenger, the bearded vulture is also known to attack and kill live prey. You can decide what to make of this bird analogy.

Thanks for reading Second Breakfast. I really am taking a break from newslettering for the rest of the year. (Maybe...)

As an adult with math-loving kids, I’ve had the nearly constant struggle of finding the “right math book” for them for many years.

Only after buying, renting, or borrowing some atrocious math books did I look into why different math books seemed “better”.

The answer, as in most things in life, is the power of incentives.

Writers of math textbooks face different incentives that drive the quality of exposition, exercises, exercise structure, and outcomes.

Once you understand how textbooks get made and who they’re designed for, it suddenly becomes much easier to choose one for your kid.

I. Why This Matters

When we started looking for math books for our kids, I had only really been exposed to the math books I used in K-12 and college. So I assumed all math textbooks were written the same way.

They aren’t.

After seeing the books my kids used in school and what I remember loving about math growing up, they were miles apart.

It seemed like some were written to take all the love and fun out of mathematics, while the others were written with love (even if it is a terse, make-you-do-hard-work, and this-is-good-for-you-even-if-it-is-painful type of love).

Why did I care, and why did this matter?

This matters because, as a parent of math-loving kids, I want my kids to see the love and wonder of doing mathematics.

After digging around, here is my hand-wavy answer to why some books are great and some are lacking: because two different systems are at play in producing math textbooks.

In broad strokes, the systems are:

1. College-level books (written by individuals)

2. K-12 books (written by committees and publishers)

Let’s first look at college-level books (and the like):

II. How College Math Textbooks Are Born

A math professor is assigned by the department (based on their seniority, interest, research focus, and so on) to teach a class.

This professor does a brief “literature review” of what textbooks would be good for the class.

This results in one or two textbooks that the professor will use.

However, every once in a while, the professor decides that the current textbooks are missing elements (exercises, topics, exposition) that would make the class even better.

So the professor creates their own notes to fit how they personally think math should be explained and learned.

This, of course, is unpaid work. But professors who write their own notes do it because they love the subject and want it taught the right way.

The professor then teaches the class for a year or two, and the notes evolve and get refined as the material is processed through teaching.

Other instructors discover the notes (TAs share them, grad students share them, math people are social and thus talk about what they’re teaching and how).

These other instructors (in the same and/or different institutions) ask to use the same notes.

Eventually, a publisher learns of the notes (they have scouts!) and approaches the professor and their institution to turn them into a book.

The book gets published, which results in a text with:

• A clear intellectual point of view

• Coherent sequence (because one person designed it)

• Exercises that are very well thought out

• Exercises that contain learning material “hidden” inside of them (which is why many mathematicians believe doing problems is where real learning happens)

As the book gets adopted, other professors and students find mistakes, and if it’s a good take on the subject, many new editions are printed.

Which is great until a new professor is assigned to teach a class somewhere and finds this book not to their liking.

So this other professor writes their own notes and, well, you can see where this will go.

Eventually, another book will be published!

All because someone cared enough about what was covered to sit down and write it.

Let’s now look at how the other system works.

III. How K-12 Math Textbooks (in the USA) Are Born

This is a very different origin story from college math textbooks.

I grew up in the USA and am most familiar with the USA, so that’s what will be covered here.

The first thing to know is that there is no single national math committee in the USA.

Which means that the curriculum taught in schools is developed by committees at the state and local levels.

Given there are 50 states and way more local levels, they don’t all align, given how different the states are.

As such, each state sets its own curricular standards of what must be taught at each grade level.

Most states have adopted the Common Core State Standards for Mathematics, which were developed to standardize mathematics education across the USA.

While well-meaning, the lack of a single national standard means each state wants something slightly different.

This means a state-level committee defines the topics and frameworks that must be covered at each grade-level class.

So while you can take High School Algebra I in every state, you’ll be learning slightly different things.

What this means for publishers, though, is that they have a choice between publishing 50 different textbooks for each subject or 1 (giant) textbook that covers all 50 states’ requirements.

They choose 1 giant textbook and then hire a team of educators and math writers to write a book that covers everything exactly as dictated by all the different curricula.

The goal here is to create a book that checks every box (because states will check) so that it can be sold in as many states as possible.

The book gets published, which results in a text with:

• 800-1200 pages

• A mish-mash of topics that have somehow been connected

• A text that meets bureaucratic requirements, not intellectual ones

• A “kitchen sink” approach and design that dilutes the conceptual focus

• Exercises that must adhere to the exact wording specified in the curriculum guide.

And not only that, the teachers in each state then have to teach from this!

Which means kids are jumping over topics for reasons they don’t understand.

All because the particular state they’re in doesn’t cover that topic, and because all the topics must be seen, the teachers rush through the book (through no fault of their own).

It’s not the teacher’s fault; it’s how the system is set up.

This gives students the impression that some topics are as “valuable” as other topics.

Let’s look at an example for a US high school calculus book.

IV. The Page Count Problem

I just used my favorite search engine to search for “high school calculus textbook”.

The first result led me to Amazon, where I saw that the recommended textbook has 1,176 pages.

That’s right, almost one thousand two hundred pages!

Compare that with the first calculus book Richard Feynman read (at the age of 13, no less) “Calculus for the Practical Man” by J.E. Thompson.

Calculus for the Practical Man clocks in at 360 pages.

A more recent example is Apostol’s Calculus I (Volume 1), a rigorous (i.e., proof-based) introduction to Calculus.

Even this book comes in at 666 pages. Though to be fair, the first two-thirds (pages 1 to 444) cover calculus of functions with one variable, including infinite series and an introduction to differential equations. The last third of Volume I introduces Linear Algebra with applications to Geometry and Analysis. If we’re comparing the Calculus book to the Calculus “book”, this book could count as 444 pages.

So why does an easier high school calculus book require 600 to 900 more pages than rigorous introductory university calculus textbooks?

Because the goal isn’t to teach calculus. The goal is to satisfy adoption committees.

Let’s look at why Committee-Written Textbooks are not suitable for math-loving kids.

V. Why Committee-Written Textbooks Feel So Different

The Committee-Written Textbooks (CWT) are written to get adopted by school districts, not to optimize learning.

CWT textbooks are risk-averse because they must match a state’s curriculum language exactly.

CWT textbooks don’t prioritize what matters and have to cover everything.

CWT textbooks are written so that other committees can do a check-box scan to make sure the content is there, so they end up with:

• Long explanations to prevent misinterpretation

• Repetitive examples

• Shallow breadth, limited coherence

And lastly, and why we care the most, is that the books are designed around classroom management and not for highly motivated learners.

Getting back to choosing a textbook.

VI. What This Means for Parents Choosing a Textbook

The books designed for school constraints are rarely the ones that work best for a motivated young math kid.

This means that when learning math outside of school, you likely won’t want:

• Bureaucracy-driven textbooks

• “Kitchen sink” mega-books

• Overly scaffolded, shallow introductions

What you should be looking for is a book written by:

• A single mathematician

• A small, unified team (editors, reviewers) that supports a clear philosophy

• Someone with a clear pedagogical mission (e.g., Gelfand, Strang, Art of Problem Solving, etc.)

When in doubt, avoid mega-textbooks and look for clarity, brevity, and conceptual focus. Ideally, you can read the introduction and see the professor/writer thanking the many years of students who took the class based only on printouts/copies of the professor’s notes.

VII. Choose better

When learning at home with a math-loving kid, choose books written by people who clearly “give a damn.”

That is, people who looked around and thought to themselves, “This could be better,” and then went out and actually wrote it.

This gives you and your kid math books that teach thinking and offer a glimpse into how a professional mathematician thinks about math.

Oh, and if your kid’s book was written by someone who cares deeply about math, the exercises are where that care really shows.

VII. Closing

That’s all for today :) For more Kids Who Love Math treats, check out our archives.

Stay Mathy!

Talk soon,
Sebastian

PS. Have questions about the above and our experiences? Hit reply or comment below.

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On September 19, 1982, Carnegie Mellon University computer science research assistant professor Scott Fahlman posted a message to the university’s bulletin board software that would later come to shape how people communicate online. His proposal: use :-) and :-( as markers to distinguish jokes from serious comments. While Fahlman describes himself as “the inventor…or at least one of the inventors” of what would later be called the smiley face emoticon, the full story reveals something more interesting than a lone genius moment.

The whole episode started three days earlier when computer scientist Neil Swartz posed a physics problem to colleagues on Carnegie Mellon’s “bboard,” which was an early online message board. The discussion thread had been exploring what happens to objects in a free-falling elevator, and Swartz presented a specific scenario involving a lit candle and a drop of mercury.

That evening, computer scientist Howard Gayle responded with a facetious message titled “WARNING!” He claimed that an elevator had been “contaminated with mercury” and suffered “some slight fire damage” due to a physics experiment. Despite clarifying posts noting the warning was a joke, some people took it seriously.

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