Cheery Friday Greetings from Barb Oakley!
It’s been a busy six weeks in North America, Europe, and Asia. The University of Leeds; Cambridge International Education; the International Congress of Mathematicians in Philadelphia; keynotes in Hsinchu for four thousand engineers and managers at the world’s largest chipmaker; teacher conferencing at Taiwan’s preternaturally beautiful Sun Moon Lake. Next week, it’s on to Frankfurt, Germany—more on that below… But let’s start with:
The Hangover That Changed Mathematics
Peter Scholze may be the most gifted mathematician alive. In 2019 he spent months on a proof so involved he could not quite hold it in his working memory, no matter how hard he tried. He’d get a concept in one arm of his “attentional octopus,” so to speak, but then feel another concept slip away. But one glorious Thursday it finally all—well, almost all—came together, with one simple step left, so he went out to a bar to celebrate with a colleague. But come Friday morning, he found himself, as he put it, “fully destroyed” with a hangover. He finished the proof that day anyway, but what with his muzzy thinking, he couldn’t be sure he had it right. In fact, part of his problem, Scholze knew, was that he was such a powerfully good mathematician he could convince practically anyone that he was right—even when he was wrong!
This is how Scholze came to ask Imperial College London’s Kevin Buzzard whether Scholze’s hangover-finalized proof might be checked using “Lean,” a program that verifies every step of an argument. (Lean is merciless—when Buzzard had started using it, it made him prove that 2 ≠ 1 before it would let him going with anything else.)
Kevin Hartnett tells the story in his magnificent new book, The Proof in the Code: How a Truth Machine Is Transforming Math and AI. I was lucky enough to be on a panel with Rutgers mathematician Alex Kontorovich at the International Congress of Mathematicians in Philadelphia about education in mathematics, and then heard Alex’s phenomenal lecture related to Hartnett’s book and the future of math, The Shape of Math To Come. If you think AI is generating a revolution in math, well, Lean is a revolution within a revolution that will allow math to leapfrog that revolution.
Incidentally, here at Learning How to Learn, we’re convinced that however fast technology is changing, the human brain still needs its knowledge foundations. The basics are important—there’s no skipping schema formation! Here’s a wonderful essay, “Why LLMs Make Learning to Code More Important, Not Less,” by Senthil Kumaran, a software developer at Uber, that states our case.
Cambridge Is on Board
I had an exhilarating visit to Cambridge International Education in Cambridge UK, where I gave the opening keynote and a workshop at their Schools Conference. Cambridge International Education is serious about science and applying “cognitive realism” in teaching. Parents, if you’re weighing international school systems for your children, this is an outstanding one to sign up for.
A Visit with John Tomsett in York—which found its way into influencing Taiwan
My hero hubby Phil and I are huge fans of James Herriot’s All Creatures Great and Small (Phil especially!) which is a good part of why we keep finding our way back to Yorkshire. So after our visit to Cambridge, we were happy to find ourselves in York having tea with the perceptive education author John Tomsett and his brilliant wife Louise (all the more brilliant because she, too, is a fan of James Herriot!)
I was particularly interested in work on social emotional learning (SEL), because this has become something of a fad in Taiwan, where I was planning to head next. John Tomsett is well-versed on SEL—he’s written thirteen books, among them This Much I Know About Mind Over Matter: Improving Mental Health in Our Schools. John also recommended Ecclestone and Hayes’s The Dangerous Rise of Therapeutic Education. I read them with interest.
Then I flew to Taiwan and, amidst many lectures, checked out the SEL scene. What I found was, sadly, that Taiwanese teachers are drowning in expectations, expected to be not only subject matter experts (Taiwanese teachers are indeed superb!), but also to be experts in neurodiversity, differentiation, and now, as students’ quasi-therapists using SEL. Emotions matter. But these varying, diverse demands can kneecap a teacher’s ability to teach. In particular, therapy and teaching pull in different directions, and a teacher told to do both at once can ultimately do neither properly.
Make Plans, if You Can, for Beautiful Toronto in October!
On Saturday, October 24, I’ll be speaking at researchED Toronto on what the neuroscience says about teaching math — the different jobs of declarative and procedural memory, what scaffolding physically consists of in the brain, and why minimally guided discovery so often hurts the students it means to help. We’ll work one example all the way down: teaching division, following John Mighton’s approach in JUMP Math. If you’ll be there, come find me!
What AI Offloading Does to the Brain—a Week in Frankfurt
Starting August 30th, Terry Sejnowski and I will be in Frankfurt co-chairing the Ernst Strüngmann Forum on “Memory, Learning, and Neural Adaptation in the Age of Cognitive Offloading.” The Strüngmann Forum isn’t a conference with keynotes and posters. Instead, some forty researchers from neuroscience, psychology, computer science, and edtech are sorted into four working groups, each assigned a set of open questions to cogitate over for a week at the Ernst Strüngmann Institute. In the end, we produce a book so everyone can see where our thinking led us.
Everybody’s talking about cognitive offloading onto ChatGPT, Claude and the like. Much of what we know comes from psychology through surveys and test scores. There are a few brain-imaging studies —but what we really don’t yet understand are the underlying neural mechanisms involved: how offloading affects the brain’s learning processes. The brain learns in part from internal prediction errors—so what happens to those signals when the answer arrives from a chatbot instead of from your own struggle? The brain structures knowledge by compressing experience—but what is there to compress when the experience was never yours? More generally, what’s worth internalizing? What can be safely offloaded? This is a vitally important question for both education and industry: The engineers and managers I spoke with in Hsinchu, and at IBM, and elsewhere, all are wondering—what happens to an engineer’s judgment after a few years of letting the tool take the first pass?
We’ve pulled together Nelson Cowan on working memory, Fernand Gobet on chunking and expertise, Kenji Doya on the neural basis of habit and motivation, Azzurra Ruggeri on curiosity, and Evan Risko on offloading itself, among many others.
I’ll report back once the dust settles. Wish us luck!
That’s all for now. Happy learning!
Barb Oakley
- Uncommon Sense Teaching—the book and Coursera Specialization!
- Mindshift—the book and MOOC
- Learn Like a Pro—the book and MOOC
- The LHTL recommended text, A Mind for Numbers
- For kids and parents: Learning How to Learn—the book and MOOC. Pro tip—watch the videos and read the book together with your child. Learning how to learn at an early age will change their life!















