Charting human thought with LLMs

https://t.co/wWtIKiwxz4

— How To Prompt (@HowToPrompt__) October 21, 2026

On 14th St. in Hoboken looking at the Empire State Building

Math, AI, and Terry Tao on a “war footing”

Elisabeth Bumiller, Why One of the World’s Greatest Mathematicians Is on a ‘War Footing’, NYTimes, Oct. 15, 2026.

Opening paragraphs:

Terence Tao is typically described as one of the world’s greatest living mathematicians, but right now he is doing very little math.

“I’m on a war footing,” he said while grabbing coffee during a two-day math workshop at the University of California, Los Angeles, that was rife with talk about the existential crisis that artificial intelligence has created in his field.

A bit later:

Until recently his job was as a bridge between the slow-moving world of higher math and the scorching speed of A.I. Dr. Tao, who uses A.I. as an assistant to run calculations, write code, search vast troves of literature and brainstorm ideas, has been experimenting with OpenAI’s models since 2023. He was an enthusiast for a “best of both worlds” future.

OpenAI’s releases have now left him feeling used. “As recently as a year ago, I had a pretty good relationship with many employees at OpenAI,” he said in a recent phone conversation.

“A lot of people I interacted with shared a very common vision of how A.I. should be used — you know, to empower scientists.” But the rush to publish new findings, he said, shows their true purpose. They “used math for what they needed, which was to evaluate their models,” he said. “At this point, I don’t see a way to constructively engage.”

His anger was clear in a post on the widely read math blog Proofs and Prompts after OpenAI’s Oct. 6 release. “I am horrified by the many person-years” of research, particularly by young mathematicians, “being casually disrupted or destroyed,” he wrote.

“Much as one cannot unhear a movie spoiler or a crossword clue, one cannot explore a problem as profitably and richly once one is aware of an existing solution.” He mourned, he added, “the path not taken, and the opportunities lost in the frantic race to develop this technology.”

Final paragraphs:

Despite OpenAI’s releases, he said, most problems at the frontiers of math are unsolved, math remains infinite and the difficulty of problems is therefore boundless. Since A.I. has given mathematicians the ability to collect data on such a vast scale, they will increasingly work in large groups collaborating on once-unimagined projects.

Dr. Tao, who sees each of his three students once a week, said every meeting is “increasingly a therapy session more than technical guidance.” His answer to them is that “if you focus on only the things you could do before, it looks bleak.”

So he has offered hope with advice that amounts to acceptance born of necessity rather than fighting a war. Problem solving is not a destination but a journey, and lessons learned along the way are often more important than the answer itself. Rather than solving a single problem on their own, they can use A.I. to solve 10 problems and find new patterns and more questions to ask.

“They will have to use their imagination,” he said. “This is a time for creativity, and I do hope students rise to the challenge. They didn’t ask for it. But I think many of them will surprise us.”

There's much more at the link.

Terence tao says we're being dragged into a new era of mathetics

Mathematician Terence Tao: "we're seeing the end of the romantic era of mathematics, the age of heroes. we're moving into an industrial era where math becomes large-scale, done in big teams like the other sciences" We're entering, rather unwillingly, a new era where exciting new things are possible, but some things are being lost

— Haider. (@haider1) October 15, 2026

Hoboken, on the street, May 30

Consolidating Context into Parametric Memory

Human intelligence grows by building on experience. We acquire knowledge, refine skills, revise beliefs, and carry what we learn into future situations. 🤔 Can LLM agents do the same? 🧠 Introducing our new work, “Cortex: Consolidating Context into Parametric Memory,” in collaboration with ByteDance Seed. #Cortex #KnowledgeEditing #LLM #Memory Our inspiration comes from biological systems consolidation: the hippocampus rapidly encodes new experiences, and interactions with the neocortex help integrate them into long-term memory. LLM agents already benefit from documents, demonstrations, and feedback in context. But those gains do not automatically persist once the context is removed. With Cortex, we study how to consolidate those benefits into model parameters, so they remain useful beyond the original context—while preserving capabilities outside the intended change. External memory preserves information for later retrieval. We explore a complementary route: integrating the useful effects of experience into the model itself. 📄 Paper: https://t.co/Gnc3t6BPNH 💻 Code (will be released soon): https://t.co/eQ6R7R62Y1 💡 What can be consolidated? Experience can call for different kinds of change: • Addition: acquire new knowledge or a new skill. • Revision: update an outdated fact or behavior. • Suppression: learn not to produce specified information or responses. We bring these context-specified changes in knowledge, skills, and behavior together under Memory Consolidation: recover the benefits of context after removing it, while preserving capabilities outside the intended change. ⚙️ How does Cortex work? We organize the approach around three questions: what to learn, where to write it, and how to make it usable without the original context. What: rehearse future uses. Cortex builds training examples around situations where the context should help. In most tasks, it generates prospective questions and answers them with the context available. Where: write into feed-forward networks. We explore two mechanisms: low-rank weight updates (Synaptic) and additional nonlinear feature channels (Structural). Both can be folded into standard model layers. How: let a model with context teach a model without it. The pre-update model itself serves as the teacher. It receives the original context; the student learns to respond without it. We align both their output distributions and internal representations, training only the newly introduced parameters. For example, the teacher can consult documentation for an unfamiliar API while producing a solution. The student learns from that supervision so it can use the API after the documentation is removed. 🔬 What counts as successful consolidation? Learning the new material is only part of the challenge. We also need to measure what happens to the capabilities the model already had. Our testbed covers five task families: • Agent experience: reuse useful strategies from prior experience. • Novel API learning: use unfamiliar APIs without the original documentation in context. • Persona steering: retain a specified change in how the model behaves. • Knowledge suppression: reduce responses containing specified information. • Factual editing: revise facts supplied through context. We measure two outcomes together: • Consolidation Rate (CR): how much of the performance gain provided by context is recovered after that context is removed. • Retention Rate (RR): how much of the original performance outside the intended change is preserved. We test single, batch, and sequential updates. Sequential evaluation asks a further question: as new experiences arrive, do earlier gains survive? 📊 What did we find? We evaluate Cortex on 4B–120B dense and mixture-of-experts models, including Qwen, Gemma 3, and GPT-OSS. • After 50 sequential factual updates on Qwen2.5-14B, Cortex-Structural achieves 88.9% CR and 99.8% RR, adding 0.74M parameters per update. • On GPT-OSS-120B, Cortex-Structural recovers the full context-provided gain on ALFWorld and slightly exceeds it (101.2% CR), while achieving 95.2% RR. • On GPT-OSS-20B, it reaches 90.7% CR in single-context API learning. • Across three Qwen backbones, the two Cortex variants achieve approximately 80–91% CR in batch factual editing. All results are evaluated without the original source contexts. This is the direction we want to explore: agents that turn useful experience into capabilities they can carry into future interactions.

— Ningyu Zhang@ZJU (@zxlzr) October 15, 2026

Reconciling symbols and neural networks

🤖🧠NEW PAPER🧠🤖 What is the relationship between neural networks & symbolic systems? Based on evidence from mechanistic interpretability, we argue for a quasi-symbolic view of cognition: Neural nets implement symbols but only approximately Link: https://t.co/j8B3IOIMpe 1/n https://t.co/zpn6q00wqq

— Tom McCoy (@RTomMcCoy) October 14, 2026

For comparison, see Relational Nets Over Attractors, A Primer: Part 1, Design for a Mind, Version 3

3 Patterns of hemisphere specialization in humans

The brain’s neat division of labor, with language on one side and attention on the other, is just one of several workable layouts. Hemispheric specialization appears to be flexible and partly inherited, not governed by a fixed template.

— Earl K. Miller (@MillerLabMIT) October 14, 2026

Robert Wright interviews Alex Gibney on his Musk documentary

Robert Wright and filmmaker Alex Gibney discuss Alex's epic new documentary about Elon Musk—an exploration of how the world's richest man got so powerful (and so weird).

0:00 Teaser
0:32 Alex’s new documentary about Elon
3:07 How Alex’s film turned epic
7:10 Simulation theory + social Darwinism = Elon?
13:36 Inside the mind of Musk
23:46 Elon’s daddy issues
26:35 Elon’s lady issues
29:14 Elon’s electoral propriety issues
36:58 Has Elon gotten weirder over time?
46:42 The damage DOGE could still do
50:14 Heading to Overtime

Discussed in Overtime:
Elon’s Trumpian side.
Is Elon a hypocrite on AI?
All-In on the Twitter-DOGE playbook.
Are Elon and Trump the new normal?
The time Bob interviewed Elon.

Mechanistic interpretability, making things up?

Researchers put a dead salmon in an fMRI scanner, showed it pictures of humans, and asked it to guess their emotions. The scan showed brain activity. In a dead fish. Now, the recent study proved that the exact same thing is happening in artificial intelligence. They call it the "Dead Salmons of AI Interpretability" When we use tools like feature attribution, SHAP values, or mechanistic interpretability to see "inside the black box," these methods often generate plausible-looking explanations from completely meaningless computations. You can completely randomize a model's weights and the "saliency map" explanation still looks perfectly valid. You can nudge the data slightly and the entire narrative of why the ai made a decision completely rewrites itself. the researchers call this a "crisis of non-identifiability." the math we use to explain ai behavior is so overdetermined that it is making up stories instead of measuring ground truth. this is a massive reality check for ai alignment and safety.. we are trusting frontier models with critical decisions based on "explanations" that are statistically equivalent to a dead fish having social emotions.. the fix? the authors argue we have to stop treating interpretability like a visualization tool and start treating it as a rigorous statistical inference problem. if your explanation survives a random model check, a label shuffle, and an intervention test.. then maybe you actually understand the model. if not, you're just looking at a dead salmon.

— Superman (@thesupermannx) October 10, 2026

Allocation of training compute for LLMs, 2024-2026

How AI shifted from a transductive paradigm (token-by-token answer completion) to an inductive paradigm (on-the-fly reasoning chain synthesis), in one chart. This is the big story of 2025 and 2026. This is what made coding agents work. https://t.co/ThLm2AH127

— François Chollet (@fchollet) October 10, 2026

Interactional synchrony among humans

'Interpersonal neural synchrony: one label, many phenomena' by Giacomo Novembre (@NovembreGiacomo), Atesh Koul & Félix Bigand https://t.co/YYl59pMmYn https://t.co/4SMD4NzNNj

— Trends in Neurosciences (@TrendsNeuro) October 8, 2026

Hoboken, Pier 13

Neil deGrass Tyson on Navier-Stokes, AI, and math

What’s with AI solving the Navier-Stokes Equation? Neil deGrass Tyson breaks down what the equation is and the controversy surrounding the solution with the help of astrophysicist Mordecai-Mark Mac Low.

Timestamps:
00:00 - What is the Navier-Stokes Equation?
02:31 - Turbulent Fluid Dynamics
07:16 - AI Solved The Millenium Problems
10:25 - What the AI Solution is Missing
18:15 - AI in Reasearch

The view from a table