Symbols, neural networks, and mathematical intelligence

Some reflections on connectionism and the basis of higher-level cognition

Bartosz Naskręcki on Twitter / X

Congrats to @LechMazur for the solution and to Terence Tao for the digestion and storytelling. You see the trend. Mathematicians are still needed if we want to make any sense of the formal proofs. For now... Maybe the next gen LLMs will simply read allthe blogs of Terry and… https://t.co/yXiISCrNAF— Bartosz Naskręcki (@nasqret) August 13, 2026

How linguistics learned to stop worrying and love the language models

Language models (LMs) can produce fluent, grammatical text. Nonetheless, some maintain that language models don’t really learn language and also, even if they did, that would not be informative for the study of human learning and processing. On the other side, there have been claims that the success of LMs obviates the need for studying linguistic theory and structure. We argue that both extremes are wrong. LMs can contribute to fundamental questions about linguistic structure, language processing, and learning. They force us to rethink arguments and ways of thinking that have been foundational in linguistics. While they do not replace linguistic structure and theory, they serve as model systems and working proofs of concept for gradient, usage-based approaches to language. We offer an optimistic take on the relationship between language models and linguistics.

Artificial intelligence is a familiar-looking monster, say Henry Farrell and Cosma Shalizi

The academics argue that large language models have much older cousins in markets and bureaucracies

The Dark Night of Mathematics

What are we really doing?

Mapping the Mind of a Large Language Model

We have identified how millions of concepts are represented inside Claude Sonnet, one of our deployed large language models. This is the first ever detailed look inside a modern, production-grade large language model.

Large language models are cultural technologies. What might that mean?

Four different perspectives

What comes next with open models

Markets, capabilities, cope, and bewilderment in the industrialization of language models.

The AI Revolution in Math Has Arrived | Quanta Magazine

AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.

One of the world's biggest mathematicians Joel David Hamkins says AI models are basically zero help for mathematics as they produce… - The Times of India

Technology News News: Joel David Hamkins, a leading mathematician and logic professor at the University of Notre Dame, has fired a withering salvo at large language models .

The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity

Recent generations of frontier language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes…

Large language models are not the problem

If a Large Language Model (LLM) can replicate your scientific contribution, the problem is not the LLM. What does it say about our field that so much of the anxiety about AI comes down to the fear that a machine could do what we do? Perhaps it says we should be doing something better.

Knowledge Collapse

AI companies are racing to mechanize mathematics. Where does that leave human understanding?

AI’s Memorization Crisis

Large language models don’t “learn”—they copy. And that could change everything for the tech industry.