Let’s make it clear: LLMs do not have emotions. An Anthropic paper finds internal representations in Claude that track emotions. Cool result, but interpreting this as evidence that Claude has emotions is fundamentally flawed: It conflates similarity in representations and outputs with similarity in the underlying processes. In humans, emotions do not merely shape what we say or do. When we fear something, something deeper happens: attention narrows, decisions accelerate, and processing is reorganized across multiple systems. Claude can speak about fear and may even encode an internal representation associated with fear. But that does not show that fear reorganizes its processing in the way it does in humans. Moreover, similar situations can produce different emotions in humans. A roller coaster can terrify one person and exhilarate another. The entire attempt to demonstrate that LLMs have emotions by finding a stable “neural signature” is flawed: Even in humans, researchers have not found consistent neural signatures for discrete emotion categories. Please stop conflating similarities in output with similarities in the processes that generate them.

I think this is the most important concept to understand right now: LLMs can’t jump. OpenAI says an internal version of Astra, its next major model, has solved ten major open problems in mathematics and theoretical computer science. This is extraordinary. And I don’t use this word lightly. During my PhD in mathematics, I worked on a problem closely related to Gromov’s conjecture. For decades, constructing a non-sofic group—an infinite group whose finite pieces cannot be approximated by finite groups—was a dream shared by many of us. Now Astra appears to have done it. This is not a toy result. This is serious mathematics. But it is not “the most significant day in the history of mathematics”, as some have claimed. This claim confuses scale with kind. Astra has solved difficult problems inside existing conceptual worlds. Calculus, topology, and scheme theory created new conceptual worlds. They did not merely answer questions. They changed which questions mathematics could ask. Induction finds patterns. LLMs are extraordinary at it. Deduction follows implications. Using symbolic AI tools, LLMs are becoming formidable at traversing chains of logic that humans missed, abandoned, or could never afford to search. But abduction is different. Abduction invents the right concept, the right representation, the right question. That is the jump. Current LLMs can fill the gaps of knowledge left by humans. But they can’t jump beyond the external boundary of existing knowledge. * Full paper in the first reply