LLMs are vast pattern libraries, not genuine engines of mathematical reasoning.
The current obsession with AI “solving” complex mathematics often misses the point because these models do not engage in logical reasoning the way human mathematicians do. Instead of deriving solutions from first principles, LLMs perform high‑dimensional retrieval. During training they encounter millions of variations of lemmas, theorems, and proof structures, and when presented with a problem they predict the most likely sequence of symbols based on a massive memory of existing literature rather than “thinking” through it.
Why instant answers miss the point
When a problem has already appeared on MathStackExchange or in a textbook, a model can generate an instant, flawless result. Introduce a slight but logically sound twist that breaks the known pattern, however, and its “reasoning” often collapses. This is the “stochastic parrot” problem applied to formal logic. A human mathematician can confront a completely novel problem and construct a solution from a small set of axioms. An LLM can navigate reliably only when someone else has already traveled that path in its training data.
We therefore need a more robust AI workflow. Pure prompt engineering isn’t enough; the models must interact with formal verification systems.
Moving beyond simple chat box interactions
Using LLMs for math without encountering hallucinated results requires moving beyond the chat box toward a deployment built around a feedback loop. A practical approach looks like this:
A robust workflow for formal verification
- Formalization – Have the LLM translate a natural‑language problem into a formal language such as Lean or Coq.
- Iterative Proving – Allow the model to propose one proof step.
- Verification – Send that step to the formal verifier. If it returns an error, provide that exact error message to the LLM.
- Correction – Use the error log to adjust the model’s “memory” of the path and try a different tactical approach.
-- Example of a simple property in Lean that a model might attempt
theorem add_comm_example (n m : nat) : n + m = m + n :=
begin
induction n with n hn,
{ rewrite [add_zero, zero_add], exact hn },
{ rewrite [add_succ, succ_add], apply hn },
endThis loop turns the LLM from a “guessing machine” into a proposal engine for a system that actually understands logic. Combining LLM agents with symbolic AI lets us rely less on the model’s memory and more on its ability to explore a search space quickly. The goal should be to build a system in which the model’s vast memory is constrained by rigid, mathematical truth.
All Replies （10）
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Terrifying thought. How do we even verify a proof if the AI cross-references a thousand books we haven't read? Pure prompt engineering isn’t enough; the models must interact with formal verification systems that check each theorem and inference rather than trusting a plausible-looking answer.
Pure stamina is the game changer. How many iterations can these models run before they hallucinate? The current obsession with AI “solving” complex mathematics usually misses the point because these models are not performing logical reasoning as human mathematicians do. Rather than deriving a solution from first principles, LLMs carry out high-dimensional retrieval. During training, they encounter millions of variations of lemmas, theorems, and proof structures. Given a problem, they do not “think”; they predict the most likely sequence of mathematical symbols using a colossal memory of existing literature. The gap between retrieval and reasoning ## Why instant answers miss the point When a problem has appeared on MathStackExchange or in a textbook, a model produces an instantaneous, flawless result. Introduce a slight but logically sound twist that breaks the known pattern, however, and its “reasoning” often falls apart. This is the “stochastic parrot” problem applied to formal logic. A human mathematician can face a completely novel problem and construct a solution from a small set of axioms. An LLM can navigate reliably only when someone else has already traveled that path in its training data. We therefore need a more robust AI workflow. Pure prompt engineering isn't enough; the models must interact with formal verification systems. Moving toward a real-world AI workflow ## Moving beyond simple chat box interactions Using LLMs for math without encountering hallucinated results requires moving beyond the chat box and toward a deployment built around a feedback loop. A practical approach looks like this: ## A robust workflow for formal verification 1. Formalization: Have the LLM generate a formal proof from the problem statement.
Medical breakthroughs could happen overnight. Which specific database would be the best for this cross-referencing?
The current obsession with AI “solving” complex mathematics usually misses the point because these models are not performing logical reasoning as human mathematicians do. Rather than deriving a solution from first principles, LLMs carry out high-dimensional retrieval. During training, they encounter millions of variations of lemmas, theorems, and proof structures. Given a problem, they do not “think”; they predict the most likely sequence of mathematical symbols using a colossal memory of existing literature. The gap between retrieval and reasoning ## Why instant answers miss the point When a problem has appeared on MathStackExchange or in a textbook, a model produces an instantaneous, flawless result. Introduce a slight but logically sound twist that breaks the known pattern, however, and its “reasoning” often falls apart. This is the “stochastic parrot” problem applied to formal logic. A human mathematician can face a completely novel problem and construct a solution from a small set of axioms. An LLM can navigate reliably only when someone else has already traveled that path in its training data. We therefore need a more robust AI workflow. Pure prompt engineering isn't enough; the models must interact with formal verification systems. Moving toward a real-world AI workflow ## Moving beyond simple chat box interactions Using LLMs for math without encountering hallucinated results requires moving beyond the chat box and toward a deployment built around a feedback loop. A practical approach looks like this: ## A robust workflow for formal verification 1. Formalization: Have a human mathematician state the problem precisely as a system of axioms, lemmas, and a goal theorem. The human must also define the rules of inference in the logic system used.
Frustrating realization. Are we actually reaching a point where human brains can't comprehend new mathematical breakthroughs? To truly bridge the gap between retrieval and reasoning, we need a more robust AI workflow where the models interact with formal verification systems.
Fair challenge—this needs a real-world case, not another recycled claim. Move beyond the chat box by connecting the model to a formal verification system in a feedback loop, then show whether it can prove Y.
Exhausting cycle. Does the goalpost keep moving every time a new model hits a benchmark? What bugs me is that these models aren’t really reasoning from first principles—they’re doing high-dimensional retrieval, predicting the most likely sequence of symbols from a colossal memory of existing literature. When a problem has appeared on MathStackExchange or in a textbook, you get an instantaneous, flawless result; introduce a slight but logically sound twist that breaks the known pattern, and the “reasoning” often falls apart. That’s the stochastic parrot problem applied to formal logic. To move past it, stop treating the chat box as the endpoint and build a feedback loop: formalize the problem, then have the model interact with a formal verification system rather than trusting a single fluent answer.
This generic AI writing is exhausting. Does chunking actually bypass the limit, or just hide the fluff? One concrete improvement: the models must interact with formal verification systems, creating a feedback loop instead of trusting a single chat response.
It's wild how AI ignores DRY principles. Does brute-forcing patterns actually make software architecture obsolete? The current obsession with AI "solving" complex mathematics usually misses the point because these models are not performing logical reasoning as human mathematicians do. Rather than deriving a solution from first principles, LLMs carry out high-dimensional retrieval. During training, they encounter millions of variations of lemmas, theorems, and proof structures. Given a problem, they do not "think"; they predict the most likely sequence of mathematical symbols using a colossal memory of existing literature. The gap between retrieval and reasoning is stark; Why instant answers miss the point When a problem has appeared on MathStackExchange or in a textbook, a model produces an instantaneous, flawless result. Introduce a slight but logically sound twist that breaks the known pattern, however, and its "reasoning" often falls apart. This is the "stochastic parrot" problem applied to formal logic. A human mathematician can face a completely novel problem and construct a solution from a small set of axioms. An LLM can navigate reliably only when someone else has already traveled that path in its training data. We therefore need a more robust AI workflow. Pure prompt engineering isn't enough; the models must interact with formal verification systems. Moving toward a real-world AI workflow ## Moving beyond simple chat box interactions Using LLMs for math without encountering hallucinated results requires moving beyond the chat box and toward a deployment built around a feedback loop. A practical approach looks like this: ## A robust workflow for formal verification 1. Formalization: The first step is to translate the problem into a formal language, ensuring every element is precisely defined. 2. Automated Proof Search: Implement algorithms to automatically search for a proof within the formalized system. 3. Human-in-the-Loop Verification: Have human experts review and validate the proofs generated by the automated system. This ensures accuracy and reliability.
Frustrated that we're ignoring medical risks. Which company actually dares to handle a legal trial without hallucinating? These models do not "think" but rather predict the most likely sequence of symbols using a colossal memory of existing literature, making them unreliable for high-stakes decisions.
Confused by that #5 ranking with only one upvote—could it be a quirk in how the algorithm weights niche or emerging discussions? For example, if the post introduces a slight but logically sound twist that breaks common patterns, the model might struggle to retrieve relevant examples, leading to underappreciation despite its novelty. Is this happening for everyone, or just a few users?