# How are Scientific Concepts Birthed? Typing Rules of Concept Formation in Theoretical Physics Reasoning

arXiv: https://arxiv.org/abs/2509.10740 · HTML: https://mlsanity.com/paper/2509.10740/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 12 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [We're Afraid Language Models Aren't Modeling Ambiguity](https://mlsanity.com/paper/2304.14399/) (2023)
- [Peano: Learning Formal Mathematical Reasoning](https://mlsanity.com/paper/2211.15864/) (2022)
- [A Transformer Model for Symbolic Regression towards Scientific Discovery](https://mlsanity.com/paper/2312.04070/) (2023)
- [From Probability to Consilience: How Explanatory Values Implement Bayesian Reasoning](https://mlsanity.com/paper/2006.02359/) (2020)
- [Explain the Black Box for the Sake of Science: the Scientific Method in the Era of Generative Artificial Intelligence](https://mlsanity.com/paper/2406.10557/) (2024)
- [Type theory in human-like learning and inference](https://mlsanity.com/paper/2210.01634/) (2022)

## Abstract (arXiv)

This work aims to formalize some of the ways scientific concepts are formed in the process of theoretical physics discovery. Since this may at first seem like a task beyond the scope of the exact sciences (natural and formal sciences), we begin by presenting arguments for why scientific concept formation can be formalized. Then, we introduce type theory as a natural and well-suited framework for this formalization. We formalize what we call "ways of discovering new concepts" including concept distinction, property preservation, and concept change, as cognitive typing rules. Next, we apply these cognitive typing rules to two case studies of conceptual discovery in the history of physics: Einstein's reasoning leading to the impossibility of frozen waves, and his conceptual path to the relativity of time. In these historical episodes, we recast what a physicist might informally call "ways of discovering new scientific concepts" as compositional typing rules built from cognitive typing rules - thus formalizing them as scientific discovery mechanisms. Lastly, we computationally model the type-theoretic reconstruction of Einstein's conceptual path to the relativity of time as a program synthesis task.