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A Perspective on Interactive Theorem Provers in Physics.

Joseph Tooby-Smith1

  • 1Department of Computer Science, University of Bath, Bath, BA2 7AU, UK.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|October 22, 2025
PubMed
Summary
This summary is machine-generated.

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Interactive theorem provers (ITPs) ensure mathematical correctness. This work explores their application in physics, advocating for the open-source PhysLean project to formalize physics results.

Area of Science:

  • Formalized mathematics
  • Computer science
  • Theoretical physics

Background:

  • Interactive theorem provers (ITPs) are computational tools ensuring the correctness of formal mathematical statements.
  • The application of ITPs is expanding across various scientific domains, including mathematics and artificial intelligence.
  • Formalizing complex scientific theories requires robust and verifiable methods.

Purpose of the Study:

  • To explore the optimal application of Interactive Theorem Provers (ITPs) within the field of physics.
  • To highlight the potential of ITPs for ensuring the rigor and correctness of physical theories.
  • To introduce and motivate the development of PhysLean, an open-source project for formalized physics.

Main Methods:

  • Reviewing existing applications of ITPs in mathematical and computational contexts.
Keywords:
interactive theorem proversphysicsproof assistants

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  • Analyzing the specific challenges and opportunities for formalization in theoretical physics.
  • Conceptualizing the architecture and goals of a community-driven project for formalized physics results.

    • Main Results:

    • ITPs offer a powerful framework for verifying complex mathematical definitions and theorems.
    • The formalization of physics presents unique challenges but offers significant benefits for theoretical consistency.
    • The proposed PhysLean project aims to foster a collaborative environment for formalizing physics.

    Conclusions:

    • Interactive theorem provers are valuable tools for enhancing the certainty of mathematical and scientific reasoning.
    • The formalization of physics through projects like PhysLean can accelerate discovery and ensure foundational accuracy.
    • Community-driven open-source initiatives are crucial for advancing the formalization of complex scientific domains.