Jonathan Gorard

Jonathan Gorard is a researcher in applied mathematics at the University of Cambridge (where he was previously a graduate student), a consultant mathematician for Wolfram Research (leading the development of the Wolfram Language's automated theorem proving, axiomatic mathematics, quantum computing and discrete-state quantum mechanics functionality) and one of the cofounders of the Wolfram Physics Project. His published research comprises novel contributions to general relativity, the foundations of quantum mechanics, quantum information theory, mathematical logic, computational complexity theory, functional analysis, combinatorics and algebraic graph theory, among many other areas. His hobbies and interests include cognitive neuroscience, psycholinguistics, analytic philosophy, abiogenesis, senescence, cryonics, hiking, running, Mediterranean food jazz piano and mixed lacrosse.

Research Interests

  • Mathematical Foundations of the Wolfram Model

  • Fundamental Aspects of (Hyper) graph Theory and Discrete Differential Geometry

  • Implications for the Foundations of General Relativity and Quantum Mechanics

  • Connections to Mathematical Logic and Theoretical Computer Science

  • Connections to Automated Theorem Proving

  • Computability and Computational Complexity Theory

  • Connections to (Higher) Topos Theory and Categorical Quantum Mechanics

  • Implications for Quantum Information Theory

Research Output

Featured
General Relativistic Hydrodynamics in Discrete Spacetime: Perfect Fluid Accretion onto Static and Spinning Black Holes
General Relativistic Hydrodynamics in Discrete Spacetime: Perfect Fluid Accretion onto Static and Spinning Black Holes

Jonathan Gorard

This study investigates the effect of spacetime discretization on accretion dynamics of a relativistic fluid onto a spinning black hole, specifically noting that accretion rates decrease with increased discretization scale and that drag force sensitivity and instabilities intensify at critical discretization values.

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Computational General Relativity in the Wolfram Language using Gravitas II: ADM Formalism and Numerical Relativity
Computational General Relativity in the Wolfram Language using Gravitas II: ADM Formalism and Numerical Relativity

Jonathan Gorard

This paper introduces the Gravitas computational general relativity framework's numerical subsystem, emphasizing its ability to perform 3 + 1 spacetime decompositions via the ADM formalism, handle complex simulations of gravitational phenomena like binary black hole mergers, and leverage adaptive refinement algorithms based on hypergraph rewriting within the Wolfram Language.

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Computational General Relativity in the Wolfram Language using Gravitas I: Symbolic and Analytic Computation
Computational General Relativity in the Wolfram Language using Gravitas I: Symbolic and Analytic Computation

Jonathan Gorard

Gravitas introduces a robust computational framework for general relativity in the Wolfram Language, featuring seamless integration of symbolic and numerical tools to handle complex spacetime geometries and solve the Einstein field equations.

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Non-Vacuum Solutions, Gravitational Collapse and Discrete Singularity Theorems in Wolfram Model Systems
Non-Vacuum Solutions, Gravitational Collapse and Discrete Singularity Theorems in Wolfram Model Systems

Jonathan Gorard

This study extends the Raychaudhuri equation to discrete spacetimes, exploring conditions under which they might exhibit geodesic incompleteness, and applies numerical simulations to predict black hole formations.

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Axiomatic Quantum Field Theory in Discrete Spacetime via Multiway Causal Structure: The Case of Entanglement Entropies
Axiomatic Quantum Field Theory in Discrete Spacetime via Multiway Causal Structure: The Case of Entanglement Entropies

Jonathan Gorard, Julia Dannemann-Freitag

This research examines a covariant approach to entanglement entropy in discrete quantum gravity, comparing causal set and Wolfram model frameworks to reveal a monotonic relationship.

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Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories
Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories

Xerxes D. Arsiwalla, Jonathan Gorard, Hatem Elshatlawy

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Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types
Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types

Xerxes D. Arsiwalla, Jonathan Gorard

The study explores how spatial structures in physics can emerge from pregeometric combinatorial models governed by computational rules, using higher category theory and homotopy types.

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