Robert G. C. Smith

PhD

I am a theoretical physicist by training, with expertise at the intersection of fundamental physics, foundational mathematics, and computation. A central theme of my research is the search for new and hidden mathematical structures. My PhD explored deep connections between string theory, perturbative quantum field theory, analytic number theory, and algebraic geometry, while drawing more broadly on ideas from across mathematics and physics. My thesis, “At the edges of infinity and the finite: Charting a path to UV completion from number theory to quantum fields and strings”, provides a sample of this work.

During my PhD, I also developed growing interest in mathematical modelling, particularly the modelling of complex and stochastic systems, with a focus on combining machine learning and computational methods to uncover and formalise hidden structure. This interest later broadened to encompass the application of advanced mathematical techniques in combination with data-driven analysis.

Machine learning and quantitative research

I am now applying this background as a machine learning research scientist, with a focus on developing new algorithms and methods for solving complex scientific and real-world problems. Of particular interest is the use of modern AI methods in combination of data-driven research, rigorous mathematics, computation, and sophisticated modelling techniques.

I am also interested in mathematical and computational biology. This interest started with developing reaction-diffusion models of morphogenesis, and later evolved into a broader interest in machine learning applications and in the use of fundamental physics concepts in evolutionary biology, including genotype-phenotype mapping, mutational robustness, phylogenetics, gene regulation, and epigenetics. I am especially interested in applying computational and machine learning methods to research problems in bioenergetics and structural biology.

Current research interests

My research interests are increasingly centred on methodological machine learning for mathematical and scientific discovery, particularly at the intersections of generative modelling, active learning, reinforcement learning, and sequential decision-making. I am also interested in scientific machine learning (SciML), inverse problems and simulation-based inference, representation learning for scientific data, and neuro-symbolic (among other) approaches to mathematical reasoning.

A recurring theme in my research is how mathematical and physical structure, uncertainty, and adaptive computational strategies can inform the development of more efficient and reliable learning systems. I am also developing an interest in probabilistic numerical methods, particularly where numerical computation intersects with uncertainty quantification, statistical inference, and learning.

My other blogs

• TracingCurves — Research blog in mathematical physics, string/M-theory, and a few choice diversions.
• Dialogues at Still Points — Reflections across literature, history, and philosophy.

Selected media coverage

• “Does -1/12 Protect Us From Infinity?” Video featured on Numberphile discussing co-authored research, with nearly one million views.

Publications

Cantor’s Paradise: Evaluating compositional and out-of-distribution generalisation in neural models of infinite cardinality
Robert G. C. Smith
Manuscript in preparation.

Dynamics-aware de novo antibody design
Robert G. C. Smith and Beth M. Titchiner
Manuscript in preparation.

Neural surrogates for generalised Turing-type models
Robert G. C. Smith
Manuscript in preparation.

UV completion in the topics
Robert G. C. Smith
Manuscript in preparation.

At the edges of infinity and the finite: Charting a path to UV completion from number theory to quantum fields and strings
Robert G. C. Smith
PhD thesis, University of Nottingham (2026).
University repository

Gauge invariance and generalized η regularization
Antonio Padilla and Robert G. C. Smith
Physical Review D 111, 125013 (2025).
DOI · arXiv

η regularisation and the functional measure
Robert G. C. Smith and Murdock Grewar
arXiv preprint, 2025.
arXiv · PDF

de Sitter vacua in O(d,d) invariant cosmology
Yang Liu, Antonio Padilla, Paul M. Saffin and Robert G. C. Smith
Physical Review D 110, 063522 (2024).
DOI · arXiv

Smoothed asymptotics: From number theory to QFT
Antonio Padilla and Robert G. C. Smith
Physical Review D 110, 025010 (2024).
DOI · arXiv