Tai-Danae Bradley
I am a research mathematician at Sandbox AQ and a visiting professor of mathematics at The Master's University where I help run the Math3ma Institute. I earned a PhD in mathematics at the CUNY Graduate Center under the supervision of John Terilla and spent some time as a postdoctoral researcher at X, the Moonshot Factory (Google X). My research interests lie in the intersection of quantum physics, machine intelligence, and category theory.
Below is a list of my research, publications, and more.
PhD Thesis
At the Interface of Algebra and Statistics
My thesis uses basic tools from quantum physics to investigate mathematical structure that is both algebraic and statistical. arXiv: 2004.05631. Here is a 10-minute trailer video:
Book
Topology: A Categorical Approach [online version]
A graduate-level textbook that presents basic topology from the perspective of category theory
with Tyler Bryson and John Terilla / published by MIT Press, 2020
Papers
The Magnitude of Categories of Texts Enriched by Language Models [PDF]
T.-D. B. and Juan Pablo Vigneaux, Theory and Applications of Categories, Vol. 44, 2025, No. 37, pp. 1256–1281.
Towards Structure-Preserving Quantum Encodings [PDF]
Arthur J. Parzygnat, T.-D. B., Andrew Vlasic, Anh Pham, Phys. Rev. Research 7, 041001 (2025) doi.org/10.1103/rph8-g15q
The Structure of Meaning in Language: Parallel Narratives in Linear Algebra and Category Theory
T.-D. B., Juan Luis Gastaldi, John Terilla. Notices of the American Mathematical Society, Vol. 71, No. 2, Feb. 2024. doi.org/10.1090/noti2868
An Enriched Category Theory of Language: From Syntax to Semantics [video 1 / video 2]
T.-D. B., John Terilla, Yiannis Vlassopoulos. La Matematica (2022) doi.org/10.1007/s44007-022-00021-2
Entropy as a Topological Operad Derivation [video]
T.-D. B. Entropy 2021, 23(9), 1195. doi.org/10.3390/e23091195
Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework
Jacob Miller, Geoffrey Roeder, T.-D. B. arXiv preprint (2021): 2106.15666
Language Modeling with Reduced Densities [video]
T.-D. B. and Yiannis Vlassopoulos. Compositionality 3, 4 (2021). doi.org/10.32408/compositionality-3-4
Modeling Sequences with Quantum States: A Look Under the Hood [video]
T.-D. B., E. Miles Stoudenmire, John Terilla. Machine Learning: Science and Technology (2020) doi.org/10.1088/2632-2153/ab8731, code available at https://github.com/emstoudenmire/parity
Translating and Evolving: Towards a Model of Language Change in DisCoCat
T.-D. B., Martha Lewis, Jade Master, Brad Theilman. Electronic Proceedings in Theoretical Computer Science 283 (2018) pp. 50-61. arXiv e-print: 1811.11041
On the Distribution of the Greatest Common Divisor of Gaussian Integers
T.-D. B, Yin Choi Cheng, Yan Fei Luo. Involve, A Journal of Mathematics, vol. 9, issue 1 (2016), pp. 27-40. arXiv: 1502.02148
Exposition
A New Perspective of Entropy [video]
A companion article to "Entropy as a Topological Operad Derivation" written for the ambitious lay person.
The Journal of The Math3ma Institute, vol. 1, issue 1, pp. 35–65. doi.org/10.55409/math3ma2022-112
What is Applied Category Theory?
A short expository booklet inspired by the 2018 Applied Category Theory conference
e-booklet, arXiv: 1809.05923
An Invitation to Category Theory
A non-technical introduction to category theory
Chalkdust Magazine, Issue 08 (2018) pp. 22-25.
online version here
Cognition, Convexity, and Category Theory
A short summary of the paper "Interacting conceptual spaces" by Coecke, et. al.
n-Category Café blog post (2018)
Videos
Linear Algebra for Machine Learning
A friendly, non-technical intro to basic ideas in linear algebra and some ways they appear in machine learning
TensorFlow YouTube channel (2021) - click here
PBS Infinite Series (Season 2)
A series of short videos produced by PBS Digital Studios about the wonderful world of mathematics
YouTube channel (2017 - 2018) - click here
In the Media
An article from Quanta Magazine: "Where Does Meaning Live in a Sentence? Math Might Tell Us" (April 2025)
A podcast interview on the CUNY GC's Alumni Aloud Podcast: "Mathematics at SandboxAQ" (November 2024)
An article from The Brilliant: "From the Basketball Court to Category Theory" (April 2023)
A video interview with Miles Stoudenmire at the Flatiron Institute: "Quantum Connect: Math & Physics Collide" (August 2022)
A podcast interview on Timothy Nguyen's The Cartesian Cafe: "Category Theory and Language Models" (July 2022)
A podcast interview on Sean Carroll's Mindscape: "Tai-Danae Bradley on Algebra, Topology, Language and Entropy" (November 2021)
An interview article in Math Horizons, volume 29, issue 2: "A Conversation with Tai-Danae Bradley" (November 2021)
A video interview on Grant Sanderson's 3Blue1Brown Podcast: "Where Math Meets Language | 3b1b Podcast #5" (September 2021)
A video interview on MΣΣT a Mathematician: "MEET at Mathematician! - Tai-Danae Bradley" (February 2021)
A podcast interview on My Favorite Theorem: "Episode 62 - Tai-Danae Bradley" (January 2021)
A podcast interview on The Local Maximum: "Episode 146 - Math, Language, and Intelligence" (November 2020)
An article from the CUNY Graduate Center: "Math3ma Blogger and Recent Alum Lands a Postdoc at Google's X - The Moonshot Factory" (November 2020)