Tai-Danae Bradley

tai [dot] danae [at] math3ma [dot] com

I am currently 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 finished my PhD in mathematics in spring 2020 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.

This website was originally created in 2015 as tool to help me transition from undergraduate to graduate level mathematics. Quite often, I'd find that the ideas of math are hidden behind a dense fog of formalities and technical jargon. Much of my transition process was learning how to fight through this fog in order to clearly see the ideas, concepts, and notions which lie beneath. Throughout this process I learned that writing—and drawing—helps immensely. Eventually I decided to share my writings and drawings on the web in hopes that others may find them helpful as well.

Below is a list of my research, publications, and more.

**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:

**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

**An Enriched Category Theory of Language: From Syntax to Semantics **[video]with John Terilla and Yiannis Vlassopoulos

**Entropy as a Topological Operad Derivation **[video]*Entropy 2021, 23(9), 1195*. doi.org/10.3390/e23091195*A correspondence between Shannon entropy and derivations of the operad of topological simplices.*

**Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework**with Jacob Miller and Geoffrey Roeder. arXiv pre-print: 2106.15666

**Language Modeling with Reduced Densities **[video]with Yiannis Vlassopoulos,

Modeling Sequences with Quantum States: A Look Under the Hood

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**with Martha Lewis, Jade Master and Brad Theilman,

**On the Distribution of the Greatest Common Divisor of Gaussian Integers**

with Yin Choi Cheng and Yan Fei Luo, *Involve, A Journal of Mathematics, *vol. 9, issue 1 (2016), pp. 27-40.

arXiv: 1502.02148

Asymptotics for the average norm of the greatest common divisor of Gaussian integers.

**A New Perspective of Entropy **[video]A companion article to "Entropy as a Topological Operad Derivation" written for the ambitious lay person.

**What is Applied Category Theory?**A short expository booklet inspired by the 2018 Applied Category Theory conference

e-booklet, arXiv: 1

**An Invitation to Category Theory**A non-technical introduction to category theory

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) ****

**Linear Algebra for Machine Learning**A friendly, non-technical intro to basic ideas in linear algebra and some ways they appear in machine learning

**PBS Infinite Series (Season 2)**A series of short videos produced by PBS Digital Studios about the wonderful world of mathematics

A video interview with Miles Stoudenmire at the Flatiron Institute (August 2022)

A podcast interview on Timothy Nguyen's **The Cartesian Cafe **(July 2022)

A podcast interview on Sean Carroll's **Mindscape** (November 2021)

An interview article in *Math Horizons**,* volume 29, issue 2 (November 2021)

A video interview on Grant Sanderson's **3Blue1Brown Podcast** (September 2021)

A video interview on **MΣΣT a Mathematician** (February 2021)

A podcast interview on **My Favorite Theorem** (January 2021)

A podcast interview on** The Local Maximum** (November 2020)

An article from the CUNY Graduate Center (November 2020)