Topos Institute

Topos Institute is a mission-driven nonprofit research institute that pioneers mathematical systems science to shape technology for public benefit. Founded in 2019 by Brendan Fong, David Spivak, and Valeria de Paiva, and incorporated on October 9, 2019 in California, the institute is headquartered in Berkeley with a UK office in Oxford established in 2024-2025. Its vision is a world where humanity flourishes through interconnected systems and processes that enable cooperation on complex issues.

The institute organizes its work through four interdependent pillars. The first is fundamental research, where the team pioneers mathematical systems science drawing on category theory to develop insights into collective sense-making and complex systems. Key research areas include categorical systems theory, polynomial functors, interacting dynamical systems, and categorical statistics. The second pillar is translational research, which translates mathematical discoveries into practical open-source tools. The flagship projects include AlgebraicJulia (a computational category theory framework built in Julia, centered on the Catlab.jl library) and CatColab (a collaborative environment for formal, interoperable, conceptual modeling). The third pillar is societal engagement, working directly with communities on pressing challenges including emerging technology risks, public health, and climate change. The fourth pillar is institution building, experimenting with a new model that vertically integrates research, technology development, and public service.

Topos has significant connections to AI safety work. Researchers Sophie Libkind, David Jaz Myers, and Owen Lynch secured funding from the UK's Advanced Research and Invention Agency (ARIA) through its Safeguarded AI programme (backed by 59 million pounds) for their proposal on double categorical systems theory for safeguarded AI. This funding prompted the establishment of Topos UK in Oxford. The work aims to develop mathematical frameworks for modeling, specification, and verification of autonomous AI systems, making them more explainable and auditable. Sophie Libkind is also a MATS (ML Alignment Theory Scholars) mentor.

The institute has also hosted the Finding the Right Abstractions workshop bringing together applied category theory and AI safety researchers, and partnered with the Government of Singapore to host the inaugural Singapore Conference on AI for the Global Good (SCAI) in December 2023.

The team includes approximately 19 employees (as of FY2024), with Brendan Fong serving as CEO, David Spivak as Senior Scientist and Secretary, and Evan Patterson as Principal Research Scientist. The governing body is chaired by Ilyas Khan (founder of Quantinuum) and Wesley Phoa. Senior advisors include John Baez, Eugenia Cheng, Dana Scott, and Edward Kmett.

Funding has come from diverse sources including the Survival and Flourishing Fund, Jaan Tallinn, Jed McCaleb, the Stanhill Foundation, Centre for Effective Altruism, AFOSR, DARPA, NSF, Mozilla, Chevron, ARIA, Atlas Computing, FQXi, Quantinuum, and the Silicon Valley Community Foundation. The institute returned a $30,000 FTX Foundation grant in full following the FTX collapse in November 2022. The organization has a 97% score and Four-Star rating on Charity Navigator.