Uploaded August 2026 | Updated September 2026, 2 weeks ago
A version of this video with audio description track is available here:
youtube.com/watch?v=OiH40eAXKwg
Topology offers a way to organize complex data by looking for shape, structure, and relationships. Yusu Wang, Ph.D., UC San Diego, and Gunnar E. Carlsson, Ph.D., Stanford University, discuss how ideas from algebraic topology move from pure mathematics into data science, machine learning, and AI. Carlsson explains why topological data analysis helps identify meaningful groups in large data sets, how examples and accessible tools can make abstract math useful, and why interpretability matters as AI systems grow more complex. The conversation connects collaboration across fields, customer-focused entrepreneurship, and the need to train mathematicians and AI researchers to help formulate real-world problems. Their exchange shows how mathematical thinking can make powerful technologies more understandable, usable, and accountable. [8/2026] [Show ID: 41487]
0:00 Meet Gunnar E. Carlsson
2:13 How Pure Mathematics Becomes Useful
4:08 How Examples Make Topology Practical
7:57 How Mathematicians Choose Real-World Problems
13:40 What the Shape of Data Reveals
19:18 How Topology Can Help Explain AI
25:02 What Future AI Researchers Need to Learn
27:04 Lessons from Startups, Industry, and Fast Ideas
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uctv.tv/donate
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Science and technology continue to change our lives. University of California scientists are tackling the important questions like climate change, evolution, oceanography, neuroscience and the potential of stem cells.
UCTV is the broadcast and online media platform of the University of California, featuring programming from its ten campuses, three national labs and affiliated research institutions. UCTV explores a broad spectrum of subjects for a general audience, including science, health and medicine, public affairs, humanities, arts and music, business, education, and agriculture. Launched in January 2000, UCTV embraces the core missions of the University of California -- teaching, research, and public service – by providing quality, in-depth television far beyond the campus borders to inquisitive viewers around the world.
(https://www.uctv.tv)
FAQ
Q: What is topological data analysis?
A: Topological data analysis applies topology, the mathematical study of shape, to data. Carlsson describes it as a way to organize complex data, identify meaningful groups, and understand how those groups are similar or different.
Q: How can topology help AI?
A: Topological methods can help examine large-scale patterns inside neural networks, including relationships between features in different layers. Carlsson says this kind of structure matters because AI systems need understanding and guidance, not just more compute and data.
Q: What does Carlsson say researchers should learn from startups?
A: A useful tool does not succeed just because the math is strong. Researchers need to understand potential users, study what people are willing to do, and think through the business case before building a startup.
A version of this video with audio description track is available here:
youtube.com/watch?v=OiH40eAXKwg
Topology offers a way to organize complex data by looking for shape, structure, and relationships. Yusu Wang, Ph.D., UC San Diego, and Gunnar E. Carlsson, Ph.D., Stanford University, discuss how ideas from algebraic topology move from pure mathematics into data science, machine learning, and AI. Carlsson explains why topological data analysis helps identify meaningful groups in large data sets, how examples and accessible tools can make abstract math useful, and why interpretability matters as AI systems grow more complex. The conversation connects collaboration across fields, customer-focused entrepreneurship, and the need to train mathematicians and AI researchers to help formulate real-world problems. Their exchange shows how mathematical thinking can make powerful technologies more understandable, usable, and accountable. [8/2026] [Show ID: 41487]
0:00 Meet Gunnar E. Carlsson
2:13 How Pure Mathematics Becomes Useful
4:08 How Examples Make Topology Practical
7:57 How Mathematicians Choose Real-World Problems
13:40 What the Shape of Data Reveals
19:18 How Topology Can Help Explain AI
25:02 What Future AI Researchers Need to Learn
27:04 Lessons from Startups, Industry, and Fast Ideas
Donate to UCTV to support informative & inspiring programming:
uctv.tv/donate
More videos from: Science Like Me +
(uctv.tv/data-science/science-like-me-plus)
More from: Data Science Channel
(uctv.tv/data-science)
Explore More Science & Technology on UCTV
(uctv.tv/science)
Science and technology continue to change our lives. University of California scientists are tackling the important questions like climate change, evolution, oceanography, neuroscience and the potential of stem cells.
UCTV is the broadcast and online media platform of the University of California, featuring programming from its ten campuses, three national labs and affiliated research institutions. UCTV explores a broad spectrum of subjects for a general audience, including science, health and medicine, public affairs, humanities, arts and music, business, education, and agriculture. Launched in January 2000, UCTV embraces the core missions of the University of California -- teaching, research, and public service – by providing quality, in-depth television far beyond the campus borders to inquisitive viewers around the world.
(https://www.uctv.tv)
FAQ
Q: What is topological data analysis?
A: Topological data analysis applies topology, the mathematical study of shape, to data. Carlsson describes it as a way to organize complex data, identify meaningful groups, and understand how those groups are similar or different.
Q: How can topology help AI?
A: Topological methods can help examine large-scale patterns inside neural networks, including relationships between features in different layers. Carlsson says this kind of structure matters because AI systems need understanding and guidance, not just more compute and data.
Q: What does Carlsson say researchers should learn from startups?
A: A useful tool does not succeed just because the math is strong. Researchers need to understand potential users, study what people are willing to do, and think through the business case before building a startup.
