The joy of abstract mathematical thinking - with Eugenia Cheng

Category theory is an abstract branch of mathematics – but did you know it can be both fun, and extremely useful for everyday life?

Watch this clear and engaging talk on category theory, as Eugenia sheds light on how her speciality can be applied to many different areas of life, including inequalities, current events, and day to day living.

This talk was recorded at the Ri on 5 April 2023.

00:00 Introduction
06:54 What is category theory?
18:30 What is abstraction?
25:41 Why is context important in mathematics?
33:04 Relationships between things
41:21 Categories – history and definition
50:08 Conclusion

Dr Eugenia Cheng is a mathematician, educator, author, public speaker, columnist, concert pianist and artist. She is Scientist In Residence at the School of the Art Institute of Chicago. She won tenure in Pure Mathematics at the University of Sheffield, UK and is now Honorary Visiting Fellow at City, University of London. She has previously taught at the Universities of Cambridge, Chicago and Nice and holds a PhD in pure mathematics from the University of Cambridge. Alongside her research in Category Theory and undergraduate teaching her aim is to rid the world of “math phobia”.

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[itamarperez]

Erik Meijer's talk on using computer programming as an abstraction layer for mathematics was enlightening, showing how it can turn abstract mathematical concepts into interactive lessons for children. This method not only cultivates a deeper understanding of mathematics but also sparks interest and motivation in learning the subject.

[vdicarlo]

I love hearing someone competent coherently express ideas that have been stewing less coherently in my own mind for years. I disliked math until someone taught me elementary algebra somewhat as the speaker suggests, and when I learned more about the general idea of a function, lots of other things started making sense. I learned a bit about what a number is from Strang's lecture proving that e is a number. Linear algebra helped with all kinds of things, including the concepts of distance, metrics, norms, the triangle rule, and inductive proofs. When I started realizing that students learn better when you start introducing some of these concepts at an earlier stage in their education, I began teaching my 9th grade class in ancient history about the nature of abstraction, using the examples they were learning in their class in geometry, as well as things like logic gates, art, and scientific simulations. I am sure some of it was not absorbed by all of them, but they all got some of it, and some got a lot. I wish my teachers had known what the speaker knows and taught the way she teaches. Brava!

[italiandarthvader]

This is by far one of the most useful talks I've watched.

[GGoAwayy]

She is a very compelling speaker. I think this is the second or third talk by her and every time its educational and enjoyable

[SaveTheManuals]

Found this talk to be informative, enlightening, witty and engaging. Thank you from Wisconsin, USA.

[StevenJiaWeiXU]

Thanks for making mathematics live, Dr. Cheng!

[tatithe]

Wow! This talk was just AMAZING! I am studying math in grad school right now and I can't even describe how she opened my eyes to so many possibilities. I might change fields lol Thank you so much Dr. Cheng!

[mikewilson]

Dr. Eugenia Cheng is such an impressive communicator of what is a difficult subject that she actually makes it intuitive. Complexity is difficult to understand, such as biology that can be difficult to explain. When we consider biological systems the function of a cell is often regarded as the starting point to understand complexity of biology, as opposed to the relations of the cell to other biological components that make up the whole organism. For example, most of us are wired to consider the function of the immune system as a discrete binary activity that identifies what is ok and what is a pathogen and therefore "bad" - but what if as philosopher Thomas Pradue suggests, we consider the relations that the immune system has with other things like the microbiome, and its role in immunology - are the relations more important or the functions? The ability to abstract the relations to unravel the complexity associated with immunology and other complex systems is unbounded. Abstraction as philosopher William James promoted is an approach to progress science as long as we are aware that we are abstracting. Very thought provoking presentation - thankyou Eugenia.

[segamai]

The way she talks is mesmerizing, I could listen to another three hours of this

[notsoaverage_d]

Love the info. this channel brings all the time!

[bp]

Sometimes I believe learning has more to do with a personal connection with the teacher. I have failed a few courses in my time. The material just didn't make sense to me when I was learning it. Somehow I would do much better in the same course after retrying it with a new teacher. Teachers come with their own problems and personalities, too. Perhaps I was simply a bad student. I won't rule out that possibility.

[Ramkumar-ujfo]

Purchased your book Joy of Abstraction. Looking forward

[danielloh]

‘There is only truth relative to context ..’ .. Fantastic! 👍

[stjepannikolic]

I sometimes wonder whether having mathematical abstract thinking skills is a curse in today's world.. Thanks for the great lecture.

[RuthMcDougal]

This is why I have always loved math but I didn’t like math in school. I have been engaging in these things without a name for them all my life. This is my first intro with Eugenia and she seems amazing.

[Kimberly-bkvx]

Loved this lecture so much! More like this please ♥️

[joelkronqvist]

This video was very illuminating to me. Thank you, Eugenia Cheng and the Royal Institute!

[Ramkumar-ujfo]

Many people see Eugenia Cheng's *The Joy of Abstraction* as a pure math book, with its letters also representing mathematical concepts.

ChatGPT ❤🎉

[iloveaviation-burgerclub-a]

Well, trigonometry helps a lot in daily life. Most of the time intuitive. Math to me it the lenguage of nature and the only lenguage where a monologue makes sense.

[jasondiasauthorpage]

Yes. I've been saying for years, as an educator but not as a mathematician, that we teach mathematics not because it applies to daily life, but because it doesn't. The ability to step out of concrete reality into abstract reasoning is a uniquely human skill. While someone might not use the formulae they learned in secondary school, they can use the skill of thinking logically, constructing proofs, rejecting false answers and so on.

Thanks for this much more sophisticated take from an actual mathematician's perspective.