How to Think Like a Mathematician - with Eugenia Cheng

How does pure mathematics apply to our daily lives?

For thousands of years, mathematicians have used the timeless art of logic to see the world more clearly. Today, truth is buried under soundbites and spin, and seeing clearly is more important than ever. In this talk, Eugenia Cheng will show how anyone can think like a mathematician to understand what people are really telling us – and how we can argue back. Taking a careful scalpel to fake news, politics, privilege, sexism and dozens of other real-world situations, she will teach us how to find clarity without losing nuance.

Eugenia Cheng 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, where she is now Honorary Fellow. 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”. Her first popular math book, How to Bake Pi, was published by Basic Books in 2015 to widespread acclaim including from the New York Times, National Geographic, Scientific American, and she was interviewed around the world including on the BBC, NPR and The Late Show with Stephen Colbert. Her second book, Beyond Infinity, was shortlisted for the Royal Society Science Book Prize.

This talk and Q&A was filmed in the Ri on 2 July 2018.

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[rah]

So I hope nobody missed the part where she said category theory is much about looking at a subject from the perspective of its relationship with other subjects or how it fits together with other subjects in order to gain a deeper understanding of it. The METHOD of applying mathematics to (insert any subject other than sociopolitics here) is all she trying to illustrate. If you couldn't use the method she illuminates to abstract that much out of the talk then it went right over your head.

[mmorizes]

To everyone complaining about the wokeness: she used those examples to explain the interconnectedness/relatedness, you could just as easily use other "non-woke" examples if you disagree with the assumptions she made. The whole point was about the power of generality and abstraction, not that you should be woke because math tells you to.

It's ironic, because the point is to analogize your thinking, which includes replacing the examples she gave that you may not have liked with examples you more agree with.

Or you could just dismiss the mode of thinking that invented the internet, computers, and now AI. I would be weary of wandering to close to the "stupid" quadrant, though.

[dong]

I like to think that throughout the lecture, she was subtly showing us that mathematicians stick to facts when working on problems. She used several facts that many people would find uncomfortable to use, such as the privilege hierarchy. She was sticking to facts over feelings and opinions (unless she explicitly mentions that what she said was her opinion), and not caring if people will get offended, cuz I think she knows people will get offended, but proceeds to state facts, which I feel like is key to think like a mathematician.

[Linguages]

Time Code
3:34 Pure mathematics is a framework for agreeing on things
4:35 Science hierarchy pure math > applied math > science...
5:56 Plan 1. Analogies 2. Interconnectedness 3. Relationships 4. Pivots 5. Intelligence
6:18 1. Analogies
13:18 2. Interconnectedness
26:54 3. Relationships
35:27 4. Pivots
40:51 5. Intelligence

[mongoharry]

The speaker points out that because they set up their problems carefully and use logic to reach their conclusions, mathematicians generally find it easy to reach consensus. I'd encourage anyone who feels that this video has gone too far in the support of any political agenda to use the same method and demonstrate its error.

[joeroganjosh]

Awful. Was this supposed to be about mathematics?

[rereadable]

This talk is, at its core, about communicating more effectively with each other. Regardless of whether or not you believe this talk is about mathematics, and regardless of your political or personal opinions and beliefs, the speaker is focused on how identifying and categorizing the world can help simplify extremely complicated situations such that the average person can understand them, with particular focus on being able to understand people on the opposing sides of binary arguments to facilitate productive conversations and solve the problems causing said arguments.


With that in mind, I suggest anyone outright dismissing or condemning the opinions of anyone else (including the speaker) in the comments might do well by themselves, and the people with whom they are arguing, to revisit the talk. You don't need to agree, bur that doesn't mean you shouldn't be respectful (if not considerate) and listen.

[MrOlgrumpy]

Spoons make us fat because they make food easier to eat, scooping the last of the ice cream, gravy etc from the bowl.

[marietaylor]

I was going to view this video for a minute or two but ended up listening to its entirety. This has opened me up to a much more in-depth way of processing information. Thank you Ms. Cheng.

[tellingfoxtales]

This woman is an excellent speaker. I don't necessarily agree with everything she says, and I also think she prioritises some things over others that I would not, but I found her talk very insightful.

[matthewwalsh]

To people calling her a racist: you and I probably agree on a fair number of political issues. I disagree with some assumptions she made in this talk. But if you watch this video and your only takeaway is that she is a racist, I think you you might have missed the forrest for the trees here...

[henrykkaufman]

Finally I see a lecture where someone makes a case that mathematics is about learning how to think. For someone with abstract enough cognition it's obvious and even sometimes frustrating, seeing everybody arguing instead of thinking, getting carried away with emotion and misinterpreting or cherry picking data that fits someone's worldview.
If your worldview consists of large, general ideas that you don't have a definition of then you don't know where you are. And those large, general ideas make you stay ignorant and feel safe at the same time.

[vicsummers]

What is your framework for falsifying white privilege?

[psyboyo]

Can we talk about math, and not politics?
"No."

[raspberries]

She lost me at "Broccoli is delicious..."

[anaidceniceroscruz]

I was panicking with my homework... I just needed to remember why I choose this career.

[yayo]

The point was you can apply maths to understand different viewpoints in politics. Therefore thinking like a mathematician.

[magnets]

@38:28 "we all feel everyday sexism all the time" - really?

[xani]

Dear RI, please, less of that, more of actual science

[daleputnam]

She gets political because that is an area of society that seriously needs more logic instead of emotional argument and opinion entitlement...I am skeptical about the optimism claim though.