Women Academics From England

"How to Bake 𝜋 is a success at explaining what mathematics is and how it is done, using simple, appealing language. It should be a rewarding read for mathematicians and nonmathematicians alike. ...[T]eachers will find plenty to borrow for... classrooms... Cheng frequently strips away technical details in order to show the big picture... [T]he book’s frequent digressions... topology, Arrow’s theorem, fair-division problems, s, the Poincaré Conjecture, the Riemann Hypothesis... [etc.]"

"I'm not interested in playing sport... because I hate the idea of losing, and I'm not interested in winning, so there's no upside and there's only potential downside..."

"If you hate the idea of being... told you're wrong, then you get put off math at a very early age because it's the one subject where you start being told you're wrong a lot, and... if you don't like that... you'll move off into some subject where... you can create things..."

"We can go through life, and this is why people do believe they can go through life without needing to know any maths... [S]o when... we go "Math is really important!" They can just go, "Well, I don't... do any of those things, and I'm just fine." ...Yeah, you can be just fine, but wouldn't you like to be better?"

"… By relating personal stories, historical examples and mathematical analogies, Cheng explains how, when we rely on simplistic concepts like female and male, and the crusty logic that accompanies those concepts, we cannot have good conversations. As Cheng puts it: “If we object to the idea that ‘men are better,’ it’s not that helpful to declare instead that ‘women are better.’ It pits men and women against each other and sets up a prescriptive framework rather than a descriptive one.” She motivates us to strip away consistent triggers for dumb fights that lead nowhere. What would she have us strip away? This is where Cheng becomes a logician. She wants to carefully think through our associations with the word “success” as they relate to gender."

"As a category theorist, Cheng researches relationships. She uses this focus on relationships to address the problem of the divisiveness of arguments around gender equality. She abstracts the ideas and reframes the discussion based on relevant character traits that she demonstrates do not have to be linked to gender. She looks for assumptions that have been made, seeks to discard them, and discovers fundamental relationships. In order to better articulate these relationships, she invents new terminology as a way of preventing futile divisive arguments. These new terms are ingressive and congressive. She defines ingressive behavior as “going into things” where the focus is on the self and is more competitive, individualistic, and adversarial. She defines congressive behavior as “bringing things together” where the focus is on community and is more collaborative, interdependent, and cooperative. She gives many examples to illuminate her definitions. ... Cheng is deeply interested in making mathematics accessible to everyone."

"[T]his is from the second Book and you can almost hear his excitement at being able to write in all these keys, that he was unable to... [do] before... [S]ometimes I think when he gets to the keys... the most far away from ones he could previously write in, things become almost simpler, because he's just enjoying the sheer joy of being in f-sharp major for the first time in his life..."

"All our dreams can come true as long as we have the right dreams... [A]s long as we think logically, this is the world where everything behaves correctly, and... where any toy we want, we can play with, as soon as we've dreamed it up."

"So this piece... is written in , like many pieces of Bach are. So the four lines... are independent lines of music that went their way... by themselves... [E]ach... could be sung by a person."

"The trouble with this is that nothing behaves logically."

"I wrote this book because I love maths, and I love food... [S]adly most people love food more than they love maths..."

"Mathematics... helps... construct and understand arguments... too difficult for ordinary intuition. ...It is a way of eliminating ambiguity... It cuts corners, answering many questions... by showing... they're all... the same question... by abstraction: throwing out things that cause ambiguity, and ignoring [irrelevant] details... until all you have to do is apply unambiguous logical thought..."

"[I]n order to study anything logically, we have to ignore all the pesky details that prevent it from behaving logically, and... move into the idealized world... rather than the real world of things... [T]his... is what... abstraction... is..."

"When I drew this picture it enabled me to understand the piece better, but moreover, it helped me understand why I didn't understand the piece, because the voices got wound... between each other in a way that was difficult to follow until I drew this diagram... [I]t enabled me to follow the lines of music as I was playing... which... enables me to play it better. ...This is the point of understanding the s inside things."

"Maths... as it's taught in school is often... boring, pointless, painful, beside the point, and doesn't show people the things that... are the most beautiful about abstract math, and what the point of it is..."

"The point is to help us. It's not there to cause people pain. The point of abstraction is to clear out the fluff in order... to see more clearly what's actually going on."

"What if the pieces of string aren't really... string, but they're s? ...[M]aybe ...early diagnosis of Alzheimer's may come from looking at... the tangledness of brain cells that mutate... So an abstract way of telling whether it's tangled is... useful."

"Math, unfortunately is presented in this very ingressive way, despite the fact that when you get to the research level, it's very congressive."

"... I wish we could educate people not just to be able to do things and know things, but to be nicer humans — and to get their self-esteem not from being better at something than someone else — but from how much they are able to help someone else do something."

"We will never be able to encompass everything by rationality alone... [T]his is a necessary and beautiful aspect of human existence."

"I believe very strongly in helping other people understand things. There's no point knowing things if you don't help other people know..."

"So instead, I like to show people, rather by analogy, why abstraction is useful... [A]bstraction is a process of analogy because... it's going to ignore certain parts of this... and... [that] situation, and... miraculously the two situations become the same, and then I can study them both at the same time, which saves me time, which is good because I'm... lazy."

"Abstraction is about digging deep into a situation to find out what is at its core making it tick. Another way to think of it is about stripping away irrelevant details, or rather, stripping away details that are irrelevant to what we're thinking about now. These details might well be relevant to something else, but we decide we don't need to think about them for the time being. Crucially, it's a careful and controlled forgetting of details, not a slapdash ignoring of details out of laziness or a desire to skew an argument in a certain direction."

"[W]e can try and apply logic to other areas of life... [I]t's very frustrating if we try... with the expectation that that works. ...[I]t doesn't mean we shouldn't try ...[I]t's always good to try and understand everything else according to logic, but... this is the fate of many mathematicians who... get... frustrated with the actual world, because nothing behaves the way we want... Whereas in the beautiful mathematical world everything does behave..."

"Infinity is a Loch Ness monster, capturing the imagination with its awe-inspiring size but elusive nature. Infinity is a dream, a vast fantasy world of endless time and space. Infinity is a dark forest with unexpected creatures, tangled thickets and sudden rays of light breaking through. Infinity is a loop that springs open to reveal an endless spiral."

"I'm going to declare that mathematics is the study of how things work... how logical things work... [I]t's the logical study of how logical things work. ...I don't think it's impossible to define. I think I just did it."

"If we strip away the paint... the windows and the non-structural walls of this building, we'll get to the structural walls... and then this building will look a lot more like a lot of other buildings... I don't know which are the load bearing walls, and I don't need to, but it's a good thing that somebody does... [T]hat's true of all abstract structures."

"[A]bstract theory often comes from wanting to be lazy, or... conserving brain power, conserving energy, because if you do the same thing over and over again, wouldn't you rather not... and just do it once... [T]hat's what abstract theory is there for... [T]hat applies to all sorts of aspects of life, not just sciences and programming"

"If you're only presented with... things you don't care about... then you won't care about having those things made easier, and so if all the problems... given are dumb... problems that don't... have anything to do with real life, then everyone.., especially young people... will immediately see that we're just talking a load of rubbish..."

"[I]f you know where the s are, you can... use things better, you can make things better. You can improve them. You can fix them when they go wrong."

"It... [abstract structure] is a beautiful thing, and sometimes all that matters is that it's a beautiful thing."

"The work I do is totally abstract... [T]he idea is that it will help other people understand things that they can then do in the world..."

"Czerski... frames the ocean as a , the blue machine, driven by the difference in solar heating between the equator and North and South poles, with complications from tidal forces, wind, differences in salinity—which, like temperature, affects density—and shape of continental land masses and undersea crust. They generate complex effects... in a great, layered mass of water that is in constant motion. ...It all adds up to a persuasive case that Earth-dwellers need to understand the ocean and work with it..."

"Keeping everything in balance is one of the functions of the blue machine, but the... gradual raising of world temperatures poses a significant threat... It is only at the very end of her book that Czerski directly addresses the environmental changes... Her concern up to that point has been to set out clearly and calmly the design of the ocean engine. But... her... closing chapter on ‘the future’... is clear... the blue machine is... resilient, but will suffer permanent damage from rising temperatures. ...sea levels; currents... diverted; the fishy inhabitants... disperse and... disappear; tropical storms.. increase in frequency and power; sub-surface areas... de-oxygenated—all... alongside... the ocean as... dumping ground for plastic and... detritus. The oceans absorb carbon... breathe out carbon dioxide... determine global temperatures, but there are limits to their capacity..."

"Helen Czerski's engaging debut book seeks to demystify physics in everyday life... this should be an invaluable primer. ...Dealing with the everyday... enables Czerski to offer a mixture of erudition and enthusiasm... keeping the discussion light, accessible and interesting."

"Ocean scientists... who have read it said they learned lots of things. So there is this assumption that popular science books are for the people who don't know anything, and that is not true because the oceanographers know the oceanography, but they don't know the stories, and I think that the stories are worth it."

"Helen Czerski has the coolest job in science—she's a bubble scientist. Or... full title... a physicist and oceanographer at University College London. When she's not doing that... a science presenter for the BBC. ...[S]he also plays badminton competitively."

"[T]he ocean world is not good at talking about itself... [A] lot of ocean scientists... assume that people should care about the ocean, because they should... [A]ctually it's much more interesting than that. There are much more interesting things to say, but you've.. got to frame it right... [I]t's the framing that we miss in these conversations. ...You ...need a skeleton to hang pieces of information on, and for most people ...you say the ocean, they've got literally nothing... It really is a void. They're just like, "I don't know what to think about that. I don't know where to even start thinking about it, so I... forget everything I hear about it. ...I ...know it's all going wrong somehow ..." ...[T]he opportunity that NOC has is to earn a place in people's perception of what their world is like, by providing some of that context. ...[T]he most powerful thing that NOC has is... the collective."

"But you have to try... [T]hat's the lesson of ocean science... It was never going to be easy. If you go back to Challenger, we're now 150 years on from the Challenger expedition... something like 400 stations around the globe... That's like going around the and checking what color the paint is... on 400 dots along the ceiling... and the Sistine Chapel doesn't change every season... and people did try, and there are fundamental principles behind it all, and so it's worth it to try."

"Scientists always think that the most important thing about what they do is the individual things that they're learning. That's not true. The most important thing... actually the gift that you have as a scientist that you've been given through the training, is a perspective on the world. ...[W]hat NOC has is an amazing opportunity to share a perspective, and not to dumb it down or to sugarcoat it, but just to say, "This is what it is." and to say that really well... [T]hat's... where you really can change people's idea of what it means to live on planet Earth, if you do that well..."

"[I]t's not just about pretty fish. We all like pretty fish, but... it's much more interesting than that, and we are shortchanging people if we don't really show what the ocean is. We all take it for granted as ocean scientists... So it's that opportunity that NOC has to do something really important. That's why I'm on board."

"My [publisher] actually said she was very moved by... the scale of trying to track these tiny bits of that are drifting around in the ocean... [S]he found something about that very... awesome, in the traditional sense of the word "awe"... The enormity of it really caught her."

"[T]he called two or three... great series, '... but when did they actually say "What is the Blue?"... Not ever addressed."

"[T]hey came back with these two photos. One from , which was ', which was the Earth rising over the surface of the moon... before they'd landed on the moon, and the other on , the last of the Apollo missions, where they had the... full disk, the fully illuminated disk... '. ...That was when people started referring to the Earth as a "Blue Planet" because you couldn't look at that and not see that it was blue... [T]hen we spent 50 years not talking about the blue."

"And so this time NASA... the Artemis missions are... very much gearing up to go back to the moon. Different setup, different politics... but fundamentally, this time... for the first time in 50 years, we're going to be far enough away to look back at the Earth and to see... this blue planet. And this time we have to see that blue for what it is. ...[T]he timing of the book... from the point of view... of the arc of human history, this time... we have to understand the blue itself, is the point."

"[E]ven the ocean scientists don't really know all the little stories, the places where it's mattered in history... [S]o I went looking for those."

"I did my degree in physics and... the telling of the history and the philosophy... is built into the telling of the subject, partly because of quantum mechanics, and partly because some of these ideas in physics are so big, you almost can't not discuss the philosophy of it... [T]he... mind blowing moment when Einstein presents general relativity and... unites these things, or these moments where Heisenberg's uncertainty principle is being worked out... [Y]ou've got to go and see why it's called that... [T]hese stories are built into physics, and in ocean science it's not really the same, and it's... not the same across the biology and chemistry and physics of the ocean, because they tend to be taught... separately..."

"So... The Blue Machine is the story of the ocean told through its messengers, passengers and voyages... [I]t's a mixture of natural history... human culture and human history... It's... a textbook dressed up as a bunch of stories."

"Any alien visitor to Earth... would look at the ocean first. Any alien visitor who wants to know the dynamics of planet Earth would look at the ocean before they looked at the land. And yet, we don't see it. ...We don't see this engine that completely defines our planet, and that has to change. ...Now is a good time for that to change."

"[T]he way I started to think about it... sometimes you get those kind of special effects where little pictures start appearing, making a , and then there's a shape left in the middle, and once you've got enough little pictures you can see the shape. But... until you've seen all those little pictures, you can't see anything. ...[T]he ocean's ...like that. The only way to really understand it, and we take this for granted as ocean scientists, is that you have to see it in lots of different ways. It's like the blind man and the elephant... One finds a trunk and thinks it's a snake. One finds a leg and thinks it's a tree. Yet you need all those perspectives, and then you start to build up a picture of what it means for an ocean to be there. ...[I]t ...bugged me that no one had done that and I thought I could find those stories."