Women Academics From England

"I think, on a , what I’d really appreciate are long books: books as day-by-day companions, to combat loneliness and fear. We have some brilliant contemporary authors who write on the big canvas, yet I feel that desert-island panic might be better combated by novels set in the past, preferably by long-dead authors who had never experienced central heating or modern dentistry. Tolstoy’s Anna Karenina, Balzac’s ' and Trollope’s ' (all with vibrant and courageous female protagonists, to spur me on to valour and fortitude) would be among my front runners. Reading contemporary novels would remind me, hour after hour, of the world I’d lost and might never regain. Tolstoy, on the other hand, reveals to me a universe I may never manage to understand in its entirety, so when I get to the end, I can happily start at the beginning again."

"From the late nineteenth century, economics gradually became a more technocratic, tool-based, science, using mathematics and statistics embedded in various kinds of analytical techniques. ... By the late twentieth century, economics had become heavily dependent on a set of reasoning tools that economists now call 's': small mathematical, statistical, graphical, diagrammatic, and even physical objects that can be manipulated in various different ways. Today, in the twenty-first century, if we go to an economics seminar, or read a learned scientific paper in that field, we find that economists write down some equations or maybe draw a diagram, and use those to develop solutions to their theoretical conundrums or to answer questions about the economic world."

"Of importance for the is that , in both his cycle books, had concentrated his energies on the statistical evidence of the economic interactions involved in the business cycle and the of these relationships rather than on the relation between the economic cycle and the exogenous causal factor. Moore's concern with evidence end statistical explanation compared to that of Jevons, and the matching change in contemporaries' responses, are both indicative of the development of the econometric approach by the early years of the twentieth century. Yet, it was some years before Moore's broad econometric approach to the explanation of economic cycles, involving a large number relationships linking different parts of the economy, was taken up by who produced the first macro econometric models in the late 1930s."

"The joint work with from that research group, ' ..., is now seen as creating a new strand. The extant philosophy of science thought about s in relation to theory: models were ways of capturing the essence of a theory. What we were doing in that little research group – and what we did in the volume Models as Mediators – was to say, if you look at the way science is practised, you see that scientists treat models as autonomous objects on which they develop arguments. They manipulate them, argue with them, extend them. Models are not in a simple relationship between theory and the world, rather they are at angles to both, so you can use them to interrogate both sides. Models as Mediators is 20 years old, and you can definitely see now that the project as a whole changed the conversation in the philosophy of science about models. I don’t mean that everybody was convinced by it, but it created a big enough presence so that, even if you didn’t agree with it, you had to take it into account. This work was part of a wider move that has been happening toward ‘the philosophy of science in practice’."

"Eccentricity has not always been encouraged by the prim editors of . Invited to list his recreations, omitted motorbikes and wrote instead: , and tennis. Identifying himself as of provided a greater source of satisfaction."

"In 1928 Edmund Blunden's ' was widely praised for its lyrical, approach. Sassoon's ', also published in 1928, set the scene for the contrast between an idyllic, pre-war world and the savagery of war explored in his ."

"The , constructed from rosy bricks and crowned with curved stone s, stands among the meadows flanking the , in the middle of England, a hundred s to the north of London. Starting life as a modest built in the , it was enlarged twice. An ambitious owner redesigned it in the , to incorporate a large carved staircase and a grand reception room on an upper floor. In the 1820s, the House gained a courtyard, a library and a lake. The estate, easily encompassed by an hour's brisk walk, is surprisingly varied in its landscape, incorporating traces of an and a trading post."

"Arthur Benson, one of the coterie of clever, literary-minded younger men whose company the ageing novelist relished, found himself incapable of sharing the enthusiasm of and for ."

"Usually dismissive of other female writers, Riding had praised Stein in the final chapter of A Survey of Modernist Poetry for using a language of divine ordinariness. It was 's idea that they should invite Miss Stein to publish something with the ."

"Today, the most famous scene from Mary's life and, perhaps, in is the stormy summer night at the on when Byron, his handsome young doctor , the Shelleys and , who was carrying Byron's child, decided to write for fun. This was the night on which Frankenstein, that best known of all Romantic works, was born. Its author was not yet nineteen. Frankenstein has become part of our lives."

"The rusts are highly specialised obligate parasites of s, s and s. The cereal rusts are amon the most destructive pathogens of economic plants ..."

"' is a large genus of which one of the best known species is ', a destructive parasite of , but including also species parasitic on economically valuable trees, such as , and many s."

"The are remarkable for diversity of both form and function. Their ability to break down and to synthesize complex substances largely accounts for their success in colonizing widely different habitats, and has them of the greatest economic importance as parasites, as s in the soil and on varied commercial products, and as the producers of s, organic acids and other substances useful to man."

"1 Hypogeous are those soil fungi which produce macroscopic partially or completely embedded in soil or humus. While showing a superficial similarity correlated with habitat, they include members of the , and . 2 The edible s have been known from very early times, and speculations as to their nature are found in Greek and Roman literature. Other groups, which are not edible, were described later. The monographs of (1831, 1842) and & (1851) are the starting-point for all modern work on these fungi."

"...The national narrative in Britain has been one of liberty, freedom, a freedom loving people, prosperity, peace, no conquests, no violence, no expropriation. A peaceful story from beginning to end. A transformation from barbarism to civilisation, but one that has been done in an extraordinary and English way. Which means recognising trouble when it’s coming and dealing with it before it happens, reforming in time, and therefore the slow march of progress. And that Whig story of English history is still phenomenally powerful."

"For me, the point of doing history has been about how understanding the past might help us to improve people’s lives in the present. You can see that so clearly in relation to women’s rights or in relation to racial inequality."

"I had an excellent conventional grammar school education, where I had a wonderful history teacher. That was very important; it instilled in me from an early age how important teaching was and what a difference it can make."

"It was an incredible learning curve, realising how historians tend to only see what they’re interested in."

"A good cook will never be embarrassed by having too much cold meat on hand, because she will be able by her skill so to vary the dishes that the appetites of those for whom she caters will never tire of it. Even a small piece of the loin of mutton may be served in half-a-dozen different ways, and be relished by those who are tired of the mutton-chop or the plainroast."

"Now the number of dishes used for breakfast is, in the majority of English dishes, very limited. Bacon and eggs are the staple, the former generally unsatisfactory, being over or under cooked, too salt or too new; it is besides expensive, a large portion of it running to fat. New-laid eggs, when they can be procured in town, are very costly, they properly, after twenty-four hours, can only be described as fresh. The mind is not, however, very enlightened on this subject, and the vendors of eggs are persuaded, or at any rate try to persuade the public, that eggs are new-laid until they are "an apology for pepper.'"

"Eggs. Put into a stewpan two s of or milk, two of good gravy, with two ounces of , a little salt and pepper, Break into this six eggs, and when they begin to set throw in the {asparagus prepared thus:—Take two dozen heads of small asparagus, cut the green tops into pieces the size of large peas, throw them into boiling water with plenty of salt, when done, drain them on a sieve. Let them be stirred over the fire with the eggs for half a minute, then pour them on to their dish and garnish them with ."

"... From the earliest days of her married life, Mrs. Heath had found all her pleasure to consist in making her home happy. To be sure, in her young days, change of scene, frequent visiting and parties were not deemed essentials to the health and happiness of the middle-class wife. The bringing up of children was not delegated to ignorant, careless nursemaids, but was the first duty and delight of mothers. Neither in her day were children looked upon as burdens, or a woman pitied because of the cares of her large family. Happiness was then found in these cares, and peace of mind in the performance of the blessed duties of maternity—duties laid upon woman by Providence and nature, and which she may not seek to abrogate without ill consequences to all her race."

"Sausages have from time immemorial found favor as a breakfast dish. But that any one should be able to eat those sold in shops after the revelations respecting them, and the great risk there is of getting diseased meat in so disguised a form, is indeed surprising. There is no difficulty whatever in making sausages at home, a will last a lifetime, and be so useful for a variety of purposes that no family should be without one."

"I cannot claim to find it easy to balance my ambitions in mathematical research with the desire to be a good parent, to be an inspiring teacher, or to effect positive social change in the world, I do feel very fortunate to be able to spend my life tackling these challenges, which are extremely interesting and important to me."

"My parents separated after my father resigned his university position to focus on his inventions, and my mother then finished her education and became a school mathematics teacher. We moved to a very cosmopolitan area of London, which was like a new birth to me; it was there that my interest in mathematics really began."

"I went to Cambridge, which represented a second major change in my life. As I learned more mathematics, I saw that it is an entire world of its own which many people choose to live in, a world in many ways more real than the real world: it feels permanent, eternal, and offers a deep sense of security because nearly everyone who understands it agrees on what is truth. By the time I had finished at Cambridge, I was very involved with mathematics and did not consider other careers."

"I learned mathematics on my own from textbooks, which is perhaps strange given that both my parents were involved in the subject. At the same time, I spent a good deal of time studying art and wanted to follow a career in that direction until I was eventually convinced by my family that I should first work for a mathematics degree to ensure that I could earn a living."

"While I was growing up, the elementary school I attended was extremely ethnically homogeneous. I was unable to escape from heavy issues concerning race, which my mother always explained in a political context."

"My research is in the field of spectral geometry, the study of how the shape of an object affects the modes in which it can resonate. A famous question in the field is, Can one hear the shape of a drum? Spectral geometry bridges different branches of science, including engineering and physics, as well as a number of different fields of mathematics. However, quite different sorts of questions are studied within each discipline. I am a mathematical analyst, which gives me an appreciation for the infinite and the infinitesimal. At the moment, one of the things I am working on understanding is the total wavelength of a surface like a sphere or something of greater complexity, such as the surface of a bagel or a pretzel. What is this total wavelength? If you strike a surface it can resonate at any one of a list of frequencies, and the wavelength of the sound produced by the vibration is inversely proportional to the frequency. In the mathematically idealized model, there are infinitely many possible wavelengths. The total wavelength should be the sum of all of these individual wavelengths except that this infinite sum equals infinity. Fortunately, a finite number can be assigned to it by a slightly elusive process called regularization. (This process is also used in mathematical physics to mysteriously obtain true answers from formulas which do not really make sense!) I first became interested in the total wavelength as a model related to a question which can be roughly stated as, can one hear the shape of the universe? However, the total wavelength shows up in many quite different areas of mathematics and I am finding these connections intriguing."

"I am a mathematical analyst, and most of my research is in the area of spectral geometry. Problems in spectral geometry are also studied by various kinds of geometers, number theorists, applied mathematicians, mathematical physicists, and others. What is Spectral geometry? Spectral geometry most usually means the study of how the geometry of an object is related to the natural frequencies of the object. These are the frequencies at which the object can vibrate. A vibrating object often produces a sound, and the frequencies can be heard as the dominant tone and the overtones of the sound. The well-known question highlighting what spectral geometry is all about is the question "Can one hear the shape of a drum?" I am a mathematical analyst, and most of my research is in the area of spectral geometry. Problems in spectral geometry are also studied by various kinds of geometers, number theorists, applied mathematicians, mathematical physicists, and others. In mathematical terms, the natural frequencies of an object (or rather their squares) are the eigenvalues of a partial differential operator called the Laplacian. This Laplacian takes each function defined on the object and differentiates it twice to give a new function. The eigenvalues of the Laplacian form an infinite sequence of numbers tending to infinity. In spectral geometry we study how these numbers depends on the shape of the object. For people who like to know the full story, I should mention that many spectral geometers (including me) who work on the Laplacian on smooth manifolds study the whole sequence of eigenvalues of the Laplacian. Now the low eigenvalues can give accurate values for the frequencies at which a real-life object vibrates, but the very high eigenvalues do not correspond to genuine physical vibrations of the object because of molecular forces and damping. These effects are not included in the model where the vibration is driven by the Laplacian alone. This means that my research is rather different from that of an engineer who wishes to model precisely the vibrations of a real-life object. In actual fact the questions I work on are more closely related to mathematics arising in quantum physics and string theory. In addition, I don't always study the Laplacian, but also the eigenvalues of other operators, which might represent other physical quantities than the frequencies of vibration. I mostly study spectral geometry for nice smooth objects such as spheres and tori, but some people work on rough objects and even discrete objects like graphs. In the last eight years, I have worked mostly on the spectral zeta function, which is an infinite sum of powers of the eigenvalues. In particular, I have worked on the zeta-regularised determinant, which is used in topology, quantum field theory, and string theory. Recently, I have been very interested in the sum of squares of the wavelength of a surface, which is related to all kinds of different things including vortex theory."

"My mother is British, from a family with a trade union background and a central interest in class struggle; she met my father, who is Nigerian, while both were students of mathematics in London. My father was a very talented mathematician, and after my parents married, he went on to a position in the mathematics department of the University of East Anglia."

"… 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."

"The premise of “Is Math Real?” is that people have different emotions about math. Some love the math and have little difficulty determining the correct answer to a problem while others loathe and dislike the math and have a difficult time ascertaining the correct response. Many times, a student is humbled or chastised for asking ‘a stupid question’. Author Cheng states that there are no stupid questions. In fact, the most profound concepts in mathematics are learned from asking the simplest of questions. As teachers and professors of math, we should welcome all questions and understand that answering questions is what helps students learn. ... “Is Math Real?” treats mathematical topics in a unique and original way. Discussions on number patterns, Platonic solids, math history, ethnomathematics, and mathematical structures presents the reader with a plethora of ideas on how one can envision mathematics."

"I love to focus on how to make mathematical activities more congressive... so when I'm teaching art students I do a lot of activities where there is no right and wrong... [W]e're not trying to achieve an answer, we're trying to explore... [W]e build something. It's more craft-like. ...[M]aybe we're trying to build s, but it doesn't really matter if you didn't... [A]long the way we discover how triangles fit together and... how versatile an equilateral triangle is... and that you can make all sorts of shapes... and some... are Platonic solids... [E]veryone can explore... and... in the world of , this is... "low floor/high ceiling" activities where there's a very low floor to entry and a very high ceiling, so if someone really does want to go far they can, but... there's no real failure, because everyone has done something. ...[I]f we do more of that, then we will stop putting off congressive people from mathematics."

"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.]"

"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."

"I'd like to talk about abstract mathematics and my experience of making it... palatable to people who may have had very bad experiences of it..."

"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'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..."

"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."

"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..."

"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..."

"[T]here are many fields where we use ingressive means to filter people, despite the fact that congressive characteristics would be more useful... and that's the thing that I would like to change."

"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."

"[S]o mathematics comes up with abstract ways of studying these, where... it... looks like pieces of string, but how can I study them as if they were pieces of string without actually waving pieces of string around... [T]here are all sorts of practical situations where it's not practical to wave... string around."

"I've invented some new words... ingressive to replace masculine and congressive to replace feminine... Ingressive is a character trait... a behaviour... about going forward... not being waylaid about what people say... being competitive and winning. Congressive is about bringing things together and... shedding light and understanding... helping people... and maybe we are presenting mathematics at school in a very ingressive way, because it's often about being right... getting the right answer."

"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."

"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."

"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'm not interested in being right... I'm not interested in winning... but I hate losing, and I don't like being wrong. ...But if it's a situation when nobody is going to lose because we're all trying to understand something together, then there's no risk of losing, and... we can all gain from it."