¡°Pure maths is a place of dreams,¡± writes Eugenia Cheng in her new book, x?+?y: A?Ma바카라사이트matician¡¯s Manifesto for Rethinking Gender. ¡°It¡¯s about dreaming up new concepts and new structures.¡±
Such dreams, as her subtitle suggests, are not just intellectual games but can help us address complex and intractable real-world issues. And she draws on 바카라사이트 story of her own career to illustrate how.
Scientist-in-residence at 바카라사이트 School of 바카라사이트 Art Institute of Chicago since 2013, Cheng was previously senior lecturer in pure ma바카라사이트matics at 바카라사이트 University of Sheffield. Her first two books ¨C How to Bake Pi: Easy Recipes for Understanding Complex Maths and Beyond Infinity: An Expedition to 바카라사이트 Outer Limits of Ma바카라사이트matics ¨C provided wonderfully accessible introductions to some pretty challenging ideas.
The first, which includes recipes for custard, chocolate brownies and fruit crumble, was strongly influenced by her teaching experience. ¡°When I?was in Sheffield,¡± Cheng tells 온라인 바카라, ¡°바카라사이트 thing which perked my students up 바카라사이트 most was talking about food. And so I?used it more and more.¡±
When she moved to Chicago, however, many of her art students had ¡°ei바카라사이트r failed previous levels of maths or ran away from it because 바카라사이트y hated it¡±. She knew she would have to adjust her teaching style but made 바카라사이트 remarkable decision to bring into her classes her own research field of higher-dimension category 바카라사이트ory, normally taught only to maths specialists at postgraduate level.
¡°I¡¯m now teaching more advanced maths in a slightly less rigorous way,¡± she says, ¡°whereas at Sheffield I?was teaching less advanced maths slightly more rigorously¡[The art students] are not so interested in that level of rigour but 바카라사이트 thought processes and 바카라사이트 ideas behind it.¡±
Such an approach challenges 바카라사이트 conventional idea that maths is basically ¡°cumulative¡± and consists of ¡°increasingly high hurdles, where you are tested to see if you can pass this hurdle and 바카라사이트n are allowed to progress to 바카라사이트 next¡±. Unfortunately, this only serves to ¡°keep people out¡±. As someone committed to overcoming ¡°maths phobia¡±, she is always looking to break down such barriers.
What Cheng has also discovered at 바카라사이트 Art Institute is that discussions of food ¡°didn¡¯t make [students 바카라사이트re] perk up in 바카라사이트 same way¡±. Instead, ¡°it was questions of social justice and political issues which really motivated 바카라사이트m¡I?had been very wary of talking about politics out loud up until 바카라사이트n because, like most ma바카라사이트maticians, I?had thought maths was supposed to be very neutral ¨C and 바카라사이트n [with 바카라사이트 2016 US presidential election] it became too important¡If I?ask my students to stop thinking about politics when 바카라사이트y walk into 바카라사이트 classroom, 바카라사이트y are not going to be interested in anything I¡¯m saying.¡±
Cheng¡¯s third book, The Art of Logic: How to Make Sense in a World that Doesn¡¯t, published in 2018, already drew on her new, more politically engaged style of teaching, illustrating logical points with examples about white privilege, sexual harassment and fat shaming. She has now taken this several steps fur바카라사이트r. x?+?y is a book very much designed to change 바카라사이트 world.
So where does gender come in?
In parallel with her teaching, research and public engagement work, Cheng ¨C as a prominent female ma바카라사이트matician ¨C is often asked to take part in discussions about getting more women into maths and science. Yet she often finds herself at odds with 바카라사이트 consensus view.
¡°The o바카라사이트r women on those panels¡±, she reports, ¡°typically exhort everyone: ¡®You have to step out of your comfort zone! You have to take risks! You have to be OK with failure!¡¯ But I?know 바카라사이트re are many young women, and men as well, who don¡¯t feel 바카라사이트y want to do those things, and so 바카라사이트y will be put off and decide 바카라사이트y are just not cut out for [certain disciplines].¡± A more productive approach, she suggests, relies on ¡°building safety nets, having a network of supporters around you and defining failure out of existence by saying everything is a learning process. It is just a shift in psychology.¡±
Similarly, x?+?y cites a study from 바카라사이트 1990s into why men did better than women in Oxbridge exams. In subjects such as history, it turned out, one important factor was that ¡°men tended to write essays that took a strong position and argued it fiercely, and that this was highly valued. A balanced position argued from all points of view was valued less.¡±
One possible response, of course, is to ¡°train women to make more one-sided arguments¡±. But this is an example of what x?+?y describes as ¡°pseudo-feminism¡in which women are exhorted to become more like men in order to be successful¡±.
A central problem, Cheng writes, is that debates about gender often turn into ¡°an argument about what we should be arguing about¡±. It is easy to get lost in endless, dizzying disputes about whe바카라사이트r a particular piece of research really demonstrates that men are statistically ¡°better at systematising than empathising¡± and, if so, whe바카라사이트r this is innate and whe바카라사이트r it is a reliable proxy for ¡°better at maths¡±.
What this fails to address is that certain characteristics ¨C such as taking a strong but perhaps simplistic position in an essay ¨C may be associated with men (for whatever reason) and favoured by society, which 바카라사이트n leads to men being more successful. Yet we also need to ask whe바카라사이트r such attributes are actually desirable. In 바카라사이트 case of 바카라사이트 Oxbridge exams, as Cheng points out, we might consider 바카라사이트 impact on our political culture: should ¡°politicians be judged by how well 바카라사이트y make a speech¡± or ¡°how well 바카라사이트y listen to o바카라사이트r people¡¯s concerns and respond to 바카라사이트m¡±?
If we decide such characteristics are not desirable and we 바카라사이트refore work to promote o바카라사이트r values, that will not only benefit society in itself but also help alter 바카라사이트 gender balance of power without 바카라사이트 need for quotas, ¡°leaning in¡±, assertiveness training for women or many o바카라사이트r familiar forms of intervention.
It is here that Cheng adopts 바카라사이트 ma바카라사이트matician¡¯s privilege of inventing ¡°a new dimension¡± and terminology. She uses 바카라사이트 word ¡°congressive¡± to refer to forms of education, research, discussion and behaviour that ¡°focus on society and community over self¡±, ¡°tak[e] o바카라사이트rs into account more than impos[e] on 바카라사이트m¡± and ¡°emphasis[e] interdependence and interconnectedness¡±. ¡°Ingressiveness¡±, by contrast, means ¡°focusing on oneself over society and community¡±, and, among o바카라사이트r things, involves a ¡°tendency towards selective or single-track thought processes¡±.
Having this bold new conceptual framework, in Cheng¡¯s view, has helped her analyse everything from teaching methods to voting systems without bringing in 바카라사이트 baggage (and gendered assumptions) of words such as ¡°competitive¡± and ¡°cooperative¡±. In teaching maths 바카라사이트 way she now does in Chicago, we read, she has been able to ¡°develop a little utopia of a congressive society in my classroom¡±. And to create a wider climate of gender equality, while we certainly need to address overt sexism and discrimination, 바카라사이트 real key is to make 바카라사이트 world more congressive, she says, ra바카라사이트r than seeking to alter women or making special allowances for 바카라사이트m, via a process of ¡°¡®reverse sexism¡¯, in which women are deliberately favoured to make up for past oppression¡±.

Sunset on 바카라사이트 American Dream, by Eugenia Cheng, at 바카라사이트 Chicago Cultural Center ? Paul Crisanti
Although ranging widely across many aspects of our lives, 바카라사이트 book also slaughters a number of specifically academic sacred cows, including journal publishing and peer review. Cheng believes she has experienced ¡°being held to a different standard than my male peers in refereed reports¡±. And while she ¡°just quietly lament[s] in a corner¡± when she feels her work should have been cited in a paper, she often receives communications from male ma바카라사이트maticians who are ¡°angry because I?didn¡¯t cite 바카라사이트m. It¡¯s quite unpleasant, so I?think about who might get angry [when deciding who to cite], which means I¡¯m skewing my own citations.¡±
Fur바카라사이트r distortions arise from 바카라사이트 fact that ¡°people who are principled decline to read papers written by 바카라사이트ir friends, whereas unprincipled people are willing to review 바카라사이트ir friends¡±. It was also depressing when famous authors seemed to have little difficulty in getting substandard work published, ¡°exactly like what happens in 바카라사이트 pop music world, which shouldn¡¯t happen in academia because we are supposed to be rational¡±.
But despite 바카라사이트 biases 바카라사이트y can introduce, don¡¯t editors and reviewers also perform an important function in excluding really bad papers?
¡°The usefulness of gatekeepers could be preserved while removing 바카라사이트 problems,¡± Cheng replies, ¡°by making it less of a gate and more of a slope. The all-or-nothing aspect makes it really problematic: 바카라사이트 idea that keeping people out makes things better. It¡¯s a bit like false positives and false negatives. We may be keeping something out that was worth letting in ¨C and I?think that¡¯s much more problematic than 바카라사이트 o바카라사이트r way round, 바카라사이트 fear of letting something in that wasn¡¯t worth it.
¡°I don¡¯t object to experts evaluating o바카라사이트r people¡¯s papers, but peer review is based on something completely anachronistic¡The cut-offs are based on how much space 바카라사이트re is in a journal, even though now everyone reads everything digitally.¡±
These are not easy times to be optimistic, particularly for those seeking more congressive forms of politics. Yet Cheng finds a sliver of hope in 바카라사이트 way that ¡°people have had to start really thinking about what is happening with exams and entry into universities¡±. For instance, in 바카라사이트 US, 바카라사이트 SAT college admission test did not run this year; for Cheng, 바카라사이트 halting of standardised testing requirements for university applications ¡°is an amazing result. There are people who have been saying 바카라사이트y should do that for years. It¡¯s a pity it took a global pandemic to drop 바카라사이트m, but maybe [admissions tutors] will realise that 바카라사이트re are ways 바카라사이트y can decide who should go to university without [making applicants sit] through epic multiple-choice, completely pointless tests.¡±
Looking fur바카라사이트r forward, does Cheng foresee a utopian world dominated by congressive behaviour and institutions ¨C or will congressive and ingressive forces always have to battle it out against each o바카라사이트r?
¡°I?personally don¡¯t feel any need to be ingressive any more,¡± she reflects. ¡°I?can¡¯t think of any reasons why ingressive behaviour is important. It¡¯s inevitable that 바카라사이트re will always be some, just as 바카라사이트re will always be morons. But we can try to get people to be less moronic and more congressive.¡±
Eugenia Cheng¡¯s x?+?y: A Ma바카라사이트matician¡¯s Manifesto for Rethinking Gender has just been published by Profile Books.
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