The Joy of Abstraction Quotes

“I have confirmed from my many years of teaching abstract mathematics to art students that I am not the only one who prefers to use abstract ideas to illuminate concrete examples rather than the other way round. Many of these art students consider that they’re bad at math because they were bad at memorizing times tables, because they’re bad at mental arithmetic, and they can’t solve equations. But this doesn’t mean they’re bad at math—it just means they’re not very good at times tables, mental arithmetic and equations, an absolutely tiny part of mathematics that hardly counts as abstract at all. It turns out that they do not struggle nearly as much when we get to abstract things such as higher dimensional spaces, subtle notions of equivalence, and category theory structures. Their blockage on mental arithmetic becomes irrelevant.”
― Eugenia Cheng, The Joy of Abstraction: An Exploration of Math, Category Theory, and Life

“A typical math education is a series of increasingly tall hurdles. If these were really hurdles it would make sense not to try higher ones if you’re unable to clear the lower ones. However, math is really more like an interconnected web of ideas;… everything is connected to everything else, and thus there are many possible routes around this web depending on what sort of brain you have. Some people do need to build up gradually through concrete examples towards abstract ideas. But not everyone is like that. For some people, the concrete examples don’t make sense until they’ve grasped the abstract ideas or, worse, the concrete examples are so offputting that they will give up if presented with those first.”
― Eugenia Cheng, The Joy of Abstraction: An Exploration of Math, Category Theory, and Life

“My wonderful PhD supervisor, Martin Hyland... instilled in me the idea of starting sentences with ‘there is a sense in which…’ because math isn’t about right and wrong, it’s not about absolute truth; it’s about different contexts in which different things can be true, and about different senses in which different things can be valid. Abstraction in mathematics is about making precise which sense we mean, so that instead of having divisive arguments... we can investigate more effectively what is causing certain outcomes to arise.”
― Eugenia Cheng, The Joy of Abstraction: An Exploration of Math, Category Theory, and Life

“It is standard in math books to exhort the reader to work through exercises, but I believe this is offputting to many non-mathematicians, as well a some mathematicians (including me).”
― Eugenia Cheng, The Joy of Abstraction: An Exploration of Math, Category Theory, and Life

“In math some authors call this ‘mathematical tourism’ with undertones of disdain. But I think tourism is fine—it would be a shame if the only options for traveling were to move somewhere to live there or else stay at home.”
― Eugenia Cheng, The Joy of Abstraction: An Exploration of Math, Category Theory, and Life