I learned about Eugenia Cheng and Is Math Real? in the summertime, a moment where asking questions revealed stories and details based on passions and needy pursuits. I’ve had the book for more than a month and there are so many stunning sentences in this book:
- 30: This leads to the topic of group theory , which makes abstract structures out of symmetries and how they are combined.
- 31: my research field, the field of category theory. This is the subject that focuses on relationships between things, and pushes that idea further and further so that we can study relationships between almost anything. Moreover, we can start to regard things as “relationships,” even if they weren’t originally relationships, in order to study them in a similar way.
- 31: And this is a crucial point: that beacuse math starts with abstraction, we can study more things mathematically if we just think of new ways to perform an abstraction.
- 32: the starting point for math is the mental gymnastics of finding ways to think flexibly about situations, in order to make connections between things that didn’t previously seem related. And having a vivid and creative imagination is very helpful in conjuring those connections into being.
- 33: In math … we remain ever flexible in our thinking: we point out senses in which things are connected, and also senses in which things are different.
- 36: Unfortunately the simple things can seem pointless if nobody explains what we’re trying to practice. Once we’re well practiced, it becomes much easier to see connections in more complicated situations, such as the spread of viruses.
- 38: it only takes thirteen steps to get us past a million.
All this typing while I sit at the pick-up. Ahh, the merits of what I’m practicing this morning as I sit in the sun: patience; and, clicking Post for the latest iteration on this blog.
washing dishes: a father’s glimpses 