How to Bake Pi
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Highlights
- Itâs a bit of a chicken-and-egg question, but I am going to argue that math is defined by the techniques it uses to study things, and that the things it studies are determined by those techniques. (Location 206)
- In math the technique we use is logic. We only want to use sheer logical reasoning. Not experiments, not physical evidence, not blind faith or hope or democracy or violence. Just logic. So what are the things we study? We study anything that obeys the rules of logic. (Location 214)
- Mathematics is the study of anything that obeys the rules of logic, using the rules of logic. (Location 216)
- Abstraction can appear to take you further and further away from reality, but really youâre getting closer and closer to the heart of the matter. To get to the heart, you have to strip away clothes and skin and flesh and bone. (Location 404)
- Road Signs Abstraction as the Study of Ideal Versions of Things (Location 406)
- Well, as I say to my students, feeling stupid for not having understood something before just shows that you are now cleverer than you were then. (Location 525)
- The amazing thing about the world of math is that mathematical things exist as soon as you imagine them. The more vivid your imagination, the more math you have access to. (Location 676)
- The point is that if you understand the principle behind a process rather than just memorizing the process, you will be much more in control of the situation, better able to fix it when it goes wrong, in a better position to modify the process for different purposes, and better able to cope in extreme situations such as missing ingredients, broken equipment, drunkenness… (Location 768)