Here is a collection of some quotes which express ideas that I found either insightful or at least entertaining.
Chuck Close’s advice (replace art with research where applicable). Sometimes difficult to follow, but the method is almost always surprisingly effective.
Inspiration is for amateurs — the rest of us just show up and get to work. And the belief that things will grow out of the activity itself and that you will — through work — bump into other possibilities and kick open other doors that you would never have dreamt of if you were just sitting around looking for a great “art idea.” And the belief that process, in a sense, is liberating and that you don’t have to reinvent the wheel every day. Today, you know what you’ll do, you could be doing what you were doing yesterday, and tomorrow you are gonna do what you did today, and at least for a certain period of time you can just work. If you hang in there, you will get somewhere.
Paul Dirac on what is important.
When you ask what are electrons and protons I ought to answer that this question is not a profitable one to ask and does not really have a meaning. The important thing about electrons and protons is not what they are but how they behave, how they move. I can describe the situation by comparing it to the game of chess. In chess, we have various chessmen, kings, knights, pawns and so on. If you ask what chessman is, the answer would be that it is a piece of wood, or a piece of ivory, or perhaps just a sign written on paper, or anything whatever. It does not matter. Each chessman has a characteristic way of moving and this is all that matters about it. The whole game os chess follows from this way of moving the various chessmen.
Friedrich Nietzsche on science.
On the whole, scientific methods are at least as important as any other result of research: for it is upon the insight into method that the scientific spirit depends: and if these methods were lost, then all the results of science could not prevent a renewed triumph of superstition and nonsense. Clever people may learn as much as they wish of the results of science - still one will always notice in their conversation, and especially in their hypotheses, that they lack the scientific spirit; they do not have that instinctive mistrust of the aberrations of thought which through long training are deeply rooted in the soul of every scientific person.
Terry Gannon on benefits and downsides of category theory (from Moonshine Beyond the Monster).
Category theory is intended as a universal language of mathematics, so all concepts should be translated into it. Much as beavers, who as a species hate the sound of running water, plaster a creek with mud and sticks until alas that cursed tinkle stops, so do category theorists devise elaborate and obscure definitions in an attempt to capture a concept that to most of us seemed perfectly clear before they got to it. But at least sometimes this works admirably – for instance no one can be immune to the charm of treating knot invariants with braided monoidal categories.
This generality of course comes with a price: it can wash away all of the endearing special features of a favourite theory or structure. There certainly are contexts where, for example, all human beings should be considered equal, but there are other contexts where the given human is none other than your mother and must be treated as such.
Julian Havel on “elementary” and “simple” (from Gamma: Exploring Euler’s Constant).
Mathematics makes a nice distinction between the usually synonymous terms “elementary” and “simple”, with “elementary” taken to mean that not very much mathematical knowledge is needed to read the work and “simple” to mean that not very much mathematical ability is needed to understand it. In these terms we think the content is often elementary but in places not so very simple. The reader should expect to make use of pen and paper in many places; mathematics is not a spectator sport!
Incidentally, this is one reason why I haven’t gotten a Twitter account: while it has many worthwhile uses, it’s also a medium that might as well have been designed for mobs, for ganging up, for status-seeking among allies stripped of rational arguments. It’s like the world’s biggest high school.
Paul Dirac being Paul Dirac.
In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite!
Boromir (paraphrasing Euclid (probably™)).
One does not simply walk into Mordor.
There is no royal road to geometry.