Saunders Mac Lane quotes

... the notions category and functor were not formulated or put in print until the idea of a natural transformation was also at hand.
-- Saunders Mac Lane

#Math #Hands #Ideas

The standard "foundation" for mathematics starts with sets and their elements. It is possible to start differently, by axiomatising not elements of sets but functions between sets. This can be done by using the language of categories and universal constructions.
-- Saunders Mac Lane

#Foundation #Elements #Done

. . . in one sense a foundation is a security blanket: If you meticulously follow the rules laid down, no paradoxes or contradictions will arise. In reality there is now no guarantee of this sort of security . . .
-- Saunders Mac Lane

#Reality #Guarantees #Foundation

. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.
-- Saunders Mac Lane

#Philosophy #Often Is #Goal

But Piglet is so small that he slips into a pocket, where it is very comfortable to feel him when you are not quite sure whether twice seven is twelve or twenty-two.

The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.

The point about zero is that we do not need to use it in the operation of daily life. No one goes out to buy zero fish.

Get up now and go and find Robert Kilroy-Silk. Smile in a warm, friendly sort of way, then punch him on the nose. Now go and find Robert on television, despite my best endeavours, this is still relatively easy to do. Wait for a close-up, same smile, and punch him on the nose. If you followed the instructions carefully, you will have noticed a distinct difference. On the one hand, you were suffused with a sense of public-spirited righteousness; on the other, you're probably dribbling blood. That's the difference between reality in life and reality on television.

He would not stay for me, and who can wonder? He would not stay for me to stand and gaze. I shook his hand, and tore my heart in sunder, And went with half my life about my ways.

I've had my run in with trouble. Fortunately, you know, one slap on the hand is usually the last time for me... I learned my lesson.

O marriage! marriage! what a curse is thine, Where hands alone consent and hearts abhor.

The Empress has been connected with the ideas of universal fecundity and in a general sense with activity.

I tried the paleo diet, which is the caveman diet - lots of meat. And I tried the calorie restriction diet: The idea is that if you eat very, very little - if you're on the verge of starvation, you will live a very long time, whether or not you want to, of course.

Writing essays and teaching composition have helped me immensely in writing poetry, because they've forced me to focus on the structure of ideas.