All practical teachers know that education is a patient process of mastery of details, minute by minute, hour by hour, day by day.
Alfred North WhiteheadRead
Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.
Interpretation
Mathematics began when it transitioned from specific instances to general propositions.
Alfred North Whitehead emphasizes the pivotal moment in the history of mathematics when thinkers started to formulate general rules and theories that applied to abstract entities rather than only specific, tangible examples. This shift allowed mathematics to develop as a rigorous science, abstracting concepts to understand broader truths about the universe.
In practice
This quote can be used in a lecture on the philosophy of mathematics to highlight its evolution.
All practical teachers know that education is a patient process of mastery of details, minute by minute, hour by hour, day by day.
The vitality of thought is in adventure. Idea's won't keep. Something must be done about them. When the idea is new, its custodians have fervour, live for it, and, if need be, die for it. Their inheritors receive the idea, perhaps now strong and successful, but without inheriting the fervour; so the idea settles down to a comfortable middle age, turns senile, and dies.
The guiding motto in the life of every natural philosopher should be, seek simplicity and distrust it.
As society is now constituted, a literal adherence to the moral precepts scattered throughout the Gospels would mean sudden death.
I consider Christianity to be one of the great disasters of the human race... It would be impossible to imagine anything more un - Christianlike than theology.
Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. "Necessity is the mother of invention" is a silly proverb. "Necessity is the mother of futile dodges" is much closer to the truth. The basis of growth of modern invention is science, and science is almost wholly the outgrowth of pleasurable intellectual curiosity.
Wherever there is a design that is highly successful in a broad range of similar environments, it is apt to emerge again and again, independently - the phenomenon known in biology as convergent evolution. I call these designs 'good tricks.'
All our science is just a cookery book, with an orthodox theory of cooking that nobody's allowed to question, and a list of recipes that mustn't be added to except by special permission from the head cook.
Perhaps scientists have been the most international of all professions in their outlook... Every time you scientists make a major invention, we politicians have to invent a new institution to cope with it-and almost invariably, these days, it must be an international institution.
A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.
Perception plays a vital role in the diagnosis of bipolar illness. Symptoms are perceived through the categories of psychiatric medicine at a given moment in history, categories which are continually shifting and being named or renamed.
I think that when we know that we actually do live in uncertainty, then we ought to admit it; it is of great value to realize that we do not know the answers to different questions. This attitude of mind - this attitude of uncertainty - is vital to the scientist, and it is this attitude of mind which the student must first acquire.
Subscribe for the occasional hand-picked quote. No noise.