All practical teachers know that education is a patient process of mastery of details, minute by minute, hour by hour, day by day.
The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.
Interpretation
What this quote means
The study of mathematics can be frustrating as it often seems beyond our grasp, despite its profound applications in understanding the universe.
Alfred North Whitehead reflects on the challenging nature of mathematics, suggesting that while it is essential for grasping vast concepts such as the weight of stars and the intricacies of molecules, it often leaves learners feeling disappointed and confused. He compares this elusiveness to the ghost of Hamlet's father, indicating that the true essence of mathematics can be difficult to apprehend fully, despite its significant contributions to science.
Themes
In practice
Example use cases
In a lecture on the importance of mathematics, one might quote Whitehead to illustrate the initial struggles students face.
More from Alfred North Whitehead
All quotes βThe 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.
Similar quotes
I have lived much of my life among molecules. They are good company. I tell my students to try to know molecules, so well that when they have some question involving molecules, they can ask themselves, What would I do if I were that molecule? I tell them, Try to feel like a molecule; and if you work hard, who knows? Some day you may get to feel like a big molecule!
When the basic status of a theory is clear, and all that needs to be cleared are details, you can collaborate. But if the main structure of a hypothesis isn't established, and you want to change the paradigm - like it was the case in the 1960s - it's better to work alone.
The image of Stephen Hawking - who has died aged 76 - in his motorised wheelchair, with head contorted slightly to one side and hands crossed over to work the controls, caught the public imagination as a true symbol of the triumph of mind over matter.
When I began in 1960, individuality wasn't an accepted thing to look for; it was about species-specific behaviour. But animal behaviour is not hard science. There's room for intuition.
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People who look for the first time through a microscope say, 'Now I see this, and then I see that,' and even a skilled observer can be fooled. On these observations I have spent more time than many will believe, but I have done them with joy, and I have taken no notice of those who have said, 'Why take so much trouble,' and, 'What good is it?'