After years of finding mathematics easy, I finally reached integral calculus and came up against a barrier. I realized that this was as far as I could go, and to this day I have never successfully gone beyond it in any but the most superficial way.
Interpretation
This quote reflects the struggle and limitations one may face in learning complex subjects like mathematics.
Isaac Asimov shares his experience of encountering a significant challenge in his study of mathematics, specifically integral calculus. Despite previously finding mathematical concepts accessible, he reached a point where he recognized the limits of his understanding, illustrating that even for those who excel in certain areas, there can be hurdles that signify the end of their mastery in a subject.
In practice
In a classroom setting when discussing the challenges of learning new subjects.
Democracy cannot survive overpopulation. Human dignity cannot survive it. Convenience and decency cannot survive it. As you put more and more people into the world, the value of life not only declines, but it disappears. It doesn't matter if someone dies.
Science does not promise absolute truth, nor does it consider that such a thing necessarily exists. Science does not even promise that everything in the Universe is amenable to the scientific process.
Democracy cannot survive overpopulation.
Although the time of death is approaching me, I am not afraid of dying and going to Hell or (what would be considerably worse) going to the popularized version of Heaven. I expect death to be nothingness and, for removing me from all possible fears of death, I am thankful to atheism.
A subtle thought that is in error may yet give rise to fruitful inquiry that can establish truths of great value.
During the century after Newton, it was still possible for a man of unusual attainments to master all fields of scientific knowledge. But by 1800, this had become entirely impracticable.
There is nothing so costly as ignorance.
We are quite rich enough to defend ourselves, whatever the cost. We must now learn that we are quite rich enough to educate ourselves as we need to be educated.
Knowing I lov'd my books, he furnish'd me From mine own library with volumes that I prize above my dukedom.
Keep your hands moving. Writing is rewriting.
We do not trust educated people and rarely, alas, produce them, for we do not trust the independence of mind which alone makes a genuine education possible.
I always wanted to grow up in a house full of books, English books, and I wanted the sort of fireplaces that worked, overstuffed chairs, that whole kind of fantasy of a bookish New England life. So the library gave me that; for the hours that I was there, I was surrounded by that atmosphere that I craved in my life.
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