The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
Interpretation
Mathematics is fundamentally rooted in symbolic logic, highlighting its logical structure and principles.
In this quote, Bertrand Russell emphasizes the profound interconnection between mathematics and logic. He asserts that recognizing mathematics as an extension of symbolic logic is a pivotal achievement, suggesting that the essence of mathematical principles lies in their logical analysis and formulation, rather than in arbitrary rules or procedures.
In practice
This quote can be used in a mathematics lecture to inspire students to appreciate the underlying logic in math.
St. Paul introduced an entirely novel view of marriage, that it existed primarily to prevent the sin of fornication. It is just as if one were to maintain that the sole reason for baking bread is to prevent people from stealing cake.
Freedom comes only to those who no longer ask of life that it shall yield them any of those personal goods that are subject to the mutations of time.
Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.
At all times, except when a monarch could enforce his will, war has been facilitated by the fact that vigorous males, confident of victory, enjoyed it, while their females admired them for their prowess.
Moreover, the attitude that one ought to believe such and such a proposition, independently of the question whether there is evidence in its favor, is an attitude which produces hostility to evidence and causes us to close our minds to every fact that does not suit our prejudices.
Extreme hopes are born from extreme misery.
The facts will eventually test all our theories, and they form, after all, the only impartial jury to which we can appeal.
All the scientists who are working on solving the problem of curing paralysis say that it won't do you any good if you don't keep your body in shape.
Astronomers can look back in time. We can look at things as they used to be. We have an idea there was a Big Bang explosion 13.7 billion years ago. We have a story of how galaxies and stars were made. It's an amazing story.
I would still very much love to change the world, and there are three or four neurological diseases that I've got a personal grudge against. I wouldn't mind mopping them up in one amazing experiment to come out of my lab, and I certainly wouldn't mind transforming hundreds of thousands of people's lives overnight with some discovery.
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number - there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
Forging differs from hoaxing, inasmuch as in the later the deceit is intended to last for a time, and then be discovered, to the ridicule of those who have credited it; whereas the forger is one who, wishing to acquire a reputation for science, records observations which he has never made.
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