One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.
Interpretation
Mathematics has unveiled its true essence through modern advancements.
Bertrand Russell emphasizes that a significant achievement in contemporary mathematics is the understanding of its fundamental nature. This insight reflects the evolution of mathematical thought and its implications for understanding reality.
In practice
In a lecture on the foundations of mathematics, this quote can highlight the importance of understanding core concepts.
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.
...in a time lacking in truth and certainty and filled with anguish and despair, no woman should be shamefaced in attempting to give back to the world, through her work, a portion of its lost heart.
Taking jobs to build up your resume is the same as saving up sex for old age.
When someone is dancing madly in a blissful state, in ecstasy after meditation, he is creating vibrations around him. They may penetrate into anyone. They can become infectious; they do become infectious. This ecstasy can go to others also; this ecstasy can be felt. Others hearts will be touched by it. And if you can create ripples around you, vibrations, you have served the world, and there is no other way to serve it - you have served the divine, and there is no other way to serve it.
An ignorant man ages like an ox. His flesh may increase, but not his understanding.
A man who always speaks the truth wholeheartedly is greater than those who do penance and deeds of charity.
Better to master one mountain than a thousand foothills.
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