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The following excerpt is from My Three Passions by Bertrand Russell.

And I have tried to apprehend the Pythagorean power by which number holds sway over the flux.

What does the author mean to say?

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Quoting Joshua Engel's answer on Quora:

It's talking about Pythagoreanism, a pre-Socratic philosophy. Actually, it's kind of hard to pin down exactly what Pythagoreanism is, but the notion "all is number" is commonly attributed to them. [...]

Russell is, I think, getting at the idea that Pythegoreanism has largely won out, that the world appears to be dominated by numerically predictable values such that even change (flux) is number.

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Human history, human life, human character are all a sea of relativity.

The numbers and their science provide some island of stability in all of this Maelstrom.

See, e.g.,

The Ancient Dialect: Thomas Carlyle and Comparative Religion Ruth ApRoberts - 1988

Cast like Bertrand Russell into a sea of relativity, he found a stability in mathematics, seeking, in Russell's words, "to apprehend the Pythagorean power by which number holds sway above the flux, ... an ideal world where everything is perfect ..."

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The paragraph in which this quote appears is as follows:

With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which number holds sway over the flux. A little of this, but not much, I have achieved.

The author has tried to gain knowledge of various kinds, such as knowledge of human nature ("the hearts of men"), physical phenomena ("why the stars shine"), and the nature of mathematics ("the power by which number holds sway over the flux").

Russell was known for his philosphical work, and in particular his work in the philosophy of mathematics, so the sentence you are asking about can be interpreted as a reference to his endeavors in this field. The phrase "Pythagorean power" is a reference to the ancient Greek Pythagoreans, followers of Pythagorus, who believed in a mystical relationship between mathematics and reality.

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