Edward Frenkel
speaker
2,304 appearances
1 recordings
1 series
first heard Apr 2023
last heard Apr 2023
Edward Frenkel’s voice in public audio — every appearance, attributed to the second.
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For instance, you know, the set of tables, the set of chairs, and so on, or set of microphones.
But it could be a set of numbers.
Could be a set of ideas, could be a set of formulas, mathematical equations.
And then we have the notion of an ordered set, ordered, like the set in which there is order, which means that for every two members of the set, we'll say which one is better than the other or greater than the other.
For instance, all numbers are ordered.
Five is greater than three, five is less than seven, and so on.
But not all sets are ordered.
So the set of beautiful equations is not ordered.
So in other words, there are many best equations.
And so...
Richard Feynman chose one, which I think one of the best, is that if you take e, the base of the natural logarithm, to the power pi i, so you have e in it, the base of the natural logarithm, you have pi, i, which is the square root of negative 1, then the result is negative 1.
So that's up there, for sure, in the pantheon of beautiful formulas, you know, that I think pretty much every mathematician would agree.
I don't know what my favorite one is.
There is an element of surprise in it.
How is it possible?
We always think of pi as the ratio between the circumference of a circle and its diameter.
Here we are taking some number to the power pi, not even pi, mind you, but pi multiplied by square root of negative 1.
Surely this is something completely incomprehensible.
And yet the result is negative 1, you see?
And if you take e to the power 2 pi i, you get 1, actually 1.
Showing 1081–1100 of 2,304 · page 55 of 116
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