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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Appearances
At school, we study solutions of quadratic equations, equations of degree two.
So you have AX squared plus BX plus C equals zero.
And there is a formula which solves it using radicals, using square roots.
And Cardano was trying to find a similar formula for the cubic and quartic equations, which would start with X cubed or X to the power of four, as opposed to X squared.
And in the process of solving these equations, he came up
with square root of a negative number, specifically square root of minus 17.
And he wrote that, I have to forego some mental tortures.
to deal with it, but I am going to accept it and see what happens.
And in fact, at the end of the four, at the end of the calculation, this weird numbers got canceled.
It kind of canceled out in the formula appeared square root of negative 17 and it's negation.
So they kind of conveniently gave the right answer, which is not involved those numbers.
So he was like, okay, what does it mean?
Mental tortures.
So you see, from the point of view,
of the thinking mind.
It is something almost unbearable.
It's almost, I feel, that a large language model, a computer running a large language model, trying to do that would just explode.
And yet a human mathematician was able to find the courage and inspiration to say, you know what?
What is wrong?
Why are we so adamant that these things don't exist?
Showing 541–560 of 2,304 · page 28 of 116
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