Nov 5, 2024
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euler's identity crisis
We’re doomed.
In an interview with the BBC, Prof David Percy of the Institute of Mathematics and its Applications said Euler's Identity was “a real classic and you can do no better than that … It is simple to look at and yet incredibly profound, it comprises the five most important mathematical constants.”
Euler's Identity is written simply as: eiπ + 1 = 0
Euler’s Identity
We have 3 wacky numbers
e = 2.71828182845904523536028747135266249775724709369995... π = 3.1415926535897932384626433832795028841971693993751... i = √-1
And...
e^(π x i) + 1 = 0
What?
There are proofs for this. But, there’s no need to. We just need to be in shock and awe.
And that is Euler’s identity.
Math can make our brains light up in the same way art and music do.
Our brains also appear to respond to mathematical beauty as they do to other beautiful experiences.
In a 2014 study, Semir Zeki, a neuroscientist at University College London, and other researchers used fM.R.I. scanners to observe the brains of 15 mathematicians while they were thinking about various equations. The subjects were shown 60 mathematical formulas two weeks before they were scanned and during and after the scan. They were also asked to rate their level of understanding of each equation and their subjective emotional response to it, from ugly to beautiful.
The researchers found a strong correlation between finding an equation beautiful and activation of the medial orbitofrontal cortex, a region of the prefrontal cortex just behind the eyes. This is the same area that has been shown to light up when people find music or art beautiful, so it seems to be a common neural signature of aesthetic experience.
Geeks, take heart: While you can’t see or hear mathematical ideas, they too are capable of arousing a sense of beauty.
No doubt you’d like to know which equation won the beauty contest. It was the so-called Euler’s identity, which is a deceptively spare but profound equation that links five fundamental mathematical constants: a mix of real and imaginary numbers that combine to make zero.
Got bored this morning. Came back from the hospital at almost 9:00 pm tonight.
Euler's identity