Mathematics is a poem that has God for its subject. Thusly might we adapt Petrarch's aphorism to our Harsh Mistress. And the poem in the title above is often cited as the Most Beautiful in all of mathematics by people who do that sort of thing. (Although let's be honest: Everybody picks this equation because Richard Feynman did.) It includes all of the fundamental constants (0, 1, e, i, and pi) and all four fundamental mathematical operations (addition, multiplication, exponentiation, and equality) and ties it up in a pretty package with a sheen of the inscrutable (unless you took a course in complex variables, raising anything to an imaginary power makes about as much sense as a Mozart opera).
Inscrutability is nice and all, but if you are looking for mystery there's far queerer things to be found in mathematics (and I don't mean Leonardo Da Vinci). Addition, multiplication, exponentiation, and equality are to mathematics as paste-eating is to your public school education: something most of us move beyond by the the time puberty shows.
Let's see if we can scare up a more exotic beauty.
For truly stinky dinosaur poop one must look to the carnivores, Michael Crichton informs us (I have no idea why I remember that line from the novel). And for truly weird mathematics, one must look to the calculus. We shall skip over calculus weirdness such as shapes with infinite surface area and finite volume or series that add up to any number you like simply by reordering their terms. No, we seek true beauty, earned through eons, not beauty that requires a knowledge and understanding of what it is, as Pete Townshend once described himself. Something written in the urstone itself, before there were paths anywhere, before there were men or suns to go upon them.
If e^iπ + 1 = 0 were scrubbed from the subway wall, here is my vote for the words of the poets that would be written in its stead:
Whereas our first poem combined 0, 1, e, i, pi, addition, multiplication, exponentiation, and equality, the new one combines e, pi, infinity, multiplication, exponentiation, equality, square root, and integration. A more mature palette, to be sure. It's also very strange. What the heck does an infinite integral have to do with pi? you should be asking right about now. (Also, please pardon my odd notation; I could spend a weekend learning LaTex or baking a Sampo or whatever the heck it is you do to write proper integral limits in HTML, or you can live with my notation and I can go outside and play. Deal.)
The integral happens to be Γ(1/2) where Γ is the Gamma function and is all sorts of important in statistics and probability. There is a perfectly reasonable explanation what all this has to do with pi, but I shan't spoil the mystery with philistine derivation. It would be like how Deep Blue spoiled some of the mystery of chess, or how the mystery of what lies beneath Juliet's burlap dress was spoiled by double suicide. Noli me tangere, Joan Jett was really singing, although, admittedly, the chorus sends a rather mixed message.
Instead, let us simply end as we began: Mathematics is a poem that has God for its subject.
Inscrutability is nice and all, but if you are looking for mystery there's far queerer things to be found in mathematics (and I don't mean Leonardo Da Vinci). Addition, multiplication, exponentiation, and equality are to mathematics as paste-eating is to your public school education: something most of us move beyond by the the time puberty shows.
Let's see if we can scare up a more exotic beauty.
For truly stinky dinosaur poop one must look to the carnivores, Michael Crichton informs us (I have no idea why I remember that line from the novel). And for truly weird mathematics, one must look to the calculus. We shall skip over calculus weirdness such as shapes with infinite surface area and finite volume or series that add up to any number you like simply by reordering their terms. No, we seek true beauty, earned through eons, not beauty that requires a knowledge and understanding of what it is, as Pete Townshend once described himself. Something written in the urstone itself, before there were paths anywhere, before there were men or suns to go upon them.
If e^iπ + 1 = 0 were scrubbed from the subway wall, here is my vote for the words of the poets that would be written in its stead:
∫-∞, ∞ e^(-x2) dx = √π
Whereas our first poem combined 0, 1, e, i, pi, addition, multiplication, exponentiation, and equality, the new one combines e, pi, infinity, multiplication, exponentiation, equality, square root, and integration. A more mature palette, to be sure. It's also very strange. What the heck does an infinite integral have to do with pi? you should be asking right about now. (Also, please pardon my odd notation; I could spend a weekend learning LaTex or baking a Sampo or whatever the heck it is you do to write proper integral limits in HTML, or you can live with my notation and I can go outside and play. Deal.)
The integral happens to be Γ(1/2) where Γ is the Gamma function and is all sorts of important in statistics and probability. There is a perfectly reasonable explanation what all this has to do with pi, but I shan't spoil the mystery with philistine derivation. It would be like how Deep Blue spoiled some of the mystery of chess, or how the mystery of what lies beneath Juliet's burlap dress was spoiled by double suicide. Noli me tangere, Joan Jett was really singing, although, admittedly, the chorus sends a rather mixed message.
Instead, let us simply end as we began: Mathematics is a poem that has God for its subject.
Footnote: "usw" is abbreviation for the German "und so weiter" meaning "and so on" or "and others in the same vein." I had to take two years of German for this Ph.D. and, dammit, I'm going to get some use out of it.
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