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" "So far, all of reality seems to be described by exquisite, elegant mathematical equations. We can’t stop now – it’s got to be beautiful all the way down!
Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. His greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In mathematics, he is perhaps best known for his discovery of quaternions.
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I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise. I still believe in abstraction, but now I know that one ends with abstraction, not starts with it. I learned that one has to adapt abstractions to reality and not the other way around. Mathematics stopped being a science of theories but reappeared to me as a science of numbers and shapes.
Prometheus: ...
List rather to the deeds
I did for mortals; how being fools before,
I made them wise and true in aim of soul. ...
But teaching you the intention of my gifts,
How first beholding, they beheld in vain,
And hearing, heard not, but, like shapes in dreams,
Mixed all things wildly down the tedious time,
Nor knew to build a house against the sun...
But lived like silly ants, beneath the ground
In hollow caves unsunned. There, came to them
No steadfast sign of winter, nor of spring...
But blindly and lawlessly they did all things,
Until I taught them how the stars do rise
And set in mystery, and devised for them
Number, the inducer of philosophies,
The synthesis of Letters, and, beside,
The artificer of all things, Memory,
That sweet Muse-mother.