A Quote by Julian Coolidge
The present author confesses that, to him, geometry is nothing at all, if not a branch of art ...
A Treatise on Algebraic Plane Curves
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Every writer must reconcile, as best he may, the conflicting claims of consistency and variety, of rigour in detail and elegance in the whole. The present author humbly confesses that, to him, geometry is nothing at all, if not a branch of art.
Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).
Descartes constructed as noble a road of science, from the point at which he found geometry to that to which he carried it, as Newton himself did after him. ... He carried this spirit of geometry and invention into optics, which under him became a completely new art.
Fractions, decimals, algebra, geometry, trigonometry, calculus, mechanics - these are the steps up the mountain side. How high is one going to get? For me, the pinnacle was Projective Geometry. Who today has even heard of this branch of mathematics?
Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
Reading is a majority skill but a minority art. Yet nothing can replace the exact, complicated, subtle communion between absent author and entranced, present reader.
Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.
My brain and body and nervous system, they see a plane ride, a long plane trip, as an opportunity to sleep with nothing coming in, nothing to do. I just go offline the minute I'm on the plane.
Crystals grew inside rock like arithmetic flowers. They lengthened and spread, added plane to plane in an awed and perfect obedience to an absolute geometry that even stones - maybe only the stones - understood.
Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.
Geometry is the noblest branch of physics.
Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary.
art is the most general condition of the Past in the present. ... Perhaps no work of art is art. It can only become art, when it is part of the past. In this normative sense, a 'contemporary' work of art would be a contradiction - except so far as we can, in the present, assimilate the present to the past.
The ludicrous state of solid geometry made me pass over this branch.
This incomparable Author having at length been prevailed upon to appear in public, has in this Treatise given a most notable instance of the extent of the powers of the Mind; and has at once shown what are the Principles of Natural Philosophy, and so far derived from them their consequences, that he seems to have exhausted his Argument, and left little to be done by those that shall succeed him.a
Reality is on a delay. For you, nothing is now. Realizing this fact is unsettling. If we can only react to the past, how do we manage to navigate the present? It's easy to spiral into a treatise on free will while in the fetal position, overthinking our forever past.
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