There is indivi-duality, not only physical-mathematical, but also in consideration of whether mathematics is invention or discovery; it is an indivi-duality invention-discovery. This is the key to next paragraph of the distinguished mathematician Langlands:
*At times, the opposite happens. I awakes and for some moments Finds a world Where actual mathematical Entities seem as as the furniture.
"It's nightmarish," I says. "It must have something to do With madness. If in the middle of the night you wake up and there's some fusion Between the mathematical objects and the real world, then a you're mad.*
And I would add that I see in his theories to the great Grothendieck as a real instigator or inspiring him. Weyl, Langlands, Serre and others follow his theory of motives, which even says Arthur would not be surprised to be elementary particles in the universe:
*Spectacular discoveries in physics Have Been foretold by mathematics. One of history's foremost mathematicians, the German Carl Friedrich Gauss, in the early 1800s Calculated a theorem on the intrinsic curvature of space, echoed in Einstein's theory of relativity Almost a century later.
In the early 1960s, American physicist Murray Gell-Mann used the math principles of group theory to organize composite particles called hadrons and to predict the existence and distribution of sub-atomic quarks. Experiments confirmed several years later Organizing Both the pattern and the quarks. I have Received the Nobel Prize in physics for esta work in 1969.
"Mathematics Allows you to see the invisible," Frenkel says.
The link Currently some exciting Physicists Involves a "duality" found Between the forces of electricity and magnetism. These forces are Said to be symmetrical - They Affect each other in the same way. In quantum physics, esta duality center is to the quest for a theory Known That unites all physical interactions in the universe, from the stars to the smallest particles.
The symmetry Between electricity and magnetism parallels One That exists in Langlands' conjectures, mathematical Involving groups associate With That automorphic forms. String theorist Edward Witten of the Institute for Advanced Studies describe the existence of esta analog as "amazing."
"We of course do not know how the story will Develop from here," I says in an email to the Star. "Maybe the physics will shed light on number theory, number theory maybe will produce insights That will help Physicists. Maybe for a long time and we will not know the two parts of the picture will mostly just Develop Independently of each other. "
Arthur will not be surprised if Eventually Physicists discover math That's elusive key motives exist as particles in the universe. That Sentimental Dismisses Langlands as fantasy. He's convinced the majority of Physicists, DESPITE Witten's giant reputation, see little value in Applying His Work.*
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