Weil's new mathematical language, algebraic geometry, had enabled him to articulate subtleties about solutions to equations that hitherto had been impossible. But if there was any hope of extending Weil's ideas to prove the Riemann Hypothesis, it was clear they would need to be developed beyond the foundations he had laid in his prison cell in Rouen. It would be another mathematician from Paris who would bring the bones of Weil's new language to life. The master architect who performed this task was one of the strangest and most revolutionary mathematicians of the twentieth century - Alexandre Grothendieck.
Alexander GrothendieckRelated topics
articulate beyond century clear geometry hope hypothesis impossible language lay master mathematician need prison prove task Riemann bonesRelated quotes
It is a fearful thing to hate whom God hath loved. To look upon another-his weaknesses, his sins, his faults, his defects is to look upon one who is suffering. He is suffering from negative passions, from the same sinful human corruption from which you yourself suffer. This is very important: do not look upon him with judgmental eyes of comparison, noting the sins you assume you'd never commit. Rather, see him as a fellow sufferer, a fellow human being who is in need of the very healing of which you are in need. Help him, love him, pray for him do unto him as you would have him do unto you.
Tikhon of Zadonsk
One of our [his] utopian ideas is the desire to overcome the limitations of the substructure, of the earthbound. We have developed this idea in a series of proposals (sky-hooks, [like Lissitzky's paper-architecture design 'Wolkenbügel' (1924)] stadium grandstands, Paris garage].. .It is the task of technology to make sure that all these elementary volumes that produce new relationships and tensions in space will be structurally safe.. .The idea of the conquest of the substructure, the earthbound, can be extended even further and calls for the conquest of gravity as such. It demands floating structures, a physical-dynamic architecture.
El Lissitsky
It must be admitted that among a certain number of advanced mathematical physicists whose work has lain mainly in the twentieth century, the ether is regarded with suspicion, or even with contempt. And some of the opponents go so far as to as to say that the nineteenth century idea of the ether has failed to establish itself, and that in consequence the whole idea of the ether is under a cloud, and that it is only upheld by a few antiquated supporters, who, though are willing to admit many modifications in the original nineteenth century notions of an ether, feel the need of a medium capable of performing the functions attributed to it.
Oliver Lodge
The theory of perspective was taught in painting schools from the sixteenth century onward according to principles laid down by the masters... However, their treatises on perspective had on the whole been precept, rule, and ad hoc procedure; they lacked a solid mathematical basis. In the period from 1500 to 1600 artists and subsequently mathematicians put the subject on a satisfactory deductive basis, and it passed from quasi-empirical art to a true science. Definitive works on perspective were written much later by eighteenth-century mathematicians Brook Taylor and J. H. Lambert.
Morris Kline
But to return to the Newtonian Philosophy: Tho' its Truth is supported by Mathematicks, yet its Physical Discoveries may be communicated without. The great Mr. Locke was the first who became a Newtonian Philosopher without the help of Geometry; for having asked Mr. Huygens, whether all the mathematical Propositions in Sir Isaac's Principia were true, and being told he might depend upon their Certainty; he took them for granted, and carefully examined the Reasonings and Corollaries drawn from them, became Master of all the Physics, and was fully convinc'd of the great Discoveries contained in that Book.
John Theophilus Desaguliers