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Collected Papers of Salomon Bochner

This academic volume gathers the published mathematical papers of Salomon Bochner, offering a thorough record of his extensive research and contributions. The collection serves as a valuable resource for mathematicians and historians of science, encompassing his foundational writings across various areas of pure mathematics, including analysis, probability theory, and differential geometry. By consolidating his scholarly output, the work provides a cohesive overview of his intellectual legacy and his influence on twentieth-century mathematics. more

Author

Salomon Bochner
Salomon Bochner

Salomon Bochner was a renowned mathematician known for his contributions to functional analysis and probability theory. His influence in the mathematical community was profound, particularly in these two areas. more

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“While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our cognition. These ultimate laws-in the domain of physical science at least-will be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves. When these relations shall be known, all physical phenomena will be a branch of pure mathematics.”

“[Before the time of Benjamin Peirce it never occurred to anyone that mathematical research] was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood alone-a mountain peak whose absolute height might be hard to measure, but which towered above all the surrounding country.”

“[In the Royal Society, there] has been, a constant Resolution, to reject all the amplifications, digressions, and swellings of style: to return back to the primitive purity, and shortness, when men deliver'd so many things, almost in an equal number of words. They have exacted from all their members, a close, naked, natural way of speaking; positive expressions; clear senses; a native easiness: bringing all things as near the Mathematical plainness, as they can: and preferring the language of Artizans, Countrymen, and Merchants, before that, of Wits, or Scholars.”

“But the World being once fram'd, and the course of Nature establish'd, the Naturalist, (except in some few cases, where God, or Incorporeal Agents interpose), has recourse to the first Cause but for its general and ordinary Support and Influence, whereby it preserves Matter and Motion from Annihilation or Desition; and in explicating particular phenomena, considers onely the Size, Shape, Motion, (or want of it) Texture, and the resulting Qualities and Attributes of the small particles of Matter.”

“Doctors have been exposed-you always will be exposed-to the attacks of those persons who consider their own undisciplined emotions more important than the world's most bitter agonies-the people who would limit and cripple and hamper research because they fear research may be accompanied by a little pain and suffering.”

“How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.”