"The "structures" are tools for the mathematician; as soon as he has recognized among the elements, which he is studying, relations which satisfy the axioms of a known type, he has at his disposal immediately the entire arsenal of general theorems which belong to the structures of that type. Previously, on the other hand, he was obliged to forge for himself the means of attack on his problems; their power depended on his personal talents and they were often loaded down with restrictive hypotheses, resulting from the peculiarities of the problem that was being studied... each structure carries with it its own language, freighted with special intuitive references derived from the theories from which the axiomatic analysis described above has derived the structure. And, for the research worker who suddenly discovers this structure in the phenomena which he is studying, it is like a sudden modulation which orients at one stroke in an unexpected direction the intuitive course of his thought and which illumines with a new light the mathematical landscape in which he is moving about."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
https://en.wikiquote.org/wiki/Nicolas_Bourbaki
Revision History
No revisions have been submitted for this quote.
Categories
Related Quotes
"It can now be made clear what is to be understood, in general, by a mathematical structure. The common character of t…"
"... in a single view, it sweeps over immense domains, now unified by the axiomatic method, but which were formerly in…"
"At the center of our universe are found the great types of structures... they might be called the mother-structures..…"
"From the axiomatic point of view, mathematics appears thus as a storehouse of abstract forms -- the mathematical stru…"
"Nicolas Bourbaki is the nom-de-plume adopted in the 1930s by a group of out standing young French mathematicians who …"
"But in the eyes of contemporary structuralist mathematicians, like the Bourbaki, the Erlanger Program amounts to only…"
"This present art, in which we use those twice five Indian figures, is called algorismus."
"It was not exactly as you say. In practice, the 12 of us never lived at home at the same time, because the family gre…"
"In this respect I recall with much sympathy the writer Virginia Woolf who wrote about this need for private space (A …"
"Hermite was born in 1822, four years before Riemann. Now in his sixties, he had become one of the standard-bearers fo…"