TY - JOUR

T1 - The origins of eternal truth in modern mathematics

T2 - Hilbert to Bourbaki and beyond 1

AU - Corry, Leo

PY - 1997

Y1 - 1997

N2 - The belief in the existence of eternal mathematical truth has been part of this science throughout history. Bourbaki, however, introduced an interesting, and rather innovative twist to it, beginning in the mid-1930s. This group of mathematicians advanced the view that mathematics is a science dealing with structures, and that it attains its results through a systematic application of the modern axiomatic method. Like many other mathematicians, past and contemporary, Bourbaki understood the historical development of mathematics as a series of necessary stages inexorably leading to its current state - meaning by this, the specific perspective that Bourbaki had adopted and were promoting. But unlike anyone else, Bourbaki actively put forward the view that their conception of mathematics was not only illuminating and useful for dealing with the current concerns of mathematics, but that this was in fact the ultimate stage in the evolution of mathematics, bound to remain unchanged by any future development of this science. In this way, they were extending in an unprecedented way the domain of validity of the belief in the eternal character of mathematical truths, from the body to the images of mathematical knowledge. Bourbaki were fond of presenting their insistence on the centrality of the modern axiomatic method as a way to ensure the eternal character of mathematical truth as an offshoot of Hilbert's mathematical heritage. A detailed examination of Hilbert's actual conception of the axiomatic method, however, brings to the fore interesting differences between it and Bourbaki's conception, thus underscoring the historically conditioned character of certain, fundamental mathematical beliefs.

AB - The belief in the existence of eternal mathematical truth has been part of this science throughout history. Bourbaki, however, introduced an interesting, and rather innovative twist to it, beginning in the mid-1930s. This group of mathematicians advanced the view that mathematics is a science dealing with structures, and that it attains its results through a systematic application of the modern axiomatic method. Like many other mathematicians, past and contemporary, Bourbaki understood the historical development of mathematics as a series of necessary stages inexorably leading to its current state - meaning by this, the specific perspective that Bourbaki had adopted and were promoting. But unlike anyone else, Bourbaki actively put forward the view that their conception of mathematics was not only illuminating and useful for dealing with the current concerns of mathematics, but that this was in fact the ultimate stage in the evolution of mathematics, bound to remain unchanged by any future development of this science. In this way, they were extending in an unprecedented way the domain of validity of the belief in the eternal character of mathematical truths, from the body to the images of mathematical knowledge. Bourbaki were fond of presenting their insistence on the centrality of the modern axiomatic method as a way to ensure the eternal character of mathematical truth as an offshoot of Hilbert's mathematical heritage. A detailed examination of Hilbert's actual conception of the axiomatic method, however, brings to the fore interesting differences between it and Bourbaki's conception, thus underscoring the historically conditioned character of certain, fundamental mathematical beliefs.

UR - http://www.scopus.com/inward/record.url?scp=0031284014&partnerID=8YFLogxK

U2 - 10.1017/s0269889700002659

DO - 10.1017/s0269889700002659

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AN - SCOPUS:0031284014

SN - 0269-8897

VL - 10

SP - 253

EP - 296

JO - Science in Context

JF - Science in Context

IS - 2

ER -