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Additional info for Levels of Infinity: Selected Writings on Mathematics and Philosophy

Sample text

Modernity has added the insight that one need not regard the sequence as a mere means for the conceptual description of a point given previously and assured to exist, but that through such a sequence the point in the continuum may be constructively generated in the first place. Every such sequence produces a point; in the arithmetically empty schema, the points are created precisely thereby. Only by means of this constructive turn is a mathematical mastery, an analysis, of continuity possible. Yet there is still a problem with the idea of the infinite sequence.

The first essay in this volume dates from that year, as the newly-appointed Weyl travelled to Jena to speak to mathematics students. 5 It gives an arresting portrait of his intellectual development and his struggle with basic questions in the foundations of mathematics. Though devoted to Hilbert, Weyl for a time sided against him in an ongoing controversy that continues to simmer under the surface of mathematical practice. J. Brouwer, a distinguished topologist four years older than Weyl, made this cause his own, under the banner of “intuitionism”: mathematics should return to its roots in human intuition, radically restricting its use of infinite quantities to those that could be grounded in possible acts of intuition.

In 2012. com Contents Introduction Levels of Infinity (1930) Topology and Abstract Algebra as Two Roads of Mathematical Comprehension (1932) Emmy Noether (1935) The Mathematical Way of Thinking (1940) David Hilbert 1862-1943 (1944) David Hilbert and His Mathematical Work (1944) Mathematics and Logic (1946) Relativity Theory as a Stimulus in Mathematical Research (1949) A Half-Century of Mathematics (1951) Axiomatic Versus Constructive Procedures in Mathematics (1953) Why is the World Four-Dimensional?

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