The Great Mathematicians
By addebook • Jun 29th, 2008 • Category: Mathematics •
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The Great Mathematicians
THE GREAT MATHEMATICIANS.
By H.W. Turnbull
Publisher: Metheun
Number Of Pages: 136
Publication Date:
ISBN-10 / ASIN: B000O8OCV6
ISBN-13 / EAN:
Binding: Paperback
H.W. Turnbull, The Great Mathematicians second edition
Methuen & Co. LTD | ISBN 0814704190 | 1933 | DjVu | 2 MB | 136 pages
For mathematics had now reached a state in which it was possible to do for the whole what Euclid tried to do for geometry,by disclosing the underlying axioms or primitive propositions, as Peano called them: and the most patient investigation has been made –notably in our own land by Whitehead and Russell–first of the subject-matter itself and
next of the very ideas that govern the subject-matter.As all this was conceived on a sublimely universal scale, it is hardly remarkable that certain paradoxes have come to light. How to face these paradoxes is an urgent problem, and there are at the present time two or three different schools of thought employed upon this. The school associated with Brouwer of
Holland has adopted a most drastic policy.They trace the presence of paradoxes to the use of indirect proofs, or more precisely to what is called in logic the law of the excluded middle. To this they object, very much as others have earlier objected to the Parallel Postulate of Euclid; indeed, it may be a symptom of the advent of a higher synthesis in arithmetic and analysis, just as the earlier was in geometry.As nothing less than the whole edifice from Eudoxus to Cantor is at stake, little wonder that these views cause a stir in the mathematical world. “Of what use” said Kronecker to Lindemann, “is your beautiful investigation regarding pi ? Why study such problems, since irrational numbers are non-existent ? ”
So back we are once more at a logical scandal such as troubled the Greeks.The Greeks survived and conquered it, and so shall we. At any rate, it is all a sign of the eternal freshness of mathematics.
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