A History of Mathematics From Mesopotamia to Modernity

226 A History ofMathematics Around 1910, Dehn and Wirtinger were aware of the tables of knots (or knot-projections) compiled by ...

Modernity and itsAnxieties 227 Type I Reidemeister move Type II Reidemeister move Type III Reidemeister move Fig. 8The three Rei ...

228 A History ofMathematics 1 2 4 3 Fig. 9Two knots, each with four crossings. The crossings on knot 1 are labelled 1, 2, 3, 4 ( ...

Modernity and itsAnxieties 229 To take a ‘proper’ historical viewpoint one needs to have some understanding of what his work mea ...

230 A History ofMathematics While Ramanujan had to receive an accelerated schooling in what then counted as up-to-date number th ...

Modernity and itsAnxieties 231 The idea ofstructureunified two apparently disparate areas of mathematics. It was to become more ...

232 A History ofMathematics solvability of all problemsas formulated by Hilbert in 1900 is equivalent to the logical Principle o ...

Modernity and itsAnxieties 233 z∈V′. The other way round is harder. Supposez^2 >6, we must decomposezas a product. For somen, ...

234 A History ofMathematics Intuitionist critique: we have no way of telling which of the two cases (1), (2) holds at each point ...

10. A chaotic end? 1. Introduction I am not thinking of the ‘practical’ consequences of mathematics...at present I will say only ...

236 A History ofMathematics proof, which is perfectly in the Hardy mode: 100 pages long, understood only by a small circle, and, ...

AChaoticEnd? 237 has its serious historians. Where are the comparable works on the development of chaos theory, category theory, ...

238 A History ofMathematics 3. The Second World War Pure mathematics (in the narrowest sense) has a meaning only as a means of e ...

AChaoticEnd? 239 There is no independent realm of mathematics, independent of intuition and life: the struggle over the foundati ...

240 A History ofMathematics Idealism—the conviction that the war was not mere national defence but the defence of civilization—p ...

AChaoticEnd? 241 Possibly. The folklore of the group is large, and growing, even though almost all of the founders are now dead; ...

242 A History ofMathematics Let us look at an example. To define the sine and cosine functions in chapter VIII (general topology ...

AChaoticEnd? 243 of teaching was the only right one. It never extended even over all of France, but where it was entrenched, it ...

244 A History ofMathematics Well, who did invent the computer? Once one examines the history carefully, there is obviously no si ...

AChaoticEnd? 245 John von Neumann, the other mathematician involved, a Hungarian refugee who turned Cold Warrior, has his suppor ...