A History of Mathematics- From Mesopotamia to Modernity

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 ...

246 A History ofMathematics could be saved, how many expensive workers replaced^8 has been much faster than any of the pioneers ...

AChaoticEnd? 247 was found to be an easily teachable and attractive subject on university courses. This could not have been the ...

248 A History ofMathematics the screen. The most popular of all was thequadratic map(justax^2 +bx+c), in two forms: real (Feigen ...

AChaoticEnd? 249 Statistics, in the form of hypothesis testing developed in the early twentieth century, gave a useful way of de ...