The idea behind both proofs of the four colour theorem is to suppose that the theorem is violated to assume, in other words, that there is some sort of map that requires five colours to fill in.
With research continuing into this strand of ancient history, it remains to be seen whether Pythagoras's theorem will come to bear the name of an old Babylonian scribe instead.
The significance to me of the Coase Theorem is that it undermines the Pigovian system.
The theorem says that the distribution of property rights, provided they are clearly assigned and transactions costs are low, has no effect on economic efficiency, because people can negotiate their way to the efficient position.
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The theorem was modified to take account of the imperfections of the market, such as tax concessions on debt, a point that Mr Miller's critics had happily seized on.
The recent scientific work on the expenditure multiplier is aligned with the Ricardian equivalence theorem as well as the views of the Austrian economists who continued to follow Ricardo even when the Keynesian revolution was ascendant.
Proofs like Wiles brilliant solution of the famous Fermat Last Theorem are long and difficult.
At Harvard (class of '72) he studied mathematics and he maintains his interest in the world of figures, socializing with math professors and even moderating a discussion about the solution of Fermat's Last Theorem.
For a comprehensive yet eminently comprehensible account of how cosmologists pieced together the history of the universe, turn to the latest book by Simon Singh, a British science writer best known for his bestselling account of the solution of Fermat's last theorem.
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He was a fine mathematician (there is a Perutz theorem in probability theory) and the plots of his Prague tales toy with chance and coincidence.
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His method relies on some fairly basic mathematics indeed, it uses another of Fermat's theorems, known as Fermat's little theorem.
As a member of the avant-garde in mathematics in France in the 1930s he made his name as a founder of the Bourbaki group, which owed its moniker to a prank theorem named after a general in Napoleon III's army.
This both increases the volatility of equity returns and transfers value from debt to equity in the presence of default risks but has little to do with the Modigliani-Miller theorem in which default risk plays no part.
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