Proofs like Wiles brilliant solution of the famous Fermat Last Theorem are long and difficult.
For Dr Perelman, transforming a conjecture into a theorem appears to have been prize enough.
The significance to me of the Coase Theorem is that it undermines the Pigovian system.
Evidently the word on the Modigliani-Miller theorem hasn't gotten out to the public just yet.
His method relies on some fairly basic mathematics indeed, it uses another of Fermat's theorems, known as Fermat's little theorem.
Although Mr Quine has no important theorem to his name he wrote on mathematical logic with ingenuity and wit.
Mr Freeman cites the Coase theorem to show why this might be so.
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Using an existing result from calculus called Brower's Fixed-Point Theorem, they proved that at least one solution could be found.
Since standard economic theory assumes transaction costs to be zero, the Coase Theorem demonstrates that the Pigovian solutions are unnecessary in these circumstances.
It involves questions like Fermat's Last Theorem and the Riemann Hypothesis.
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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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 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.
Merton Miller and his colleague Franco Modigliani posited their capital structure irrelevance theorem in the late 1950s, when the dollar was as good as gold at least for foreign creditors.
However, the famous Fermat's Last Theorem tells us that if the numbers are not squared but, say, multiplied three times (cubed) then no numbers can be found that will work.
The theorem concerns a three-dimensional space with no boundaries.
In 1820, German mathematician Karl Friedrich Gauss proposed cutting an enormous right triangle into the Siberian pine forest, creating a monument to the Pythagorean theorem big enough to see from outer space.
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.
The Coase Theorem essentially states that if trade in an externality is possible and there are no transaction costs, bargaining will lead to an efficient outcome regardless of the initial allocation of property rights.
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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 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.
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.
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.
The Phillips "theorem" caused no end of mischief after the collapse of the gold-based international monetary system in 1971: Leaders tried to manipulate the value of money to create prosperity but ended up creating less growth and more instability.
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.
With a nod toward Bayes theorem, Ludlow basically wants to confuse the advertisers trying to profile him and the algorithmic machines that are trying to make predictions about him by throwing lots of false information about himself onto their radars.
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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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The next step is to find the mathematically simplest versions of such maps. (What is meant by simplicity in this case is actually quite involved.) Dr Gonthier then showed that all these maps can, in fact, be re-coloured with only four colours, establishing the theorem by contradiction.
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