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Books > Science & Mathematics > Mathematics > Mathematical foundations
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A History of Mathematical Impossibility (Hardcover)
Loot Price: R919
Discovery Miles 9 190
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A History of Mathematical Impossibility (Hardcover)
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Many of the most famous results in mathematics are impossibility
theorems stating that something cannot be done. Good examples
include the quadrature of the circle by ruler and compass, the
solution of the quintic equation by radicals, Fermat's last
theorem, and the impossibility of proving the parallel postulate
from the other axioms of Euclidean geometry. This book tells the
history of these and many other impossibility theorems starting
with the ancient Greek proof of the incommensurability of the side
and the diagonal in a square. Lutzen argues that the role of
impossibility results have changed over time. At first, they were
considered rather unimportant meta-statements concerning
mathematics but gradually they obtained the role of important
proper mathematical results that can and should be proved. While
mathematical impossibility proofs are more rigorous than
impossibility arguments in other areas of life, mathematicians have
employed great ingenuity to circumvent impossibilities by changing
the rules of the game. For example, complex numbers were invented
in order to make impossible equations solvable. In this way,
impossibilities have been a strong creative force in the
development of mathematics, mathematical physics, and social
science.
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