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Sunday, June 28, 2015

Mathematics and the Real World

Sunday's reflection:

"There are voices in the modern mathematical community that bemoan the state of mathematics today. While relishing the intellectual freedom bequeathed by the non-Euclidean revolution, mathematicians of the twentieth century carried their subject farther and farther from a contact with the real world, until their logical constructs became so abstract and arcane as to be unrecognizable by a physicist or engineer. To many, this trend has transformed mathematics into little more than a pointless exercise in chasing tiny symbols across the page. One of the most vocal critics of this trend is mathematics historian Morris Kline, who wrote:
'Having formulated the abstract theories, mathematicians turned away from the original concrete fields and concentrated on the abstract structures. Through the introduction of hundreds of subordinate concepts, the subject has mushroomed into a welter of smaller developments that have little relation to each other or to the original concrete fields.'
"....In response there can be made an intriguing argument that mathematical theories, no matter how seemingly abstract, often have surprising applications to very solid, real world phenomena.  Even the non-Euclidean revolution, the subject that did so much to sever the bond between mathematics and reality, has found its way into modern physics books, for the relativistic theories of today's cosmologies rely heavily on a non-Euclidean model of the universe. Such a reliance was certainly not foreseen by the nineteenth-century mathematicians who investigated the subject for its own sake, yet it now forms a part of applied mathematics necessary for inclusion in the physicist's tool-kit."

-- William Dunham in "Journey Through Genius" (1990)


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