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Friday April 4 - Friday April 4 2008 Early 20th century can...

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Friday April 4, 2008 Early 20 th century can be characterized by one huge trend. = move towards abstraction. -moving on from late 19 th century, from things like group, vector theory, which were the beginnings of abstract math. -started really taking off. Why?? -Were starting to get really positive results from abstract work eg) Riemann working on the Manifold Thoery -generalization of geometry. As abstract as it gets. -no practical consequendces, no real use in the least, etc 1905- Einstein produced one of his first papers on the theory of relativity. -to the astonishment of the mathematical world at the time, he described the entire universe using the basis of manifold theory. Ie space is curved.. how to describe it? It’s a manifold. Space and time? It’s four dimensions= a 4 dimensioned manifold -physicists took off, an enormous take off for this type of work -quantum theory came about, locating position of electron by probability within an electron cloud These applications were unexpectedly quick and immediate. -eg. X-Rays developed, atom bomb, utopian ideas of energy from nuclear reactions… changing at an enormous pace. 1900, most didn’t even have electricity. By 1920,30 Xrays were so well known, superman had xray vision. Another trend- “we didn’t expect this, we weren’t looking for any application! We were doing the rigorization of calculus.” -highly practical, enormous results, rigorized it using SET theory. Not a very practical theory, it was very abstract. SET theory was invented before Calculus needed it for rigorization. (defining limits, functions, etc, using this theory to DO it) =pattern that things were come up with not for need, but because ‘just for fun’ that ended up with practical results. Therefore…. Since this has happened in the past, it will continue to happen (abstract math eventually becoming practically useful) -eg develop Groups, Vectors, Fields, Topology 1941 Hardy wrote a book for public use, called ‘A mathematcian’s Apology” saying his field was so abstract, it couldn’t possibly be applicable. Gauss: ….number theory is even
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