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Archive for the ‘Math’ Category

One of the Guiding Principles of Modern Mathematics

Posted by mfluch on May 7, 2009

The following quote is from Everett C. Dade article on Group-Graded Rings and Modules:

One of the guiding principles of modern mathematics is that the main difficulty in any subject should be to find the right way to look at it. Once this proper viewpoint is found the theorems become obvious and their proofs routine if not trivial. Make the right definitions and the rest will take care of itself.

Nuff said. :-)


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Applied Number Theory

Posted by mfluch on January 2, 2008

This might give you an idea what to do when math lectures get boring. Can you keep up?

Factoring Time

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57 – The Grothendieck Prime

Posted by mfluch on December 26, 2007

The following anecdote about the number 57 is quoted from Allyn Jackson’s article “Comme Appelé du Néant – As If Summoned from The Life of Alexandre Grothendieck”:

One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

Grothendieck is considered one of the greatest mathematicians of the 20th century. He thought in great generalities but yet thinking in concrete examples was not his strength. Note that 57 is equal to 19 times 3…

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Group Theory in a Nutshell

Posted by mfluch on December 26, 2007

The following statement is atributed to the mathematician James Neuman (though I did not find any other reference than Wikipedia’s article on group theory):

The theory of groups is a branch of mathematics in which one does something to something and then compares the results with the result of doing the same thing to something else, or something else to the same thing.

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