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Square roots have no unexpected linear relationships
IMO medalist Iurie Boreico has an article in an issue of the Harvard College Mathematics Review about his favorite problem: Let be distinct squarefree integers. Show that if are not all zero, then the...
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Mathematical historical fiction
Bill Gasarch is right – writing technical posts is tiring! (I’ve been trying to finish the next GILA post for days.) So I’ll share some more thoughts instead. Today’s thought was triggered by David...
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Exceptional structures
Recently Isabel Lugo asked about problems that are hard for intermediate values of some parameter, and in discussing the question I got to thinking about exceptional structures in mathematics such as...
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Some examples of graded algebras
Often in mathematics we work in an algebra with the property that the “degree” of an element has a multiplicative property. For example, in a polynomial ring in variables we can define the degree of a...
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IMO 2009 and proof systems
The problems from IMO 2009 are now available. I haven’t had much time to work on them, though. There are two classical geometry problems, which I already know I won’t attempt. While I am well aware...
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Standard Young tableaux and Robinson-Schensted-Knuth
Earlier I mentioned that the theory of Young tableaux is the source of one of my favorite proofs. Today I’d like to present, again from the theory of Young tableaux, one of my favorite pairs of proofs....
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