jueves, 24 de enero de 2013
viernes, 4 de enero de 2013
relabelling
relabelling and groups of permutations
A nice cite from Eric Bell concerning groups is: Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.
A nice cite from Eric Bell concerning groups is: Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.
lunes, 24 de diciembre de 2012
martes, 11 de diciembre de 2012
sábado, 24 de noviembre de 2012
domingo, 11 de noviembre de 2012
time is all we have
blog sobre aprovechar el tiempo. Mirar atrás y disfrutar de lo que has hecho. Dar un pequeño repaso a mi existencia
domingo, 28 de octubre de 2012
are mathematics invented or discovered?
discovery or invention?
In the LinkedIn group about mathematics "Math, Math Education, Math Culture" Opher Liba asked an old and recurrent question in mathematics: Invention or Discovery? This was the title. Many people contributed to this interesting topic. I am not going to make a summary of all the relevant opinions, some of which were quite elaborated. Just let me highlight the new term proposed by Jonathan Visona: innovery (a mixture of invention and discovery). I will limit myself to reproduce my entry.
I am one of those who think that mathematics is nothing more (and nothing less) than a language: http://www.cut-the-knot.org/language/MathIsLanguage.shtml
Is the language (theormems, propositions, corollaries) already in the grammar (axioms) that specifies it? Well, in some sense it is, but on the other hand you do not care for every possible sentece that can be expressed in the language (leaving aside incompleteness results), but for those sentences or sets of sentences (theories) that are of interest for some practical or theoretical reason.
My opinion is that mathematics are discovered, but the way in which we put everything together and make it "understable" is invented.
Today's quote naturally belongs to J.W.Gibbs: Mathematics is a language.
In the LinkedIn group about mathematics "Math, Math Education, Math Culture" Opher Liba asked an old and recurrent question in mathematics: Invention or Discovery? This was the title. Many people contributed to this interesting topic. I am not going to make a summary of all the relevant opinions, some of which were quite elaborated. Just let me highlight the new term proposed by Jonathan Visona: innovery (a mixture of invention and discovery). I will limit myself to reproduce my entry.
I am one of those who think that mathematics is nothing more (and nothing less) than a language: http://www.cut-the-knot.org/language/MathIsLanguage.shtml
Is the language (theormems, propositions, corollaries) already in the grammar (axioms) that specifies it? Well, in some sense it is, but on the other hand you do not care for every possible sentece that can be expressed in the language (leaving aside incompleteness results), but for those sentences or sets of sentences (theories) that are of interest for some practical or theoretical reason.
My opinion is that mathematics are discovered, but the way in which we put everything together and make it "understable" is invented.
Today's quote naturally belongs to J.W.Gibbs: Mathematics is a language.
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