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Andrés Villaveces - about mathematics
Check out the new forum Open Problems in Mathematical Logic, maintained by Scanlon, Slaman and Steel!
Ojo: hay un nuevo foro, de la Sociedad Colombiana de Matemáticas. Haga clic aquí para visitar el foro - la idea de Carlos Montenegro es que se convierta en un espacio de discusión de los matemáticos del país.
For now, not much. I plan to put here some sites of people whom I read on occasion - and whose opinions come back every once in a while - on doing mathematics, some issues on the relevance of some parts of it, even on teaching mathematics.
Warning: I abhor a good 80-90% of what passes for discussions on teaching math, and of what philosophers in Philosophy Departments claim mathematics is. I personally think most philosophers of mathematics have absolutely no clue on what mathematics is. So, these links will be (by necessity) non-exhaustive and will reflect a very personal perspective. Notice, however, that I think a very select few mathematicians and (even) philosophers of mathematics have sometimes extremely interesting insights on this activity. I plan to devote this page to some of that.
Gian-Carlo Rota
at some point, reading some of the works by Rota and discussing them with one of his disciples (Mark Ettinger, then a student of H. J. Keisler in Madison), I got extremely interested in some of his insights. I still think that some of the sentences written in his Indiscrete Thoughts are among the most piercing I have recently read. I have only very partially begun to understand his obsession with phenomenology. With Alejandro Martín, we have translated several of his essays into Spanish. Check our Rota site here (very much under construction).Fernando Zalamea
works in between mathematics, philosophy and general criticism of culture. Based in Bogotá (he is part of the faculty at Universidad Nacional de Colombia), he is currently writing several essays in Barcelona. He has won awards for his essays in México, Colombia and Spain. His long-winded essays deal with various issues, including the quest for ways of "glueing back" the shattered pieces of culture that the twentieth century left - he claims that the impression of general cultural fracture and shattering stems from a serious misunderstanding and lack of conceptual (and technical) tools to "glue" our shattered cultural world. He has proposed various (necessarily partial) ways of working toward a "multiperspective" glueing by means connected (but not restricted) to intuitionistic logics, sheaf logics, other Peircian logics.Doron Zeilberger
of Rutgers is extremely interesting, even if you (like I often do) completely disagree with some of his opinions. He has a wide readership, and ponders matters dealing with computers and mathematics. He pretends in some of his opinions that computer algebra will completely change the way we understand mathematics. But he also dwells on issues like refereeing (and its shortcomings), pure math vs "applied math", unity of mathematics, ... In any case, I believe he sometimes writes very interesting things in his opinions columns - even when I completely disagree with his conclusions.Aquiles Páramo
at Universidad de los Andes has opened a very interesting seminar where current issues on teaching mathematics are discussed in a nonstandard way. I have not attended a single seminar session, but have followed the discussions on the webpage. Perhaps the most interesting aspect is the irony with which Páramo makes the combination of very different opinions possible - discussions that would be horribly bitter in other contexts seem somehow to work in his seminar.