Coming Soon:

The following books by Robert Paul Wolff are available on Amazon.com as e-books: KANT'S THEORY OF MENTAL ACTIVITY, THE AUTONOMY OF REASON, UNDERSTANDING MARX, UNDERSTANDING RAWLS, THE POVERTY OF LIBERALISM, A LIFE IN THE ACADEMY, MONEYBAGS MUST BE SO LUCKY, AN INTRODUCTION TO THE USE OF FORMAL METHODS IN POLITICAL PHILOSOPHY.
Now Available: Volumes I, II, III, and IV of the Collected Published and Unpublished Papers.

NOW AVAILABLE ON YOUTUBE: LECTURES ON KANT'S CRITIQUE OF PURE REASON
LECTURE ONE: https://www.youtube.com/watch?v=d__In2PQS60
LECTURE TWO: https://www.youtube.com/watch?v=Al7O2puvdDA

ALSO AVAILABLE ON YOUTUBE: LECTURES ONE THROUGH TEN ON IDEOLOGICAL CRITIQUE



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Wednesday, October 2, 2013

MY GRANDNIECE EMILY

I have linked before to the blog of my grandniece Emily, who is studying math in Budapest.  Here is another of her posts on her classes.  This one is the best description I have ever read of what it is actually like to study serious math.  You can find it here.  I would admit her to my doctoral program in a shot, if I ran one. 

Let me say just a word about this subject, with reference to Michael Llenos' comment yesterday.  There is an enormous difference between those of us who can, with hard work, master some bit of serious math, and people like Newton or Einstein or John von Neumann, who actually make the stuff up brilliantly.  At one point in my career [mid-seventies] I studied Game Theory rather seriously, eventually teaching a graduate course in which I went through von Neumann's proof of the Fundamental Theorem of Game Theory [that every  mixed-strategy two-person zero-sum game has at least one solution], complete with a full-scale proof of L. E. J. Brouwer's Fixed Point Theorem.  That is hard stuff, but I did it more by brute force than by any real mathematical insight.  By contrast, my old friend Robert Ackermann once told me that the great Russian-English mathematician Besicovitch could "see" objects in n-dimensional vector space.  He would "look" at such an object [say, an n-simplex] and rotate it in his imagination until he could see that something was just true of it.  Then he would go about the tedious business of actually producing a proof of what he could immediately intuit to be true.

Of all the things I cannot do [such as throw a curve ball or play the viola well or tap dance], there only two that I really would give a great deal for.  One is some facility with foreign languages and the other is the sort of formal mathematical intuition that Besicovitch and von Neumann and the rest had.  Lord, it must be wonderful to have that ability!

Meanwhile, I can read Emily's blog and enjoy vicariously her engagement with real math.

3 comments:

Michael Llenos said...

Besicovitch could see an n-simplex in his mind and without reasoning think up a mathematical proof concerning it? I am impressed. I never heard of anyone that gifted in math before. Sounds like the great mathematical genius John Nash.

By the way, I saw on a tv show that megladons today can grow up to 100 feet in length. I thought that there may be some still left that can only grow up to 60 feet in length. That still makes them giants though. I went scuba diving in highschool and saw no sharks. Of course, that doesn't mean they are not out there.

ren said...

There was an economist named Abba Lerner who could see three-dimensional diagrams in his mind. Before taking up the dismal science, he worked for a tailor in London. --ren

Robert Paul Wolff said...

I trust the suits fit!