Remembering Paul Halmos

October 2, 2011 4 Comments

Sunday October 2 is the 5th anniversary of the death of Paul Halmos.  Remembered for many mathematical contributions in fields such as operator theory and functional analysis, he is probably best known for his amazing ability to write about mathematics – especially mathematical textbooks.  However, what I love best about Halmos was his ability to write about mathematics for the non-mathematician.  He always seemed to have a way to express the beauty and wonder of mathematics in such a way that everyone would stop and think, “maybe mathematics isn’t as bad as I thought.”

Some of my favorite works by Paul Halmos:

  • I Want to Be a Mathematician … an automathography – This is a phenomenal autobiography, taking you deep into the life of an actual mathematician.  Not only do you learn about the research aspects of mathematics, but also about the human side of the subject.  It is a great read!
  • Paul Halmos: Mathematics as a Creative Art – This is a synopsis of a lecture Halmos presented in Edinburgh, Scotland in 1973.  It’s hard to summarize what he speaks about as it includes just about every aspect of mathematics but, if you ever want to know what a mathematician does or what people see in mathematics, then read this.  It is just a beautifully written piece.

Some of my favorite quotes by Paul Halmos:

  • “Don’t just read it; fight it!  Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary?  Is the converse true?  What happens in the classical special case?  What about the degenerate cases?  Where does the proof use the hypothesis?”
  • “It saddens me that educated people don’t even know that my subject exists.”
  • “Mathematics is not a deductive science, that’s a cliché … What you do is trial and error, experimentation, guesswork.”
  • “The heart of mathematics is its problems.”
Paul Halmos is a wonderful ambassador for mathematics, even 5 years after his passing.  In fact, it’s people like him who helped me discover the beauty and wonder of mathematics.  Thank you, Paul.

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