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Gödel’s Lost Letter is Two Years Old

February 1, 2011


Happy second birthday

All this is a special post, GLL is now two years old.

Today I want to thank you all for your support the last two years. This is the second anniversary of the start of this project, and I am very grateful to all for your support and interest.

I had hoped to get to {2^8} posts by this time, but so far this is the {250^{th}} post—close but not equal to a power of two. Well we should get there soon, and I hope you stay interested as we go on to the next power of two.

Birds and Frogs

On this special occasion I thought I would share something that I recently enjoyed greatly. It was reading a book titled, “The Best Writing on Mathematics 2010,” and is available here. I really enjoyed the book, the essays were diverse, well written, and several raised unusual topics. I suggest it to you with no reservations.

I will single out just one essay that was wonderful—it was written by Freeman Dyson and is on his division of mathematicians into two types: birds and frogs.

Dyson is a Fellow of the Royal Society, famous for his work on many aspects of physics and mathematics. Besides his deep contributions he is one of the best writers on any subject; his writing is a joy to read. I plan to discuss his work and how it relates to complexity theory another day. He has not won a Nobel prize, which led Steven Weinberg, a winner of the Nobel Prize for physics, to state that he was “fleeced” by the selection committee.

As you might guess birds soar above and create whole new theories.

Frogs are problem solvers, who work down in the muck, trying hard to make progress on open problems.

Dyson says that he is a frog, but he knows many birds. Birds build theories that help unify and open up new areas of mathematics, while frogs work on the ground. They solve problems one at a time. Both birds and frogs are needed to advance the field, both can make huge contributions, but they are very different in their approach to research.

He then goes on to discuss famous mathematicians that he has known, and further to classify them as birds or frogs. He considers Kurt Gödel as a bird and John von Neumann a frog. I agree that von Neumann was a frog—he was one of the greatest problem solvers of all time. Yet the classification of Gödel I find a bit puzzling. I would think that Gödel was unique, perhaps a bird and frog. He was a bird for creating a whole new view of mathematics with his Incompleteness Theorems, but he was also a frog in that he had to solve some quite difficult technical problems to prove his new theorems. He had to create whole new methods that were groundbreaking.

Open Problems

I again thank Ken and Subruk for their great support of this project. I especially thank you all who read, comment, agree, disagree, and interact with the blog. Thanks again.

Can we do a better job in the coming year? I hope so.

12 Comments leave one →
  1. February 1, 2011 3:37 pm

    Thanks for spending the time to post and answer our questions. It has been extremely enlightening ,and for me at least, inspiring as well.

    Not only has the content been great, but also the discussions held in the comments. It’s nice to see that in an Internet full of noise, a few distinguished people can still hold a civil, informative conversation (a trait that I fear is fast disappearing).

    Paul.

  2. February 1, 2011 4:06 pm

    Congratulations on two years, and may many more follow.

    Interesting take on problem solvers and theory builders. The best case is when the two types of researchers work together, solving hard problems by using new theory.

  3. February 1, 2011 4:44 pm

    It is good news whenever a new Gödel’s Lost Letter and P=NP column appears … and whenever a wonderful book like Mircea Pitici’s Best Writing on Mathematics: 2010 appears … and it is especially good news, whenever that book includes a Foreword by Bill Thurston that begins:

    The goal of mathematics is to develop enhanced ways for humans to see and think about the world. Mathematics is a transforming journey, and progress in it can better be measured by changes in how we think than by the external truths we discover.

    So today we have all won what gamblers call “a trifecta” … three good things at the same time!🙂

    Please permit me to borrow from Thurston’s foreword, in thanking you Dick and Ken, for your hard work in the past two years, which does so much to enhance how we “see and think about the world”, thereby helping us all—so kindly and patientlyl—with our shared “transforming journeys.”🙂

  4. Ross Snider permalink
    February 1, 2011 4:47 pm

    Didn’t von Neumann practically invent (at least) functional analysis and game theory? Obviously von Neumann was a great problem solver – but he also I think fits the frogird ‘blended’ category.

    • February 1, 2011 5:16 pm

      In fields as various as quantum information theory, complexity theory, game theory, theoretical computer science, PDEs, and microscopy, John von Neumann’s writings reveal that he was neither frog nor bird … he rather was what Scott Aaronson calls a prophet … and consciously so.

      We are all of us, in large measure, still following the prophetic roadmaps that John von Neumann laid down … more so than can be said of any other individual mathematician in history. That is why perhaps it is fair to assess von Neumann, uniquely, as neither bird nor frog … but something different altogether.

  5. February 1, 2011 10:48 pm

    Happy birthday

  6. caRh permalink
    February 2, 2011 1:10 am

    Why not crows-vs-frogs or birds-vs-beavers? With birds-vs-frogs (especially if “bird” is “eagle”, which perhaps eats “frog” for breakfast…) I sense an implication that birds have higher status than frogs in this business.

    In any case, “bird” and “frog” seem to be more like _states_ in which a mathematician may find himself in throughout his career, possibly switching between the two. Of course, a mathematician may find himself predominantly in one of the two states.

    Indeed, both classifications above, Gödel’s and von Neumann’s, seem puzzling.

    Happy birthday.

  7. Carsten Milkau permalink
    February 2, 2011 6:34 am

    Happy Birthday GLL!

    Many thanks to Dick, Ken and all commenters for the insights and enjoyment found in their posts.

  8. proaonuiq permalink
    February 2, 2011 7:29 pm

    Birds and Frogs or maybe Beavers (http://www.math.rutgers.edu/~zeilberg/Opinion95.html).

    But what about Mules and Moles ?

    Moles try to find the deepest theory, no matter if they have to go underground in their search: posterity is the game. Do they think they will see a different sun when reaching the other extreme of the earth ? Will they see anything at all ?

    Mules trot happily from problem to problem; hybrid and sterile they are apparently not concerned by posterity; they seem to be just making a living of mathematics. But if Mules could speak…

    …they would say: congrats for the second year !!

  9. February 3, 2011 2:17 pm

    “Can we do a better job in the coming year? I hope so.”

    I hope so too, but what you’ve done so far will be hard to match.

  10. leibnizengine permalink
    March 6, 2011 1:54 am

    Should we close the chapter ?

    Please read my proof :

    http://leibnizengine.wordpress.com/2011/02/23/p-np/

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