FW: Edsger Dijkstra, famous computer scientist, on teaching math and on doing math

Kreinovich, Vladik vladik at utep.edu
Mon Mar 1 14:55:24 EST 2021

FYI, I hope Yulia and Vladimir do not mind that I forward their memories  to yet another mailing list

From: Yulia Kahl
Sent: Monday, March 1, 2021 12:32 PM

I have wonderful memories of Professor Dijkstra from my undergraduate days at U.T. Austin, where I took a class from him on Mathematical Methodology. He taught us the value of symmetry, to avoid useless words and symbols, and to be active participants in the learning process. One of our activities was to compare proofs and to evaluate them. I still treasure my notes from his class, especially his typewritten introduction. Luckily, a gentleman has transcribed it, and it is now accessible to everyone:


Best wishes,


From: Vladimir Lifschitz <lifschitzv at gmail.com<mailto:lifschitzv at gmail.com>>
Sent: Wednesday, February 24, 2021 4:04 PM

Dear All,

Krzysztof Apt and Tony Hoare are trying to put together scientific testimonials that would clarify the influence of Edsger Dijkstra's work on other people's research and shed light on his interactions with others.  I’d like to share with you my contribution to this document.  When completed, it will be posted in the Dijkstra Archive (https://www.cs.utexas.edu/users/EWD<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.cs.utexas.edu%2Fusers%2FEWD&data=04%7C01%7Cmichael.gelfond%40ttu.edu%7C7beaa4844fcc44ec994008d8d910aae6%7C178a51bf8b2049ffb65556245d5c173c%7C0%7C0%7C637498012894019995%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=y1d2FDL4eFR9zWroHQ1exU98WmZPg2H1vT1ODqyY5MI%3D&reserved=0>) under the title "Edsger W. Dijkstra: a Tribute."

Best wishes,


Friendship with Edsger and Ria was a wonderful gift that Austin gave us when my wife and I moved here in 1991.  Losing them many years later was a great personal loss.

Edsger was interested in “streamlining” mathematical arguments, and his views on the organization of proofs had a profound effect on my professional work. As an undergraduate, I had learned that proof can be best understood as natural deduction—introducing and discharging assumptions.  Conversations with Edsger convinced me that, in many cases, it is better to present a proof as a chain of equivalent transformations.  As an example, Edsger took the list of theorems that students in my logic class had been given as exercises on the use of Peano axioms, and showed me how to prove them in the Dijkstra/Scholten “calculational style.”  The proofs were concise and elegant, like every other product of his thought.

This was an eye-opener. Examples of calculational proofs in Edsger’s writings were so impressive that I even asked myself whether every possible use of natural deduction in classical logic can be replaced, in principle, by calculational reasoning.  The answer turned out to be yes (published in the Annals of Pure and Applied Logic in 2002).

Using simple, economical notation is an important rule of mathematical writing that I learned from Edsger.  No unnecessary subscripts!  One day he showed me a place in a draft that I had asked him to review, where formulas included (I am ashamed to admit) two levels of subscripts, and said: “I showed this page to my students as an example of how NOT to write mathematics.  I didn’t tell them, of course, who the author is.”
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