5 ms·

Read Dijkstra, read Dijkstra. He is the master of us all.

by rumbler 13y ago

ColinWright 13y ago
For those who don't recognise this reference, it is a paraphrase of Laplace, who said, "Read Euler, read Euler. He is the master of us all."
- stiff 13y ago
  And the irony is that Euler was a really poor mathematician by Dijkstra's standards...
  - ColinWright 13y ago
    Interesting you should say that - do you have some supporting evidence? Could you point us at the material from which you draw that conclusion?
    - Someone 13y ago
      I think the evidence is https://en.wikipedia.org/wiki/Leonhard_Euler#Contributions_to_mathematics_and_physics https://en.wikipedia.org/wiki/Leonhard_Euler#Contributions_t...: "While some of Euler's proofs are not acceptable by modern standards of mathematical rigour..."
      - ColinWright 13y ago
        Perhaps Dijkstra would've understood that Euler was obtaining correct results while working in an era when mathematical rigor was (by modern standards) almost entirely absent. To appreciate Euler's work in context would almost certainly prevent one from considering him a poor mathematician.
      - epo 13y ago
        Wikipedia is "evidence"? Considering we are discussing Dijkstra, this is beyond irony.
    - stiff 13y ago
      Read the following EWD to get sneak-peak at Dijkstra's view of mathematics: http://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EWD1268.html http://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EW... Dijkstra's dream was reducing mathematics to formal logic, Euler's approach was almost on the opposite end of the spectrum, he used a lot of intuitive arguments sometimes dabbling in areas that didn't get a solid logical foundation for centuries to come.
      - btilly 13y ago
        In Euler's defense, he did his work before Fourier accidentally proved that everything mathematicians believed at that point rested on quicksand.
        gruseom 13y ago
        Can you expand on this? What did Fourier prove and why was it accidental and what was the quicksand?
        btilly 13y ago
        What Fourier proved is that every function could be written as a sum of sines and cosines. However his proof worked for "functions" like step functions, which were not at the time accepted as functions, and which could not be sensibly analyzed with the infinitesmal techniques of the day. It is hard to overstate the shock that came from a sum of nicely behaved functions turning into the pathological step function. If that was possible, what else could go wrong? And if infinitesmals could not be trusted, how could Calculus be put on a rigorous footing? The question of how to put mathematics on a secure footing were central to 19th century mathematics, and the issues lead directly to set theory, and the unavoidable dead end discovered by Goedel. (Ironically the work in logic that came out of that eventually lead to nonstandard analysis, which in turn justified the infinitesmal approach and most of the infinitesmal arguments. But by then mathematics didn't much care.)
        gruseom 13y ago
  - frozenport 13y ago
    Dijkstra's standard would have included number of publications, which perhaps only Gauss or Erdos would have toped.
    - ColinWright 13y ago
      Except that by count of pages, Euler is the most published mathematician ever. Who is the most prolific mathematician? Either Leonhard Euler, if counting by single authorship, or Paul Erdös, if counting by collaborative publications. -- http://wiki.answers.com/Q/Who_is_the_most_prolific_mathematician http://wiki.answers.com/Q/Who_is_the_most_prolific_mathemati... The most prolific mathematician of all time, publishing close to 900 books. -- http://www.guardian.co.uk/culture/2010/apr/11/the-10-best-mathematicians http://www.guardian.co.uk/culture/2010/apr/11/the-10-best-ma... Euler's work in mathematics is so vast that an article of this nature cannot but give a very superficial account of it. He was the most prolific writer of mathematics of all time. -- http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Euler.html http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Euler.h... He is considered to be the pre-eminent mathematician of the 18th century, and one of the greatest mathematicians ever to have lived. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. -- https://en.wikipedia.org/wiki/Leonhard_Euler https://en.wikipedia.org/wiki/Leonhard_Euler

Read Dijkstra, read Dijkstra. He is the master of us all.

by rumbler 13y ago

Read Dijkstra, read Dijkstra. He is the master of us all.

For those who don't recognise this reference, it is a paraphrase of Laplace, who said, "Read Euler, read Euler. He is the master of us all."

stiff 13y ago
And the irony is that Euler was a really poor mathematician by Dijkstra's standards...
- ColinWright 13y ago
  Interesting you should say that - do you have some supporting evidence? Could you point us at the material from which you draw that conclusion?
  - Someone 13y ago
    I think the evidence is https://en.wikipedia.org/wiki/Leonhard_Euler#Contributions_to_mathematics_and_physics https://en.wikipedia.org/wiki/Leonhard_Euler#Contributions_t...: "While some of Euler's proofs are not acceptable by modern standards of mathematical rigour..."
    - ColinWright 13y ago
      Perhaps Dijkstra would've understood that Euler was obtaining correct results while working in an era when mathematical rigor was (by modern standards) almost entirely absent. To appreciate Euler's work in context would almost certainly prevent one from considering him a poor mathematician.
    - epo 13y ago
      Wikipedia is "evidence"? Considering we are discussing Dijkstra, this is beyond irony.
  - stiff 13y ago
    Read the following EWD to get sneak-peak at Dijkstra's view of mathematics: http://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EWD1268.html http://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EW... Dijkstra's dream was reducing mathematics to formal logic, Euler's approach was almost on the opposite end of the spectrum, he used a lot of intuitive arguments sometimes dabbling in areas that didn't get a solid logical foundation for centuries to come.
    - btilly 13y ago
      In Euler's defense, he did his work before Fourier accidentally proved that everything mathematicians believed at that point rested on quicksand.
      - gruseom 13y ago
        Can you expand on this? What did Fourier prove and why was it accidental and what was the quicksand?
        btilly 13y ago
        What Fourier proved is that every function could be written as a sum of sines and cosines. However his proof worked for "functions" like step functions, which were not at the time accepted as functions, and which could not be sensibly analyzed with the infinitesmal techniques of the day. It is hard to overstate the shock that came from a sum of nicely behaved functions turning into the pathological step function. If that was possible, what else could go wrong? And if infinitesmals could not be trusted, how could Calculus be put on a rigorous footing? The question of how to put mathematics on a secure footing were central to 19th century mathematics, and the issues lead directly to set theory, and the unavoidable dead end discovered by Goedel. (Ironically the work in logic that came out of that eventually lead to nonstandard analysis, which in turn justified the infinitesmal approach and most of the infinitesmal arguments. But by then mathematics didn't much care.)
        gruseom 13y ago
- frozenport 13y ago
  Dijkstra's standard would have included number of publications, which perhaps only Gauss or Erdos would have toped.
  - ColinWright 13y ago
    Except that by count of pages, Euler is the most published mathematician ever. Who is the most prolific mathematician? Either Leonhard Euler, if counting by single authorship, or Paul Erdös, if counting by collaborative publications. -- http://wiki.answers.com/Q/Who_is_the_most_prolific_mathematician http://wiki.answers.com/Q/Who_is_the_most_prolific_mathemati... The most prolific mathematician of all time, publishing close to 900 books. -- http://www.guardian.co.uk/culture/2010/apr/11/the-10-best-mathematicians http://www.guardian.co.uk/culture/2010/apr/11/the-10-best-ma... Euler's work in mathematics is so vast that an article of this nature cannot but give a very superficial account of it. He was the most prolific writer of mathematics of all time. -- http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Euler.html http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Euler.h... He is considered to be the pre-eminent mathematician of the 18th century, and one of the greatest mathematicians ever to have lived. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. -- https://en.wikipedia.org/wiki/Leonhard_Euler https://en.wikipedia.org/wiki/Leonhard_Euler