Re: Erd?s - the most prolific mathematician of all time

On 2/1/2024 3:25 PM, Peter Moylan wrote:

On 02/02/24 02:29, db wrote:

On 30.01.2024 18.29, occam wrote:

On 30/01/2024 16:03, J. J. Lodder wrote:

occam <occam@nowhere.nix> wrote:

[...]

You say Euler wins 'by any reasonable criterion'. I hope you do not
include 'pages of math' in that criterion.  That is an even less
convincing criterion than the number of publications.
>
If I play my usual game of 'who would I rather share a desert
island with - Euler or Erdos?'  - I'd probably choose Euler. But
that's only because Erdos sounds like a weirdo who was detached
from reality, to the exclusion of anything that was not
mathematics.

>
I am right now reading electrochemistry papers written around
1890-1906 and it struck me how much space they were given, so the
language is very detailed and slow moving, on many pages per paper.
Maybe this applied to maths papers in Euler's time.

 I suspect that part of the difference is that we've developed ways of
saying things more precisely and more compactly since then. Sometimes
even a simple change in terminology can lead to more compact statements.
 In my researches the following paper turned out to be important.
 E. Stiemke, Uber positive L ̈osungen homogener linearer Gleichungen.
Mathematische Annalen, 76:340–342, 1915.
 It's a result that is apparently well-known in the mathematical
economics literature, but nobody ever gives a proof; they just cite
someone else who also fails to give a proof. Nobody mentions Stiemke,
and in fact I've now forgotten how I managed to track down that paper. I
needed the proof for a result of mine on stability of interconnected
systems.
 The paper is hard to read, and not only because I don't read German.
Even after I'd painfully translated it into English, and checked my
translation with a native speaker of German, I still couldn't understand
his proof. His language was too unclear.
 Eventually I realised that his main theorem would be more understandable
if expressed in the language of matrices. (Matrices were well-known by
1915, but perhaps some mathematicians considered them to be too
new-fangled to use.) After that I was able to find my own proof, which
was very different from Stiemke's proof. I still don't understand his proof.
 My point here is that a change of notation reduced the problem to one
that was more clearly and compactly stated, and easier to prove.
 

 >>> If I play my usual game of 'who would I rather share a desert
 >>> island with - Euler or Erdos?'  - I'd probably choose Euler. But
 >>> that's only because Erdos sounds like a weirdo who was detached
 >>> from reality
             were  Euler  or  Gauss  regular (normal) guys?