Guest Blog by
He is the Kruskal that did the MST algorithm,
the Kruskal Tree Theorem
and work on
However, this post is not on any of those topics.
Its a response and reflection on my post about the monotone subequence theorem.
In your post
on the monotonic sequence theorem
you said the following.
In those days it was harder to find out if someone else had
done what you had done since they didn't have google, but it may
have (in some cases) been easier since there were so many fewer
researchers- you could just call them. OH- but long distance was
expensive back then.
Yes, long-distance phone calls were expensive then. That's why
mathematicians seldom used phone calls for that purpose. They used
mail -- postal mail, of course.
Now that email has become almost universal, and is seen as slow and
stodgy compared with text messaging and other modes of communication
that I haven't kept up with, people have no real idea what
communication was like 50 years before.
The same thing was true 50 years ago. We didn't know then how
communication was done 50 years before that. In England, at least, it
was quite common for a well-to-do person to send a letter to a friend
to propose having dinner out together, or going to a play together,
or lots of other possibilities. They would expect to get a reply
within say 4 hours, time enough to send another message confirming
the arrangement for that evening.
In London at least, there were 4 deliveries/pickups per day, at least
for the upper classes.
When my wife and I visited England in the 1950s and stayed with my
sister who had moved there with her British husband, we personally
observed the following, which we had been told about. When a post
office mail person come to the red "post box", which displayed the
pick up times, he stood there waiting until the specified pick up
time, to the minute (by his watch). Only then did he open the box and
take out the letters and post cards. Everyone relied on the displayed
pickup times, and would hurry to the box just in time, knowing that
if they got there by the posted time the mail would go out right
away. Watches were not so accurate then, so I imagine that the post
office pick up people checked their watches against Big Ben or other
large public clocks.
My own dissertation also indicates how things had changed:
Paul Erdos was telling lots of people about a conjecture due to a Hungarian
mathematician, Vazsonyi, he was friendly with who he said "had died",
meaning that he left mathematics for a well-paying job with some
company -- I think it was an airplane manufacturer. I was one of many
people who heard him describe this conjecture. Roughly a year later,
I had put a lot of work into this problem, but was still not close to
a solution. By chance I bumped into Erdos at the Princeton Junction
station. We chatted. I don't know how the conversation turned to the
Vazsonyi conjecture -- probably I told him I had been working on it.
He said, oh, you must read a recent paper by Rado (a British
mathematician, also from Hungary). I quickly went to the library and
found his paper, which I read with fear and trembling. Had I been
It turned out that he had made significant progress, but hadn't
cracked the nut. His work combined with mine finally led to a solution.
Today, the equivalent of those two chance conversations can happen
via Google and email. I feel certain that science of many kinds is
developing much more rapidly than it used to for this reason (except,
perhaps, in fields where progress is kept secret for reasons of