Discussion Groups / English Usage / November 2006

The News.polyu.edu.hk entity posted thusly:

To our knowledge, we have never had an undetected error.

It brings to mind the proverbial saying:
"There are none so blind as those who will not see".

It also contains a hint of:
"Don't cross your bridges until you come to them".
--

Somebody once circulated a list of categories of questionable proofs
found in the research literature. You example is a borderline case. It
might be in the "It is obvious that ..." category, but it might equally
be in the class "Proof by no counter-example".

Years ago I gave a research student of mine a conjecture - something to
do with a class of programming languages, I think, although it might
also have had something to do with telephony - that looked promising,
and asked him to check whether it might be true. A week later he
returned with a "proof". I looked through it, and quickly found an error
in his reasoning. He couldn't see the error, so I explained it by using
the error to construct a counterexample to the "theorem".

The following week, he came back with a theorem saying "Except for the
following counterexample, ...".

I told him he was missing the point. The conjecture was clearly false.
To illustrate it, I showed him a second example.

You wouldn't believe it! One week later, he had a revised theorem saying
"Except for the following two counterexamples, ...". I had no choice but
to steer him towards a less theoretical research topic.

"What the eye doesn't see the heart won't grieve over."