Have come across a problem in mathematics in an important prestigious field, which is number theory. And was able to demonstrate with publication in a formally peer reviewed mathematical journal. The problem is severe enough that the response from the mathematical community was to avoid, including that the chief editor tried to delete the paper out of the electronic publication.
What I did was show that you can present a mathematical argument, correct under ALL mathematical rules established, which gives an incorrect conclusion.
That was back in 2004. When the mathematical community did not act with the appropriate response realized had a bigger problem and endeavored since then to verify my own argument, and was able to so do with secondary means. I found another way to prove the same thing.
Relevance to national governments: mathematicians working for you who are number theorists may not be actually qualified for their positions. This problem can allow them to have invalid research which appears correct by established measures.
You can check. These people are NOT actually effective, of course. But with a problem that has been in the field since the late 1800's they have built a support structure around themselves.
They should not hold security clearances. They should not be relied upon for any mathematical research your government needs.
It is your job as governments to determine when these things are true. Good luck.
James Harris
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