Whenever Mathematicians (or engineers or other such people
with a sound working knowledge of mathematics) have tried to
provide solutions to historical problems, the quite justified,
I think, reaction of Historians has been to reject the conclusions
pointing out the historical unlikelihood of the results in most cases.
For instance, it's usually difficult for Mathematicians to grasp
the basic historical fact that if one of their conclusions implies
a greater degree of sophistication in the people they deal with
than is warranted by the body of other evidence we have on
that culture, then the conclusion is suspect because it exceeds
that people's capability. It's more reasonable to conclude that the
new alleged evidence is the result of a misinterpretation than to
change our whole perception (based on millions of independent
pieces of evidence gathered over the years) of the people involved
and their culture, based on that single new element.
Likewise, Historians often misinterpret (either exaggerating or
minimizing) the mathematical or other accomplishments of a given
culture due to their lack of understanding of the data they are
dealing with.
Hopefully, this problem will be solved once scholars doing research
on these subjects agree to actively consult and work with their peers
in the relevant fields involved before writing anything they might
regret later.
I cannot provide right away examples of debatable results by
Mathematicians dealing with historical problems, but in several
congresses and conferences I have had to strongly object to
conclusions by Chemists, Engineers and even Physical
Anthropologists obtained with total disregard as to the historical
validity and relevance of their alleged discoveries.
Juan Jose Castillos