While the very formidable Carl Friedrich
Gauss had explored the binomial theorem as a teenager and made a
name for himself

in the international astronomical
community by his accurate predictions of the orbit of the
newlyobserved asteroid Ceres, there are 
other indications that Arthur Conan Doyle
might have had someone else in mind. A possible
candidate is Simon Newcomb (18351909) 
The Binomial Theorem has a long history
going back to Euclid in the 4th century BC and Pingala in India
in the 3rd century BC. 
In the 10th century Indian mathematician Halayudha wrote a
commentary on Pingala and the 10th century Persian mathematician 
Abu Bakr ibn Muhammad ibn al Husayn
alKaraji also wrote at length on what became known as Pascal's
Triangle. From China there 
was similar work by Yang Hui (12381298)
as well as his predecessor Jia Xian (10101070). Blaise Pascal
(16231662), despite poor 
health for many years, managed to collect and extend many
results in 1658, but it was Newton's work in the 1660s that
really made the 
binomial theorem a powerful tool. Newcomb's own work on the
Binomial Theorem was not notable, although he did make a great
many 
contributions to astronomy. Of interest in the context of BEISA
is the use of older French observations of planetary positions
by 
Newcomb to correct marine navigation tables (based
on smaller samples and fewer years). It is not obvious why Doyle
chose the 
Binomial Theorem or asteroid orbital calculations as high water
marks for Moriarty. 
With considerable regret, we must go further back in time to
1810. Alas, not to watch the Feanorian mind of Gauss at work,
but rather 
to confront a mystery worthy of Sherlock Holmes. 
© 2018 Peter F. Zoll. All rights reserved. 