Moriarty may have been inspired in part by two real-world mathematicians. If the characterisations of Moriarty's academic papers are reversed, they describe real mathematical events. Carl Friedrich Gauss wrote a famous paper on the dynamics of an asteroid[18] in his early 20s, and was appointed to a chair partly on the strength of this result. Srinivasa Ramanujan wrote about generalisations of the binomial theorem,[19] and earned a reputation as a genius by writing articles that confounded the best extant mathematicians.[20] Gauss's story was well known in Doyle's time, and Ramanujan's story unfolded at Cambridge from early 1913 to mid 1914;[21] The Valley of Fear, which contains the comment about maths so abstruse that no one could criticise it, was published in September 1914.

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So, ok. The point here is that Doyle's Moriarty is described as the author of two major works in math, one of which is "a treatise upon the binomial theorem, which has had a European vogue. On the strength of it he won the mathematical chair at one of our smaller universities", and the other "The Dynamics of an Asteroid, a book which ascends to such rarefied heights of pure mathematics that it is said that there was no man in the scientific press capable of criticizing it". These are mentioned respectively in The Final Problem and in The Valley of Fear.

Whoever wrote that paragraph on Wikipedia argues that this looks like Doyle took Gauss' and Srinivasa Ramanujan's work and swapped subject matter and reception. Ok, reasonable enough. Minor detail: The Final Problem was written when Ramanujan was 6 years old. Doyle can't have decided to make Moriarty's work about the binomial theorem in 1893 because of work Ramanujan didn't make known outside of India until 1913. Lacking that aspect of the alleged swap, there's no compelling argument to say Doyle characterised one of Moriarty's work as 'so hard nobody else understands it' as a reference to Ramanujan, even if that particular bit was written in 1914. So the swapping argument is... kind of empty?