There is not much actual mathematics in this sequel which, like its predecessor, features a version of Sherlock Holmes portrayed by Robert Downey Jr. as more of an action hero than the one in Sir Arthur Conan Doyle's stories. However, as in the original books, Holmes' arch enemy, Professor Moriarty, is decisively portrayed as being a professional (and evil) mathematician.
The film features a shot of Moriarty's blackboard and a code based on Pascal's Triangle. Both of these mathematical details were devised by Alain Goriely and Derek Moulton of Oxford University's Mathematical Institute, with the intention of making them not only mathematically but also historically accurate. Unfortunately, both fly by so quickly that it is not possible to see anything but the quickest glimpse of either of them. (At least, I was not able to, while viewing it as an in-flight movie. Perhaps by pausing an HD version, one could do better.)
Aside from that, the only interest this Website has in this film is in its portrayal of a mathematician. He is certainly shown as being highly intelligent, as well as influential and famous. (People are always asking him to sign copies of his manuscript on asteroid dynamics and he was selected to help coordinate the international political dialogue which is at the center of the plot.) Of course, he is also portrayed as being utterly heartless and devious. (By coincidence, he is portrayed by Jared Harris who also plays mathematician Hari Seldon in the Apple TV+ adaptation of Foundation.)
Finally, I would like to remark on the most mathematical comment made in the film. At one point, Holmes tries to negotiate with Moriarty, asking him not to harm the newly married Doctor Watson. Moriarty's reply is that "in celestial mechanics, whenever two bodies collide, there is always damage of a collateral nature". (Well, perhaps I'm paraphrasing. As I said, I saw the film on an airplane and was not able to copy down the exact wording. Please correct me if you know exactly what he said.) In any case, this is a silly remark since there certainly is no such rule in celestial mechanics!
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