Of course, this is quite amazing. Often people with savant syndrome can do these feats of math. However there is also a class of people who can do this with even more creative problems.
There was a BBC documentary one time that investigated this guys calendar math skills. He wanted to know whether he was a savant or something else. After testing the researchers told him he was in that special class. They had given him a calendar problem that was not algorithmic and yet he was able to rattle off the dates as fast as he could speak.
Some folks with this special math ability are synthetes ie they associate numbers with colors, shapes or smells or some other sensory phenomena and then use it to compute the answers. However its not clear how they can do this and its completely different for each person. The only common denominator is that the areas neighbor one another in the brain and there seems to be cross communication going on between these areas giving rise to this special skill.
There is also the Tractenberg arithmetic rules which can be taught to anyone that allows you to do multiplication of large number without the need for summing the intermediate results. Summing is embedded in the method. The original goal of the system was to eliminate use of multiplication tables and the associated method of multiplying with each digit and then summing the shifted intermediate values to get the answer.
https://en.wikipedia.org/wiki/Trachtenberg_system
There's a beautiful movie called Gifted where the young star learned the system for the movie. SHe portrayed an undiscovered math prodigy protected by her uncle from the external forces of expectation and failure who had destroyed her mother leading to her mother committing suicide.
Personally when I was in elementary school, I wanted to be smart and would sometimes compute small numbers and recite the answerback to someone who challenged me. The trick was I'd ask the kid a question and while they were thinking of the answer I did the computation and surprised them with the answer. I did this a couple of times and then felt it was better to quit while I was ahead.
I did have a friend who could in fact do this but I didn't meet him until highschool. He was an MAA champion and got on the MAA team for a competition in Europe with the British and Russians. Sadly, the US team got trounced because their training was on multiple choice test questions whereas the British and Russian kids had fill in the blanks type problems. This occurred sometime in 1967 or 68 but I never knew when. My friend later told me the story of what happened.
There's also a BBC documentary of kids training for the international math olypiad. Many of these kids are savants in math. Others are autistic and focus on math.
https://watchdocumentaries.com/beautiful-young-minds/
More on savants:
and this one on Daniel Tammet, a synthete savant who learned Icelandic in two weeks:
