The human brain can do things beyond our ken, and one of them is instantiated by this video I was sent. In this very short video, 14-year-old math whiz Aaryan Nitin Shukla, a “human calculaator.” Here’s what Wikipedia says about him:
Shukla won the 2022 Mental Calculation World Cup at the age of 12 years old, setting event records in multiplication and square roots in the process. Additionally, during the record attempts portion of the event, he broke the organizer’s record for division and multiplied two 20-digit numbers together in 1 minute and 45 seconds.
Shukla returned to the Mental Calculation World Cup in 2024, winning the event for a second consecutive time, while winning all five categories and scoring more points per category than any prior competitor. Additionally, he set the following records during the event:
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- Mental Calculation World Cup calendar date record (answered all 100 dates given correctly in 1 minute)
- Mental Calculation World Cup multiplication record (breaking his prior record)
- Mental Calculation World Cup square roots record (breaking his prior record) (answered all 90 problems given with 86 correct and 4 incorrect)
- World record for addition (addition of 10 10-digit numbers, with an average time of 7.808 seconds over 10 questions)
- World record for square roots (square root of 6-digit numbers to 8 significant digits, with an average time 3.378 seconds over 10 questions).
See for yourself. The adding up of 100 4-digit numbers, with each addition taking half a second, is stupendous. Total time, including being shown all the numbers flashing by on a screen, is 30 seconds, and of course he got it right.
This is surely part of the performance in Dubai described below (notice the Dubai skyline):
In late 2024, Shukla set six new Guinness World records — three related to Flash Anzan, two related to multiplication, and one related to division — in a showcase event in Dubai.
Something about our brain makes this possible, and there’s something special about Shukla’s brain. What is it? Well, we won’t know in our lifetimes. We can see the output, but we can’t see the machinery.
Savant abilities are amazing. I don’t see any way we can expect to enable them in ordinary brains, though.
So cool. My Ph.D. advisor’s autistic son could specify the day of the week that I was born simply by knowing my birthday. I think there is a known shortcut that he used but, if so, he discovered it on his own.
These feats of calculation are indeed amazing. Part of it must be the way memory is organized, since calculations using long numbers requires keeping many, many numbers in one’s head at the same time. The calculations themselves are easy—4 x 4 for example—but holding the strings of numbers and their carry-overs is a huge challenge. If savants have discovered and are using shortcuts, we should try to learn what those shortcuts are. Maybe such calculations are possible for larger numbers of people than appears to be the case.
There’s at least two methods for working out the day of the week from the date. It’s actually pretty simple, I learned it as well. I can’t do it any more though. You need to memorise the formula and then a couple of key dates and years. Then you just work out the difference between the date you are given and one of those key dates. It took me a long time to do it mentally but it’s not too difficult and it’s pretty impressive. Just look up doomsday rule.
The algorithm to calculate days of week is simple enough. Suppose someone is born on April 8, 1960. What day of the week was that? First I need to know April 8 in some given year, say this year. Knowing that today is Thursday, September 25, 2025, I can figure out Tuesday, April 8, 2025.
Normal nonleap years have 365 days and 365 = 1 (mod 7) since 365 = 7×52 + 1. Thus nonleap years shift the day of the week by 1 while leap years having 366?days shift the day of week by 2. Therefore the shift to calculate is
shift = nonleap + 2xleap.
Since nonleap years plus leap years equals total years we can more simply say
shift = total + leap.
Between April 8, 1960 and April 8, 2025,
total = 65
To count leap years, I ignore the fact that 1960 was a leap year since the leap day of that year happened before April 8. Thus the leap years relevant are
1964, 1968, …. , 2024.
To count that set use formula
leap = (last – first)/4 + 1.
Thus for our calculation,
leap = (2024 – 1964)/4 + 1 = 16
We have
shift = total + leap = 65 + 16 = 81 = 4 (mod 7)
The shift is 4 and April 8, 2025 was Tuesday. To get the earlier April 8, 1960 count backwards by 4 from Tuesday and we get Friday. Conclusion: April 8, 1960 was a Friday.
When doing these calculations all numbers that arise can be reduced modulo 7 which keeps the numbers small. When using this to calculate historical dates, you must adjust the leap year count to take into account the fact that 2000 was a leap year but 1900 and 1800 were not leap years. Dates earlier than 1760 or so are irrelevant since the old Julian calendar was in use.
Everyone memorises the offsets for months and years, so you just need to add three numbers (day, monthcode, yearcode), and spit out the result modulo 7. I’m sure there are further shortcuts.
I did some of this long ago. It works.
https://www.geeksforgeeks.org/maths/trachtenberg-system/
As a mathematical biologist, I am pretty good at these things. Let’s see: 19 + 37 = 46? 66? Whatever. But I do know that x + y = z.
FSV x, y, z.
You can actually get within about 1% of the answer without doing any sums. If they are random numbers between 1,000-9,999, the mean will be very close to 5,500, and the total near to 550,000. That’s closer than Joe achieved, and he sets a high bar.