# Shakuntala Devi: Genius or Trickster?

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Shakuntala Devi is regarded by many as a genius and some others as a fraud. There is no doubt that she possessed extraordinary abilities in calculations

This is Shakuntala Devi in 1969

So, one thing is clear, she demonstrated again and again, under different situations, a tremendous ability to calculate really complex calculations. That itself should mark her as a genius.

#### So how did Shakuntala Devi calculate so quickly?

Peter S Magnusson provides what is perhaps one of the most comprehensive answer to this question. We reproduce some parts of his analysis

1. He calls her art Mathemagic and places her in the league of notable “mathemagicians” include Martin Gardner, Arthur T Benjamin, Raymond Smullyan, and Persi Diaconis. See this short video by Benjamin, Start at the back end of the Video.

2. She knew the ‘Trade’ well and prepared for it. He details with one example

• Cube root of 61,629,875.
• The third root of an 8-digit number will have exactly three digits (because it will be between 215 and 464).
• The third digit is trivial, because a number cubed, modulo 10, only depends on the last digit. In fact, most of the digits are identical – if the last digit of a cube is 1, 4, 5, 6, 9, or 0, then it’s the same in the root; 2 and 8 swap places as do 3 and 7. So we know the last digit is “5”.
• The first digit is trivial too, in an 8-digit cube it can only be 2, 3, or 4. In this case 61 is close to 64, which is 4 cubed.
• In fact, it’s very close, so we know the answer will be just below 400, because 400 cubed is 64,000,000. Now, what 3-digit number is just below 400 and ends in 5?

3. Her preparation included remembering Logarithmic tables

• The problem, as posed, was to take the 23rd root of this number 916,748,676,920,039,158,098,660,927,585,380,162,483,106,680,144,308,622,407,126,516,427,934,657,040,867,096,593,279,205,767,480,806,790,022,783,016,354,924,852,380,335,745,316,935,111,903,596,577,547,340,075,681,688,305,620,821,016,129,132,845,564,805,780,158,806,771
• To answer this he assumes Devi may have memorized 1000 logarithms to 5 digits
• He says the choice 23rd root of a 201-digit number was not accidental. The log tables needed are much smaller. For a 201-digit number, the 23rd root will have the first 3 digits in the range of 496 to 548. That’s not 1000 different logs to remember, that’s only 53, that’s 95% less stuff to remember for that stage. Because 9-digit numbers can be anywhere from 185 to 207 digits long. Limiting it to 201 digits simplifies it a lot.

So what this tells us is Shakuntala was smart, worked hard and prepared really hard to deliver such mind blowing accuracy. In what she did, she was both an artist and a mathematician. When combined, what we saw was a genius in action.

#### Shakuntala, the biopic will be released on Amazon Prime on July 31st

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