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Many students believe that people who are good at maths were simply born fast. Shakuntala Devi, India's "human computer", looks like proof. But a psychologist who measured her mind found something more useful for the rest of us. This post covers her most carefully recorded feats, what the testing showed, a worked example of the kind of shortcut she used, and a practice routine you can start this week.
What could Shakuntala Devi do?
The most careful record of her calculations is a paper by the psychologist Arthur Jensen, "Speed of information processing in a calculating prodigy" (Intelligence, 1990). He quotes the Guinness Book of Records (1982): on 18 June 1980 she multiplied two 13-digit numbers picked at random by the Computer Department of Imperial College, London, 7,686,369,774,870 × 2,465,099,745,779, and gave the correct answer, 18,947,668,177,995,426,462,773,730, in 28 seconds. He also cites a 1977 demonstration at Southern Methodist University where she found the 23rd root of a 201-digit number in 50 seconds, confirmed by a computer.
Her life story is told in her obituaries. The Hindu (2013) reports that her father, who had joined a circus, noticed her memory for numbers when she was three, and that she began public demonstrations at six. She had no formal schooling. The BBC obituary notes that she died in Bengaluru in April 2013 and wrote books such as Fun with Numbers and Puzzles to Puzzle You.
What did the scientist find when he tested her?
Jensen first watched a 1988 demonstration at Stanford, where audience members wrote problems on the board from computer printouts. She answered each in under a minute, usually in seconds. He handed her two cards at once: the cube root of 61,629,875 and the 7th root of 170,859,375. She answered 395 and 15 almost before his wife could start the stopwatch.
Then she spent about three hours in his Berkeley laboratory doing simple reaction-time tasks: pressing a button when a light came on, picking the odd light out of three, and checking whether a digit appeared in a short list. Jensen compared her times with those of college students and older adults on the same tasks.
Her basic speed was not exceptional. Jensen wrote that her "rather unexceptional reaction times" contrasted so sharply with her calculating speed that her skill "must depend largely on the automatic encoding and retrieval of a wealth of declarative and procedural information in long-term memory rather than on any unusual basic capacities." He added that a motivational factor that sustains "enormous and prolonged interest and practice" probably matters more than general intelligence or raw speed.
He gave an everyday example. Most people answer 4 × 25 as fast as 4 × 3, even though they never learned a 25 times table, because they know facts like "four quarters make a whole". Devi had built that kind of web of facts for an enormous range of numbers.
Worked example: a cube root in your head
You can do Jensen's first card yourself. The trick works for perfect cubes only.
Step 1: learn the last digits of cubes. Cubing 0 to 9 gives last digits 0, 1, 8, 7, 4, 5, 6, 3, 2, 9. Every last digit appears exactly once, so the last digit of a perfect cube tells you the last digit of its root. A cube ending in 5 has a root ending in 5; a cube ending in 7 has a root ending in 3.
Step 2: find the last digit. 61,629,875 ends in 5, so the root ends in 5.
Step 3: find the leading digits. Remove the last three digits to get 61,629. Find the largest whole number whose cube is at most 61,629. Since 39³ = 59,319 and 40³ = 64,000, that number is 39.
Step 4: combine. The root is 395. Check: 395³ = 61,629,875.
Common mistakes:
Using it on a number that is not a perfect cube. The method gives a wrong answer with no warning. Check by cubing.
Mixing up 2 and 8, or 3 and 7. A cube ending in 8 has a root ending in 2, not 8.
Dropping the wrong number of digits. Always remove exactly three, because each extra digit of the root adds about three digits to the cube.
A practice routine built on the research
Jensen pointed to studies by the psychologist K. Anders Ericsson, in which ordinary college students who started with a memory span of 7 digits could recall more than 80 digits after about 200 practice sessions over two years. Skill with numbers can be built.
Week 1: squares to 30. Learn them until recall is instant. Test yourself in random order.
Week 2: cubes to 20 and the last-digit table. Do five cube roots a day from your own list of perfect cubes.
Week 3: friendly facts. Collect shortcuts like 25 = 100/4 and 125 = 1000/8. Use them in every calculation you meet in physics or chemistry.
Every day: estimate first. Before using a calculator, say an approximate answer aloud. Compare.
Our post on deliberate practice explains how to make practice like this effective, and the story of D. R. Kaprekar shows another Indian mathematician's love of number patterns. When a calculation goes wrong and you cannot see where, the Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer.
Start today: write the last-digit table for cubes from memory, then find the cube root of 103,823 without a calculator.
