Mathematicians often imagine puzzles for recreational purposes. And Leonhard Euler (1707–1783) — one of the most ingenious mathematicians of the 18th century and arguably of all time, came up with a puzzle in 1782 which an Indian mathematician solved 177 years later!
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It goes like this: Imagine that there are 36 officers belonging to six different military regiments, each regiment having six officers of different ranks. How does one arrange them in the form of a square such that each row and column has six officers, and no rank or regiment appears more than once in a row and column?
When Euler came up with his puzzle, he was able to solve most of it using Latin Squares but couldn’t complete it. Thereafter, Euler concluded that there did not exist a solution for the puzzle. In 1901, another mathematician from France, Gaston Tarry, tried and deemed the puzzle impossible to solve.
Mathematicians pondered over this puzzle for a long time and finally, in 1959, Sharadchandra Shankar Shrikhande and his mentor R.C Bose proved Euler’s conjecture wrong and solved the puzzle
So who is Sharadchandra Shankar Shrikhande? Read on to find out.
The puzzle and an Indian mathematician
Euler penned nearly 900 books during his career on a range of topics like optics, acoustics, lunar motion, calculus, geometry, algebra, and number theory.
Though the brilliant math wizard lost his eyesight early in life, his remarkable ingenuity and industrious nature were not undeterred.
However, in 1959, Shrikhande, Bose, along with their collaborator E T Parker, solved Euler’s puzzle. At the time of discovery, Shrikhande and Bose were in the Department of Mathematical Statistics at the University of North Carolina, Chapel Hill. Shrikhande was pursuing his PhD at the University where Bose joined as permanent faculty in 1949.
“Bose, Ernie (Parker) and I,” said Shrikhande, “had the rare privilege of seeing our works reported on the front page of the Sunday Edition of the New York Times.”
Major Mathematical Conjecture Propounded 177 Years Ago Is Disproved; 3 MATHEMATICIANS SOLVE OLD PUZZLE the headline had screamed of the NYT on April 26, 1959.
The three men, reported the New York Times, “are now known among their colleagues as ‘Euler’s spoilers’”. Their feat was announced in the annual meeting of the American Mathematical Society held in New York in April 1959.
Shrikhande and his life
Shrikhande, who had a very humble beginning, was born on 19 October 1917 in a family of ten siblings in Madhya Pradesh. His father worked at a flour mill in Sagar where they lived and strove hard to educate his children. Shrikhande was a bright student and consequently won several scholarships which helped him complete his BSc Honours degree at the Government College of Science, Nagpur. Here, he not only received the first rank but was also a gold medalist.
Finding a job was a struggle. But Shrikhande finally joined the Indian Statistical Institute (ISI) where he received some financial stability. This is where he met RC Bose, who acquainted him with the theory of statistical design of experiments. This is the knowledge which ultimately helped them solve the Latin square puzzle.
Thereafter, he went on to have a short stint as a lecturer of mathematics at the same college where he had studied.
A scholarship programme helped Shrikhande join the University of North Carolina as a PhD student, where his wife Shakuntala and their children soon joined him. They later returned to India in 1953 and lived in Nagpur till 1958. After this, he joined Chapel Hill as a visiting professor. “My two years’ stay there till 1960, was the most productive period of my research career,” he once wrote. In 1963, he joined the University of Bombay, finally retiring in 1978.
Between 1983-86, he served as the director of the Mehta Research Institute in Allahabad. Shrikhande and Shakuntala’s three children – Mohan, Asha and Anil, grandchildren and great grandchildren make for a big happy family. Sadly, in 1988 Shakuntala passed away after which Shrikhande moved to the US to live with his children.
In 2009, the ‘Euler spoiler’ returned to India and settled in Vijayawada in an ashram for underprivileged girls run by the in-laws of one of his granddaughters.
In the field of science India’s contribution needs no introduction. And among the giants who put India on the map of the world, belongs the name of Sharadchandra Shankar Shrikhande who solved a puzzle that had remained an enigma for 177 years!
(Edited by Saiqua Sultan)