Legend has it, the Czar of Russia challenged the brilliant mathematician Leonard Euler with a puzzle he couldn’t solve, despite years of effort. 177 years later, three mathematicians finally cracked it—two of them Indian.
Euler, born in Switzerland, made a name for himself in St. Petersburg, Russia, working under the protection of the czars. His mathematical genius thrived, solving complex problems for both the Academy and the government.
The famous puzzle asked by the Russian Czar, as believed, went like this: Can 36 officers, from 6 regiments and of 6 different ranks, be arranged in a square so that no row or column repeats a rank or regiment? It stumped Euler.
Years later, Euler was almost blind then, when he wrote a paper, introducing the concept of “Graeco-Latin squares.” He conjectured that no such squares exist for certain numbers, including 6 & 2. This became known as Euler’s Conjecture, made in 1782.
Euler’s conjecture was widely accepted for 177 years. He believed no solution existed for numbers like 6, 10, 14—so-called “oddly even” numbers. His conclusion: Latin squares (which arrange elements without repetition in rows and columns) wouldn’t work for these cases.
177 years later, fast forward to 1959, a young boy was stopped by his teacher on the school stairs.
“Have you seen today’s New York Times?” the teacher asked.
Confused, he shook his head. “Your father’s name is in it.”
On that day, The New York Times ran a story that shook the math world: Euler was wrong!
Three mathematicians—Shrikhande, R. C. Bose, and E. T. Parker—proved his 1782 conjecture incorrect, sending shockwaves through the community.
The kid was Mohan, the second son of the brilliant mathematician Sharadchandra Shankar Shrikhande. Born in a middle-class Marathi family in Madhya Pradesh, Shrikhande’s journey to global fame was anything but easy.
The post-World War II economic crunch made his family’s life difficult, but a small advertisement changed everything. It led him to the Indian Statistical Institute in Kolkata, where his story began.
Later, he earned a scholarship to the University of North Carolina, where he worked with Prof. R. C. Bose. Together with Parker, their intense correspondence and work bridged geometry, combinatorics, and statistics, disproving Euler’s famous conjecture.
The proof was monumental—a striking unity of applied and pure science, one of the most iconic mathematical breakthroughs of the 20th century. Shrikhande’s contribution was so pivotal that it forever changed how we understand orthogonal Latin squares.
Their proof, elegantly blending geometry, combinatorics, and statistics, shattered a 177-year-old belief. The legendary Euler had made a rare mistake.
The world noticed. A New York Times headline in 1959 screamed “Euler’s Spoilers,” celebrating the three mathematicians who disproved the master.
Shrikhande’s journey was far from over. After returning to India in 1960, he joined Banaras Hindu University and later, the University of Bombay, where he became a beloved teacher.
His quirky habits endeared him to his students. He often used discarded envelopes from incoming mail to jot down his research. These throwaway covers bore much of his groundbreaking work.
Not just known for his work on Euler’s puzzle, Shrikhande also made waves with the Shrikhande Graph—a structure that intertwines algebra, group theory, and topology.
Euler may have guessed wrong, but Shrikhande and his colleagues proved that even the greatest minds can be challenged. And in doing so, they paved the way for future generations to think beyond the impossible.
Prof. Shrikhande’s life mirrored the unique graph named after him—one-of-a-kind.
Sources:
Euler, L. (1707). Leonhard Euler (1707-1783). ams.org/bookstore/pspd
Hardikar, J. (2020, May 8). Indian Maths Genius Who Debunked Euler’s Theory, Made it to NYT Front Page Dies at 103. News18. news18.com/news/opinion/i
Shrikhande, S. S., Sr. & Nithyanand Rao. (2018). Euler’s spoiler turns 100. In Asia Pacific Mathematics Newsletter (Vol. 8, Issue 1, pp. 15–17). asiapacific-mathnews.com/08/0801/0015_0
Andersen, L. D. (2007). Chapter on The history of latin squares. Department of Mathematical Sciences, Aalborg University. Research Report Series No. R-2007-32 vbn.aau.dk/ws/portalfiles
