Dr. Ziaur Rahman :
Oxford, March 2019 – In a quiet, historic café, Professor Andrew
Booker sat deep in thought. A cup of coffee rested beside a sheet of paper filled with equations and numbers—33, 42, 114, 165. For years, he had been working to unravel a mathematical mystery that had persisted for nearly a century—a challenge originally linked to the legendary mathematicians Srinivasa Ramanujan and G. H. Hardy.
The story dates back to 1919, when G. H. Hardy visited an ailing
Ramanujan in a hospital. As Hardy took a seat beside him, he remarked: “The taxi I came in had a rather dull number—1729.”
Ramanujan, with a faint smile, replied, “No, Hardy, 1729 is far from dull! It is the smallest number expressible as the sum of two cubes in two different ways: 1729 = 1³ + 12³ = 9³ + 10³.”
Since then, 1729 has been known as the ‘taxicab number,’ and it
sparked deeper inquiries into similar mathematical structures. The broader question it inspired involves Diophantine equations—polynomial equations where only integer solutions are sought. One of the most famous forms of such an equation is: x³ + y³ + z³ = k, where mathematicians have long attempted to find integer solutions for various values of k. Some numbers yielded solutions quite easily, such as: 10 = 1³ + 1³ + 2³. However, others, like 33, remained elusive for decades.
In 2019, Professor Andrew Booker of the University of Bristol employed a supercomputer to finally resolve this long standing enigma. After 65 years of unsuccessful attempts, he discovered a solution for 33: (-80538738812075974)³ + (80435758145817515)³ + (12602123297335631)³ = 33.
This discovery was a landmark achievement in the field of number theory. Yet, even as he sat in the Oxford café, Booker knew that the challenge was far from over. Beyond 33, several numbers—including 42, 114, and 165—remained unsolved, presenting an enduring puzzle for mathematicians and computer scientists alike.
(The author is Associate Professor, Department of ICT, MBSTU)
