D. R. Kaprekar: The Recreational Mathematician

Dattatreya Ramchandra Kaprekar (1905–1986) was an influential Indian recreational mathematician who made remarkable contributions to number theory despite working outside the world of professional academic research. He became widely known for identifying several fascinating classes of natural numbers, including Kaprekar numbers, Harshad numbers, and self numbers, as well as discovering the famous Kaprekar’s constant. His work demonstrated that mathematical creativity and insight can emerge from passion and curiosity rather than from prestigious research institutions alone. Today, many of his discoveries continue to inspire mathematicians, teachers, and students around the world because of their simplicity, elegance, and surprising numerical patterns.

Kaprekar received his secondary education in Thane and later studied at Fergusson College in Pune. His exceptional mathematical talent became evident during his college years. In 1927, he won the prestigious Wrangler R. P. Paranjpye Mathematical Prize for presenting an original mathematical work, an achievement that highlighted his innovative thinking and analytical ability. He later attended the University of Mumbai, where he completed his bachelor’s degree in 1929.

Although Kaprekar possessed extraordinary mathematical talent, he spent most of his professional life as a schoolteacher at a government junior school in Devlali from 1930 until 1962. Unlike many famous mathematicians who worked in universities or research institutions, Kaprekar conducted his investigations independently during his free time. His dedication to mathematics despite limited academic support makes his achievements even more impressive. Over time, his discoveries gained international recognition and became important examples in recreational mathematics and number theory.

One of Kaprekar’s most celebrated discoveries is Kaprekar’s Constant, 6174, identified in 1949. This constant is reached through a fascinating process involving four-digit numbers with at least two distinct digits. By arranging the digits in descending and ascending order and subtracting the smaller number from the larger one repeatedly, the result eventually reaches 6174 in no more than seven steps. This numerical phenomenon continues to amaze students and researchers because it reveals hidden patterns within ordinary numbers and demonstrates the unexpected beauty of mathematics.

Kaprekar also introduced Kaprekar numbers, positive integers whose squares can be split into parts that add back to the original number. For example, $45^2 = 2025$, and $20 + 25 = 45$. In addition, he studied Harshad numbers, meaning “joy-giver” in Sanskrit, which are divisible by the sum of their digits. 

He also described self numbers, or Devlali numbers, which cannot be generated by adding any number to the sum of its digits. Another contribution was his study of Demlo numbers, formed from the squares of repunits such as 1, 11, and 111, creating beautiful palindromic patterns like 121 and 12321. Through these discoveries, Kaprekar showed that mathematics can be both playful and deeply meaningful.
D. R. Kaprekar: The Recreational Mathematician

Jagadish Chandra Bose

Jagadish Chandra Bose was born in the 30th of November 1858 in Faridpur in Dacca District. His father Bhagaban Chandra Bose was a Deputy Magistrate.

Jagadish Chandra Bose had his early education in village school in Bengla medium.  In 1869, Jagadish Chandra Bose was sent to Calcutta to learn English and was educated at St. Xavier’s School and College. He graduated with degree in science from St. Xavier’s College Calcutta in 1879.

In London he first studied medicine. But he repeatedly fell ill. So he had to discontinue the course. In 1880, he received admission and studied Natural Science in Christ Church College, Cambridge.

At Cambridge, he worked with a professor of physics, Lord Rayleigh. It was here that he befriended with the famous biologist Dr Sidney Vines and became interested in biology.

Returned from Cambridge in 1885, he was appointed a Professor of Physics in Presidency College, Calcutta. Here, he initiated his experiments in various areas in physics and botany.

He invented wireless telegraphy in 1895 a year before Guglielmo Marconi patented his invention.

He converted a small enclosure adjoining a bathroom in the Presidency College into a laboratory. He carried out experiments involving refraction, diffraction and polarization.

Chandra Bose received the D.Sc degree of London University in 1896 for his work on the determination of wavelength of electric radiation by diffraction grating.

In 1915, he left the university to found the Bose Research Institute, Calcutta.  He was able to interest the world’s scientists in his work and his fame grew. Jagadish Chandra Bose died on November 23, 1937.
Jagadish Chandra Bose