As 2024 was coming to a close, I started paying attention to the number, 2025. Something about it was very warm, cuddly, and well-behaved. I couldn’t exactly tell why, but I just had this inkling that I should slow down, pay attention, and befriend this number.

“There is something in this number 2025 for you to discover and celebrate,” my intuition told me.

To see the soul of the number, I knew I needed to identify its prime numbers. But in the rush of life, who has time to do a prime-number decomposition? I let it pass.

Then, one day in early December, my colleague Dimitris broke the news to me. “Next year is going to be historic,” he said.

“Oh?” I responded.

“It’s 2025. That’s a perfect square — 45 squared!”

“Ah, how cool!” I exclaimed.

“The last time this happened was before you and I were born,” he continued. “And by the next time it happens, we will both be dead. So, this is the only time we’ll be living through a year that’s a perfect square.”

He was referring to the years 1936 (that’s 44 squared), and 2116 (that’s 46 squared).

My heart leapt with joy. What a special year indeed. I had no doubt this was what my intuition had been trying to tell me, even though I wasn’t listening.

Then, I had a flashback to a remarkable story I had come across when I was a college student. It is a story about a woman called Shakuntala Devi. Before we get into it, let me tell you a bit about her.

Shakuntala was born to a poor family in India. Her mother was 14 when she married Shakuntala’s father, who was 60 at the time. Her father was a lion tamer and a human cannonball in a circus troupe. “He also used to do card tricks,” she once recalled, “memorising the entire sequence of a deck. Once, he was unable to perform and asked me to step in. I was about three at the time. Soon, my shows became the highlight of the circus. Gradually, I started travelling to schools, colleges and universities to perform. By the time I was five, I was the family’s sole breadwinner.”

She didn’t get a school education, since her family could not afford it. But years later, Shakuntala got to travel around the world showcasing her remarkable mastery of numbers. One day, she arrived at Southern Methodist University in America where, in an epic encounter, she was challenged by mathematicians to compete against a mainframe computer. A professor went up and wrote a 201-digit number on the blackboard and asked her to compute the 23rd root of this number (a number which, if you multiplied it by itself 23 times, would get you to this 201-digit number on the board).

A UNIVAC 1108 computer at the U.S. Bureau of Standards was mobilised with over 20,000 instructions to solve the 23rd root problem. It got to the answer in one minute.

Shakuntala, on the other hand, took 50 seconds to declare that the 23rd root of that 201-digit number was 546,372,891.

And she was right.

It is reported that “she created a sensation in the U.S; American newspapers called her ‘The magician of mathematics,’ ‘The world’s most calculating woman,’ and ‘The Houdini of numbers.’”

But this story has a twist, and here’s where it goes from mystifying to magical. Very few people seem to know this part of the story.

It turns out, the professor who had labored to write the 201 digit number on the blackboard had made a mistake in two places, changing the number from what it was supposed to be to something different. We can understand why a mere mortal would fall prey to such errors — after all, you’re writing 201 digits in a certain precise sequence on the board. 

And yet, Shakuntala calculated the 23rd root of the number he was originally meant to write, not the 23rd root of the number he mistakenly wrote on the board.

How could this happen? How could she know what number he was supposed to write?

There’s one logical explanation.

If Shakuntala had been mentally computing the answer in some brute-force way, like a computer running millions of calculations, she would have, if she were successful, gotten to the 23rd root of the 201-digit number the professor had mistakenly written on the board.

But instead, she must have used a different approach, seeking to discover the essence of the 201-digit number, knowing it was one of the rare numbers which was a whole number multiplied by itself 23 times. Very few 201-digit numbers will have a whole number as their 23rd root — most will have a complex stream of decimals.

By ignoring the details in that 201-digit number, and focusing instead on getting a feel for it, distilling it to its essence — perhaps, by seeing its first few digits to get a sense of its size — she must have arrived at her answer through a healthy dose of intuition, on top of whatever analysis she might have done. Along the way, the professor’s two mistaken digits would have been washed away or auto-corrected in her mind. Unconsciously.

That is what I have always loved about mathematics. Logic helps, analysis helps, facts and numbers help — but behind it all lies the play of intuition. That is where all mathematical breakthroughs arise.

Perhaps that is as true in our search for truth within any other sphere of human pursuit as it is in mathematics. The equations of creation are all there, hidden in the ether, and they reveal themselves to those among us who pause to pay attention and go deep. Like Shakuntala did with the 201-digit number, and Dimitris did with the number 2025.

Where in your life are you experiencing soul-stirrings, inklings, tiny tugs? Are you making space to listen to your intuition and follow its wise whispers?

Warmly,
Hitendra

Note 1: When I first sat down to recount this story, I Googled Shakuntala. If you do the same, all you get are accounts of how a professor wrote a 201-digit number on the board and Shakuntala found its 23rd root in 50 seconds, beating the computer. They won’t tell you that the professor wrote the wrong number, and Shakuntala still got the right answer.

But that was what I remembered learning in college. Was my memory failing me on this? It was such a beautiful story — the idea that I might have recalled it wrong broke my heart.

And then, in a flash, I remembered sitting in the library at St. Stephen’s College, India, reading old issues of the Mathematical Intelligencer, which is a wonderful journal for math lovers. “That’s where you came across this story, Hitendra,” I told myself. 

I raced back to the internet, found the website for this journal, and located an article from 1983 called “Genius and Practice” on Shakuntala Devi. Voila! This was the one-page article I had read some 35+ years ago, which noted the two errors in the number the professor had written for Shakuntala. 

So, by learning of this article today, please know that you are partaking in the same pleasure I felt that day, sitting in the library of St. Stephen’s College, in the late 1980s.

Note 2: If you have read this newsletter up to this point, you deserve a special treat, so here it is. 

One of my favorite stories about Shakuntala is about the time she was stuck at an airport, late at night, due to a flight delay. She noticed the man next to her had a long box with him. 

“What kind of musical instrument do you play?” she asked him. 

It was a sitar, he let her know.

She told him she was very fond of listening to India’s sitar maestro, Ravi Shankar, and especially his collaboration with the great violinist, Yehudi Menuhin. “You’ve listened to it and liked it?” the man asked, showing an interest in what she was saying.

She told him, “If you are really serious about being a good sitar player, you should take classes from Ravi Shankar.”

He smiled, and responded, “I am Ravi Shankar.” 

“Oh!” she exclaimed. “I am going to be sharing this story for the rest of my life!”

Later, as they were boarding their flight, Shankar asked her for her name.

“Shakuntala Devi,” she replied.
“Oh!” Shankar exclaimed. “I am going to be sharing this story for the rest of my life!”

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