In 2013, a new user named Cleo stormed the online mathematics forum with unproven answers. Today she is an urban legend. But who was she? Editor’s choice for 2023.
Introduction
Welcome, math geniuses! I’m Tulika Bose, the first multimedia publisher at Scientific American. If you miss that famous column by Martin Gardner in Scientific American from the 1950s – don’t worry, we have some fantastic math content in the new year.
Cleo, the unknown evil in the online mathematics world
In 2013, Ron Gordon, a patent agent and former physicist from Massachusetts, spent enough time on an online mathematics forum called Math Stack Exchange to qualify for a full-time job. Gordon solved 2954 math problems over a decade on Math Stack Exchange, but he became famous for his answer to one particular integral. On November 11, 2013, a user on Math Stack Exchange asked a question:
“I need help calculating this integral: the integral from negative one to one of one divided by x times the square root of one plus x over one divided by x times the natural logarithm of 2x squared plus 2x plus one, all divided by 2x squared minus 2x plus one, dx.”
This integral was extraordinarily complex, with many parts to it. The original poster tried using some computer programs, but none could provide what is called a “closed form” for the answer – the exact, concise solution. Five minutes after posting the question, someone commented:
“Do you have any reason to believe that there is a closed form for this terrifying thing?”
Then, after four and a half hours from the original post, the answer came:
“I equals 4 times pi times the inverse sine of the square root of the golden ratio.”
The answer came from a user named Cleo. She was a new account with only one previous answer. Cleo provided no comments, proof, or explanation – just a single link above the golden ratio symbol, which leads you to the definition of the golden ratio.
The impact of Cleo on Math Stack Exchange
Cleo’s swift answer stirred controversy in the Math Stack Exchange community, which typically showcases their work. There was one comment:
“I stick to what Hamming said: ‘The purpose of computing is insight, not numbers. Unless the result itself is particularly useful, I do not agree that it is an answer.’”
Ron Gordon, the patent agent and former physicist, did not see much value in Cleo’s simple answer. However, it influenced his determination of the final solution. Gordon spent most of the weekend writing the solution, which took up half a legal pad to resolve the problem.
It turned out that Cleo was correct. Ron published the complete answer, which immediately began gathering positive votes from community members. Many were astonished by the techniques he used to solve the problem. It was eventually published on the subreddit r/Math under the title “Master of Integrals.”
Speculations about Cleo’s identity
Opinions among experts about Cleo vary. Some believe she might have been Stephen Hawking – or was Stephen Hawking – or Maryam Mirzakhani, the Fields Medal winner. There are those who think she is Terence Tao, one of the greatest living mathematicians, who confirmed via email that he is not Cleo.
There are also those who believe Cleo could be Ramanujan – the Indian math genius who lacked advanced math education but produced astonishing theories. It seems they may have struck the same nerve almost a hundred years apart.
Conclusion
On
Although Cleo created something in her own way, it seems that no one knows who she was or why she did it. Recently, speculation has been reignited thanks to a viral TikTok video about Cleo. Since then, one user on Twitter has claimed to be Cleo, but he provided no evidence, and while some people buy it, many do not. Who is Cleo? She seems to have been very skilled at math – although some experts suspect that a computer may have been involved.
Cleo’s own profile, which hasn’t been updated in seven years, offers no clues. It says: “My real name is Cleo, I’m female. I have a medical condition that makes it very difficult for me to participate in conversations or post long answers, I apologize for that. I love math and I do my best to be helpful on this site, even though I realize that my answers may not be useful for everyone.”
But – but – I wondered, “Has this always been her profile?” I thought about checking again, so I went to the Internet Archive, pasted her address, and clicked on a snapshot taken in 2013 because, remember, nothing on the internet can truly disappear. Her profile was different back then. And guess who she quoted?
“In my sleep, I had an unusual experience. There was a red screen made up of a flow of blood, as if. I was watching it. Suddenly, a hand began to write on the screen. It became my center of attention. It wrote many missing integrals. They stuck in my mind. As soon as I woke up, I wrote them down.” – Srinivasa Ramanujan
Then Cleo wrote: “Remember, you are not bound by a single alternative system. You can invent your own system at any time you wish – just use your intuition and imagination.”
The Science, Quickly podcast is produced by Jeff DelViscio, Tulika Bose, Kelsie Harper, and Karen Yong. The theme music is composed by Dominic Smith.
Don’t forget to subscribe to the Science, Quickly podcast wherever you get your podcasts. For more science news and in-depth articles, go to ScientificAmerican.com. And if you enjoyed the show, rate it or write a review!
For Science, Quickly from Scientific American, I’m Alison Parshall.
Tulika Bose is the multimedia publisher at Scientific American.
Alison Parshall is a news editor at Scientific American and often covers topics in biology, health, technology, and physics. She edits the magazine’s contributor column and previously edited the advanced section. As a multimedia journalist, she contributes to the Science, Quickly podcast at Scientific American. Her work includes a three-part series on artificial intelligence in music-making. Her work has also appeared in Quanta Magazine and Inverse. Parshall graduated from the Arthur L. Carter Journalism Institute at New York University with a master’s degree in science, health, and environmental reporting. She has a bachelor’s degree in psychology from Georgetown University. Follow Parshall on Twitter @parshallison.
Karen Yong is a documentary filmmaker based in New York. Her projects have received support from Field of Vision, the Singapore International Film Festival, IN-DOCS, and the Tribeca Film Institute. Her work has appeared in Scientific American, Hakai Magazine, and The Atlantic. She holds a master’s degree in science writing from Columbia University’s Graduate School of Journalism and is also a graduate of the Tisch School of the Arts at New York University.
Leave a Reply