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If you are short on time, just read the Timeline section and the Conclusion.
Credit to u/EnergySensitive7834 for bringing up the initial evidence. Their post + comment section serves as a foundation of ideas from which I’ve build this report. You can find the post here:
That story was too good to be true
Cleo is a popular and controversial figure on Mathematics Stack Exchange (which is kinda like a math help forum) due to her method of providing answers. Between 2013 and 2016, Cleo posted numerous mathematical solutions to integral questions, often without any accompanying explanation or proof only a few hours after the original question was posted. This led to debates within the community about the usefulness of such answers and how she could have arrived at such answers at extraordinary speeds. Some users felt that answers without explanations did not contribute to the educational purpose of the platform and were akin to looking up results in an integral table. Others admired the speed and brilliance of Cleo’s solutions despite the lack of steps.
Below is a video of one of my favourite creators (Up and Atom 🤩) outlining this:
https://www.youtube.com/shorts/CzUT4CpzcrA
Here are a list of common theories I’ve seen users propose on chat forums like reddit and Quora:
| Theory | Comment |
|---|---|
| Cleo is a real person and is actually solving the integrals. | Not testable without finding the actual identity behind Cleo |
| The secret account of a math genius like Terence Tao or some other person. | Same as above. Interestingly, Terence actually confirmed via email that he was not Cleo (source). |
| A computational expert who solves problems using a program like Wolfram Mathematica. | Could be, but they would need a very advanced tool ahead of what we have now available to the public. |
| She could have differentiated a function $\frac{d}{dx}f(x)$, then posted the following question on an alt account: $\int \frac{d}{dx}f(x)\ dx$, and then answering “$f(x)$” on the Cleo account shortly after. This would explain her only answering integration questions. | Would have been a great explanation, but a lot of her answers are to definite integral questions where this method cannot be used since in a lot of cases, there exists no elementary antiderivative to the integral. Rather, the solutions involve invoking residue theorem and other non-trivial techniques. |
| Multiple users with alt accounts working together to answer each other’s questions. Or a single person doing this who has a lot of time on their hands. | I think this is the most plausible explanation. |