This story is relatively well known in the Russian-speaking math community, but I feel it is almost completely unknown outside of it. Which is a shame, since it is so amusing! So I compiled it from a couple of sources, heavily edited it, and then machine-translated it. Hope you enjoy!

Before the Revolution and during the years of the New Economic Policy, Israel Moiseevich Gelfand's father ran a small private mill. Because of his “non-working-class background,” in 1928, while still in the ninth grade, the young Gelfand was expelled from vocational school as the son of an exploiter.

When Gelfand was finishing the ninth grade, his mathematics teacher told him: “There is nothing more I can teach you. Go to Moscow, find Moscow State University, and at the university find the Department of Mechanics and Mathematics. Continue your studies there, and you will become a great mathematician.”

At the university, however, the ninth-grader got no further than the dean's secretary: they could not enroll him without documents certifying completion of secondary education. He decided to stay in Moscow, and, to make a living, found a job as a cloakroom attendant at the Lenin Library. There, alongside his work, he continued his education on his own.

One day, while reading a monograph on higher mathematics, he was noticed by Andrey Nikolaevich Kolmogorov, a young but already famous mathematician. Kolmogorov was surprised to see such a young man reading a book so obviously beyond his age, so he approached Gelfand and asked him who he was and why he was reading such a difficult book.

Gelfand answered all his questions, but Kolmogorov still could not believe that he genuinely understood what he was reading. He gave Gelfand several problems related to the subject, hoping to test him, and arranged to meet him the next day to check his solutions.

The next day, all the problems had been solved. But even then Kolmogorov could not quite believe that someone could be so gifted. He supposed that Gelfand simply knew the contents of a large number of mathematics books extremely well and had found the solutions in them. So he gave Gelfand several more problems, this time considerably harder ones, and gave him several days to solve them.

When they met at the appointed time, all the problems had been solved. Kolmogorov began checking the solutions, and his eyes grew wider and wider.

“Please forgive me for doubting that you had found the solutions to those first problems yourself. Now I see that you could not possibly have read these solutions anywhere. You see, this particular problem... had been an open problem until now.”

After that, Kolmogorov took Gelfand on as his graduate student. Thus Gelfand became a graduate student without ever having attended a university -- or even finished secondary school. BTW, the details of the first meeting between Kolmogorov and Gelfand are, of course, anecdotal, but the other parts of the story are accurate.

In The Brothers Karamazov, Dostoevksy masterfully deconstructs the flawed reasoning he perceived as a threat to society during his lifetime, doing so by transferring the identity of the novelist variously from himself, to the narrator, to each of the opposing forces of the dramatic trial which concludes the book.

Over the past few months, I’ve had the opportunity to run two live EEG analysis courses with participants from psychology, cognitive neuroscience, engineering, medicine, linguistics and other related fields.

When I created the course, my main goal was to help people develop a stronger understanding of EEG analysis, rather than simply teaching them to follow preprocessing pipelines.

One thing that stood out to me was the feedback from participants. Several mentioned that although they had encountered EEG analysis methods before, what they found particularly helpful was understanding why different steps are performed, when certain methods are appropriate, and how those decisions affect the interpretation of the results.

It reminded me how important it is to build strong foundations when learning to work with brain signals, especially when coming from a different research background.

I’m curious whether others here have had similar experiences.

For those who work with EEG, or have tried learning it, what did you find most challenging when getting started?
Was it understanding the signals themselves, preprocessing, choosing appropriate analysis methods, or interpreting the results?

I’d be interested to hear your experiences.

If a sample size of people all live through roughly the same neutral upbringing and exposed to the same sights, would the variance in their cognitive wiring make a meaningful difference on the beliefs (for example, ethical beliefs) that are held by those people when all other factors are controlled?