The recent revolution in DNA sequencing gave researchers a new way to study the link. In 2016, for example, researchers in England surveyed hundreds of thousands of people and linked 74 different gene variants to how long the participants stayed in school.

Image Sir Francis Galton Credit... Eveleen Tennant Myers

Some of those variants were in genes active in the developing brain, perhaps influencing relevant traits — everything from how well people learn new words to how motivated they are by long-term goals.

Yet the connection between genes and education remains murky. Each gene variant, on average, accounts for just a few weeks of the total. And when researchers try to estimate how important these variations are in entire populations, they end up with different figures. Some researchers estimate the proportion at 21 percent; others have put it at as high as 40 percent.

Either figure means that a lot of variation cannot be accounted for by genetics. Factors in the environment may explain some of the variation: a family’s wealth, for example, or the quality of schools children go to, or their exposure to pollution.

When the first DNA-based studies of educational attainment came out in 2013, a geneticist named Augustine Kong sifted through the results. At the time, Dr. Kong was working at DeCode, a genetics company based in Iceland, and so he was able to look for some of the variants in the company’s database of Icelandic DNA.

Dr. Kong wondered if other researchers had missed something very important. “It suddenly occurred to me that part of this effect could be coming through the parents,” he said. “And then I got obsessed with the idea.”

Children, after all, get their genes from their parents. It was possible, Dr. Kong reasoned, that genes could influence how far children got through school by influencing their parents’ behavior rather than the actions of the children themselves.