By David Leonhardt

Much of human progress depends on innovation. It depends on people coming up with a breakthrough idea to improve life. Think about penicillin or cancer treatments, electricity or the silicon chip.

For this reason, societies have a big interest in making sure that as many people as possible have the opportunity to become scientists, inventors and entrepreneurs. It’s not only a matter of fairness. Denying opportunities to talented people can end up hurting everyone.

If you’re a regular reader of this column, you may recognize the name Raj Chetty. He is a Stanford professor who helps lead the Equality of Opportunity Project, which I consider the most important research effort in economics today.

Chetty and his colleagues have spent years analyzing millions of anonymous tax records. Before, researchers had to rely on surveys, which are expensive and unreliable. (Do you know how much money your parents made when you were 10 years old?) The tax records allow for a new understanding of the paths that lives take.

The project’s latest paper, out Sunday, looks at who becomes an inventor — and who doesn’t. The results are disturbing. They have left me stewing over how many breakthrough innovations we have missed because of extreme inequality. The findings also make me even more frustrated by new tax legislation that will worsen inequality. This Congress is solving economic problems that don’t exist and aggravating those that do.

The key phrase in the research paper is “lost Einsteins.” It’s a reference to people who could “have had highly impactful innovations” if they had been able to pursue the opportunities they deserved, the authors write. Nobody knows precisely who the lost Einsteins are, of course, but there is little doubt that they exist.

The researchers worked with the Treasury Department to link the tax records with patent records. Doing so allowed them to study the backgrounds of patent holders (and the study focused on the most highly cited, significant patents). The researchers — Chetty, Alex Bell, Xavier Jaravel, Neviana Petkova and John Van Reenen — were also able to link these records to elementary-school test scores for some patent holders.

Not surprisingly, children who excelled in math were far more likely to become inventors. But being a math standout wasn’t enough. Only the top students who also came from higher-income families had a decent chance to become an inventor.

This fact may be the starkest: Low-income students who are among the very best math students — those who score in the top 5 percent of all third-graders — are no more likely to become inventors than below-average math students from affluent families. That’s a betrayal of American ideals.

“There are great differences in innovation rates,” Chetty said. “Those differences don’t seem to be due to innate ability to innovate.” Or as Steve Case — the entrepreneur who’s now investing in regions that venture capital tends to ignore — told me when I called him to discuss the findings: “Creativity is broadly distributed. Opportunity is not.”

The gap between rich and poor is just one of the worrisome findings. The middle class has innovation rates closer to that of the poor than the affluent. Children from the southeast are less likely to become inventors. So are African-Americans, Latinos and women.

The gaps are enormous, too. Among upper-income students who excel at math, 6.5 out of every 1,000 from are ultimately granted a patent. For low-income math standouts, the number is 1.2. Our society appears to be missing out on most potential inventors from among the poor, middle class, women, African Americans and southerners.

These groups span the political left and right — a reminder that Americans of different tribes have a common interest in attacking inequality.

How can we do so? We can stop showering huge tax breaks on the affluent and reinvest the money where it’s needed. We can work to narrow educational inequities. Yet the new research suggests there is also one simpler approach to try.

Chetty thinks it’s one of the most striking patterns in the data. Children who grow up exposed to a particular type of invention or inventor are far more likely to follow that path. Growing up around patent holders for, say, amplifiers makes someone far more likely to become an amplifier-related inventor. Similarly, girls who grow up in areas with a lot of female patent holders — like central New Jersey (a biotech hub) or Honolulu — are more likely to become inventors.

Recreating these social networks and role models elsewhere won’t be easy, but it is surely worth trying, given the stakes. There is an opportunity for foundations, universities and companies to cultivate lost Einsteins and help turn them into potential innovators.

“We do a pretty good job at identifying the kids who are good at throwing a football or playing a trumpet,” Case said. “But we don’t do a particularly good job of identifying the kids who have the potential of creating a phenomenal new product or service or invention.” We all suffer for that failure.