Suppose you accept the persuasive data that inequality has been rising in the United States and most advanced nations in recent decades. But suppose you don’t want to fight inequality through politically polarizing steps like higher taxes on the wealthy or a more generous social welfare system.

There remains a plausible solution to rising inequality that avoids those polarizing ideas: strengthening education so that more Americans can benefit from the advances of the 21st-century economy. This is a solution that conservatives, centrists and liberals alike can comfortably get behind. After all, who doesn’t favor a stronger educational system? But a new papershows why the math just doesn’t add up, at least if the goal is addressing the gap between the very rich and everyone else.

Brad Hershbein, Melissa Kearney and Lawrence Summers offer a simple little simulation that shows the limits of education as an inequality-fighter. In short, more education would be great news for middle and lower-income Americans, increasing their pay and economic security. It just isn’t up to the task of meaningfully reducing inequality, which is being driven by the sharp upward movement of the very top of the income distribution.

It is all the more interesting that the research comes from Mr. Summers, a former Treasury secretary who is hardly known as a soak-the-rich class warrior. It is published by the Hamilton Project, a centrist research group operating with Wall Street funding and seeking to find third-way-style solutions to America’s problems that can unite left and right.

In their simulation, they assume that 10 percent of non-college-educated men of prime working age suddenly obtained a college degree or higher, which would be an unprecedented rise in the proportion of the work force with advanced education.

They assume that these more educated men go from their current pay levels to pay that is in line with current college graduates, minus an adjustment for the fact that more college grads in the work force could depress their wages a bit.

There is no doubt that in this simulated world with a more educated labor force, middle-income workers earn more — $37,060 in simulated 2013 earnings for a person at the 50th percentile, compared with $34,000 in the real world, a 9 percent improvement.But that improvement brings that 50th-percentile worker only back closer to the inflation-adjusted level of income he enjoyed in 1979, which was $37,838. Meanwhile, the 90th-percentile worker in this simulation holds onto (and indeed improves upon) the sharp income gains of the past 34 years. Annual earnings at the 90th percentile climbed from $75,700 in 1979 to more than $100,000 in both the actual 2013 data and the simulation with higher education levels.

Add it all up, and the Gini ratio, a frequently used measure of income inequality, would decrease only to 0.55 from 0.57 in this scenario of drastic educational improvement. It would still be far higher than the 0.43 recorded in 1979.

None of this is to say that a better educational system isn’t desirable. The 9 percent income gain for middle-income men evident in the authors’ simulation is a big deal.

“Increasing the educational attainment of men without a college degreewill increase their average earnings and their likelihood of being employed,” the authors write. And even if it doesn’t do much to reduce overall inequality, they find it does reduce inequality within the bottom half of the income distribution, by increasing the earnings of those near the 25th percentile of earnings (in 2013, those making $6,100 a year, compared with $8,720 in the simulation with higher education).

In other words, it’s worth pursuing more and better education for working-class Americans on its own terms, because it will improve their lives and economic potential. Inequality, meanwhile, is a deeper problem, and its potential solutions remain ideologically divisive.