There’s a new exhibit at the National Portrait Gallery that you really should check out called “American Cool.” It’s a collection of photographs — mostly in black and white, of course — of the “coolest” Americans in history. As with any such collection, there are obvious selections (James Dean, anyone?), some that may vex you (Walt Whitman, wha?), and all sorts of grist for debate (Susan Sontag, hmm?).
The curators even created an “Alt-100 List” of those who didn’t make the cut. (Sorry, Dennis Hopper and Joe Namath.) What struck me, though, is the almost complete absence of businesspeople on the list. In fact, there was only one. Maybe that’s to be expected. Since when has business ever been cool? Well, actually right about now, you could argue. Isn’t Silicon Valley the coolest place on the planet these days? A combination of Athens in the Golden Age, Paris in the 1920s, and London in the 1960s? Apparently not to the curators of the National Gallery exhibition. Ergo, Mark Zuckerberg, Marissa Mayer, Jeff Bezos (I know, Seattle), Larry Ellison, Sheryl Sandberg, and none of their fellow geeks are on the cool list — or even the alt list. To be fair to the current Silicon Valley crowd, neither is Henry Ford or Warren Buffett or even an iconoclast like John DeLorean.
It’s very likely that to the minds of the curators, success and (gasp) making money would actually disqualify someone from making the list. And after all, that’s pretty much at the core of what makes someone a noteworthy businessperson. Or is it? In fact, there is a growing group of individuals who are making their mark by achieving success measured to a large degree in a different way. They are businesspeople, but they succeed not by growing market share or reaping mammoth salaries, but by solving problems and facilitating social change.
Branded “social entrepreneurs” by a singular activist named Bill Drayton, the founder and CEO of an organization called Ashoka, they may never be more than a slice of the global economy, but they are increasingly vital. If you are interested, you can find out about social entrepreneurs in a documentary film called Who Cares? (by Brazilian filmmaker Mara Mourão), a screening of which Fortune sponsored at the Annapolis Film Festival. Some of the subjects of the film, such as Nobel Peace Prize winner Muhammad Yunus and Premal Shah of Kiva, you may know, while most of the others, who are doing incredible work creating new markets and systems in the developing world and here at home, will be unfamiliar.
There’s John Mighton, a Canadian mathematician and founder of JUMP Math, which is an alternative method of teaching math that produces measurably higher results and improves self-esteem. And Joaquim de Melo, a former priest who created the Banco Palmas in a Brazilian slum to keep what little money there was in the community to rebuild it. The bank now has some 30 branches throughout his country.
I think you will find all of the men and woman in Who Cares? remarkable. And dare I say — National Portrait Gallery curators, take note — pretty damn cool too.
BTW, did you figure out who the only businessperson on the list is? It’s Steve Jobs, of course. (Note that I said no current Silicon Valley folks.)
This story is from the April 28, 2014 issue of Fortune.