Mobile payment company Square today added former Obama Chief Economic Advisor Larry Summers to its board of directors.

If you didn’t follow Summers’ political career, you may recall him as Harvard’s President in The Social Network. Although the movie is fictional, earlier this year Summers said the scene in which he dismisses the Winklevoss twins’ claim that Facebook was their idea “was pretty accurate.”

“We are proud to have Larry join our board and we welcome his insight and decades of leadership to our growing company,” Square founder (and Twitter co-founder) Jack Dorsey said in an emailed statement. “Square is at a key point in our trajectory and we know Larry will contribute tremendous wisdom and expertise toward our continued success.”

Square’s growing board of directors could be an indication of that success. Earlier this month Square added influential venture capitalist Vinod Khosla to its board (he’s behind Khosla Ventures and was one of the co-founders of Sun Microsystems).

Summers was the Treasury Secretary until 2001, previously serving as deputy secretary and a chief economist at the World Bank.

He stirred up controversy in 2005 during a speech in which he remarked, as documented by the Boston Globe, that the “innate differences” between men and women might result in fewer women succeeding in science and math careers. The Independent reported on Summers’ apology for the comments.

San Francisco-based Square provides sleek credit card readers to businesses and makes it possible for customers to pay merchants with just their name. The company aspires to replace cash registers entirely. The iPad-based card readers also help businesses update their inventory, add specials, and track customer behavior. Based on credit card information registered on the service, the Card Case app, launched back in May of 2011, is a virtual wallet which allows customers to pay and then store receipts electronically. Read more about Card Case here.

“Square is at a key point in our trajectory and we know Larry will contribute tremendous wisdom and expertise toward our continued success,” Square founder and CEO Jack Dorsey said in a statement.

Summers (pictured above, right, talking to Obama Treasury Secretary Timothy Geithner) also served as one of President Clinton’s Treasury Secretaries, from 1999 to 2001. After leaving that post, he took the lead at Harvard for five years. In the Obama administration, Summers was director of the White House Economic Council, as well as the president’s Chief Economic Advisor. He left at the end of last year to return to Harvard.

In Silicon Valley, Summers may be best known as the president of Harvard in The Social Network. In that film, a large amount of which was fictionalized, the president is portrayed as being unable to grasp the significance of the Facebook application being hatched under his roof and therefore dismissing the concerns brought to him about it by the Winklevoss twins.

Less well known, perhaps, is the fact that Summers was (and this is factual) Facebook COO Sheryl Sandburg’s mentor and thesis advisor while she was at Harvard (more than a decade before either Mark Zuckerberg or the Winklevii graced its leafy campus). Sandburg later followed Summers both to the World Bank and then to the Treasury Department, where she became his chief of staff.

Sandburg also defended Summers’ track record on women after the controversial 2005 speech.

In a 2008 post on the Huffington Post, Sandburg wrote that Summers has been “a true advocate for women throughout his career.” He expressed himself poorly during the speech, she said, and the reason he made the speech in the first place was that “he cared enough about women’s careers and their trajectory in the fields of math and science to proactively analyze the issues and talk about what was going wrong.”