As a student at Harvard in the 1970s, Bill Gates impressed more than one faculty member with his mathematical brilliance.
He proposed an elegant solution to what's known as "pancake sorting," and his insights were published in the journal Discrete Mathematics in 1979, in a paper co-bylined with then Harvard professor Christos Papadimitriou.
Professor who knew Bill Gates as a student at Harvard: He was the smartest person I'd ever met
Bill Gates, right, chairman and founder of Microsoft Corp., watches a video presentation prior to giving the keynote address at the annual meeting of the Washington Software Association in Seattle, Wash., Jan. 28, 1992. Looking on is Paul Grey, president of Softchec, Inc. of Kirkland, Wash. (AP Photo/Jim Davidson)
Bill Gates, Microsoft's billionaire co-founder, holds the packaging for the Microsoft Windows software at the Comdex computer convention in Chicago,Ill., where Microsoft Corp. officially introduce Windows for personal computers, April 6, 1992. The software giant orchestrated a lavish stage show at semiannual Comdex convention to kick off the new Windows, which went on sale worldwide. (AP Photo/Mike Fisher)
Microsoft Chairman and CEO Bill Gates answers a question during a news conference Monday, May 18, 1998 in Redmond, Wash. A lawsuit filed by the Department of Justice and state attorney generals from 20 states sought a preliminary injunction that would force Microsoft to include the major rival to it's Internet browser. (AP Photo/Barry Sweet)
PARIS, FRANCE - SEPTEMBER 4: Microsoft president Bill Gates demonstrates Microsoft's Windows 95 program from his automobile prior to a press conference in Paris 04 September. Gates was also to meet 500 top computer executives as part of his campaign to launch the company's new software. AFP PHOTO (Photo credit should read Michel GANGN/AFP/Getty Images)
Microsoft Chairman Bill Gates waits to speak at an event organized by his company Tuesday, May 5, 1998, in New York. Gates was joined by more than 50 representatives of the PC industry to emphasize the importance of an on-schedule release of MicroSoft's Windows 98 operating system next month. (AP Photo/Marty Lederhandler)
Microsoft Corp. Chairman Bill Gates and his wife Melinda announce in Seattle, Thursday, Sept. 16, 1999, the creation of the Gates Millennium scholarship progam . The couple are donating $1 billion over the next 20 years to finance scholarships for minority college students. (AP Photo/Stevan Morgain )
Microsoft Chairman Bill Gates sits on stage during a video portion of the Windows 95 Launch Event Aug. 24, 1995, on the company's campus in Redmond, Wash. The word "start" is spelled out behind Gates. A Harvard University dropout, Gates co-founded Microsoft with Paul Allen in 1975. By 1980, he had licensed his MS-DOS operating system to IBM for its inaugural personal computer. Microsoft's Windows 95 computer operating system and Internet Explorer browser debuted in 1995 at the dawn of the Internetage. Gates is considered to be the world's richest private citizen with an estimated worth of 90 billion dollars. (AP Photo)
Microsoft Chairman and CEO Bill Gates adjusts his glasses as he delivers a speech on "Generation I," the first Internet generation, at The New York Institute of Technology, Thursday Oct. 28, 1999. The school also honored Gates with the NYIT President's Medal Leadership Award. (AP Photo/Richard Drew)
President Clinton listens to Microsoft Chairman Bill Gates in the East Room of the White House Wednesday, April 5, 2000, during the White House Conference on the "new economy." The president challenged Gates and other of the country's greatest economic minds to forecast what could derail the current super-charged economy. (AP Photo/Susan Walsh)
Bill Gates, chairman and chief software architect of Microsoft Corp., right, and Andrew Grove, chairman of the board of Intel Corp., left, pose with computers, ranging in age from those produced 20 years ago to the laptops of today, during a celebration in San Jose, Calif., Wednesday, Aug. 8, 2001. The celebration was in honor of the 20th anniversary of the IBM PC. On right is the IBM 5050 computer and on left is Compaq computer from 20 years ago. In center are three present day laptops. (AP Photo/PaulSakuma)
Microsoft Corp. Chairman Bill Gates explains some of the features of the Windows Media 9 Series platform during a keynote address Wednesday, Sept. 4, 2002, in the Hollywood section of Los Angeles. According to Gates, the new software platform offers benefits for the media and entertainment industry, comsumers in the home and in how businesses communicate. (AP Photo/Rene Macura)
American Microsoft Chairman and co-founder Bill Gates, left, walks with Indian Minister for Information and Technology Pramod Mahajan at the latter's residence in New Delhi, India, Tuesday, Nov. 12, 2002. Gates is on a visit to the South Asian nation, and will meet with industry leaders and other government officials in New Delhi, Bombay and the southern software hubs of Hyderabad and Bangalore. (AP Photo/Ajit Kumar)
Former South African President Nelson Mandela, left, speaks as Bill Gates, listens at an HIV/AIDS youth forum at the University of Witwatersrand in Johannesburg on Monday Sept. 22, 2003. (AP Photo/Themba Hadebe)
Microsoft chairman Bill Gates speaks to a gathering of advertisers and internet industry representatives during the Fifth Annual MSN Strategic Account Summit held at the company's headquarters in Redmond, Wash., Friday, March 26, 2004. Gates spoke about the future of advertising on the internet. (AP Photo/Andy Rogers)
Queen Latifah shares a laugh with Microsoft chairman Bill Gates in a "living room" set as Microsoft holds its Digital Entertainment Anywhere event to introduce its Windows Marketplace, a system offering consumers a broad selection of software and hardware, in Los Angeles, Tuesday, Oct. 12, 2004. The company unveiled the latest version of its operating system for those who want to use computers primarily for entertainment, whether at home, at the office or while traveling with portable devices. Selections of Queen Latifah's music were used in the demonstration. (AP Photo/Reed Saxon)
Microsoft Chairman Bill Gates, left, speaks Tuesday, Nov. 9, 2004 at Microsoft Corp.'s annual shareholders meeting in Bellevue, Wash. Looking on at right are CFO John Conners, CEO Steve Ballmer, and top lawyer Brad Smith. (AP Photo/Ted S. Warren)
Bill Gates of Microsoft holds an Iriver music player as delivers the keynote kickoff address of the Consumer Electronics Show Wednesday, Jan. 5, 2005 at the Las Vegas Hilton. The trade show, which occupies 1.5 million square feet of exhibit space and attracts 120,000 attendees to Las Vegas, begins with Gates' speech.(AP Photo/Joe Cavaretta)
Microsoft Corp. co-founder Bill Gates gestures during his keynote address at the RSA Conference in San Francisco, Tuesday, Feb. 15, 2005. Microsoft Corp. will give away software to battle spyware, adware and other privacy-invading pests, Gates said. (AP Photo/Paul Sakuma)
Microsoft Corp. Chairman Bill Gates gives the keynote address Monday, April 25, 2005 in Seattle at the 2005 Microsoft Windows Hardware Engineering Conference. Gates focused on the transition to 64-bit computing and the future of the company's next operating system, code-named "Longhorn." (AP Photo/Ted S. Warren)
Bill Gates of the U.S., co-founder of the Bill and Melinda Gates Foundation and Chairman and Chief Software Architect, Microsoft Corporation, speaks during a press conference, prior to adressing the 58th World Health Assembly at the United Nations in Geneva, Switzerland, Monday, May 16, 2005. The Fifty-eighth World Health Assembly takes place May 16-25, bringing together delegates from WHO's 192 member states to discuss key public health issues. (AP Photo/Keystone/Laurent Gillieron)
Microsoft chairman Bill Gates, left, addresses the annual Microsoft Research Faculty Summit as part of the opening plenary session with Maria Klawe, Dean of Engineering at Princeton, Monday, July 18, 2005, at the company's headquarters in Redmond, Wash. (AP Photo/Elaine Thompson)
Microsoft Corp. chairman and chief software architect Bill Gates holds up the new Palm Treo smart phone during a joint news conference with Palm Inc., Monday, Sept. 26, 2005 in San Francisco. Palm announced that it has gone into business with former rival Microsoft Corp. to launch a Windows-based Treo smart phone, marking the first time that a Palm product will run on an operating system other than Palm's. (AP Photo/Paul Sakuma)
Israeli Prime Minister Ariel Sharon, left, shakes hands with Microsoft founder and Chairman Bill Gates during their meeting in Tel Aviv, Israel Wednesday Oct. 26, 2005. Gates arrived in Israel Tuesday evening for a 24-hour visit. (AP Photo/Barkay Wolfson) ** ISRAEL OUT **
Former President Bill Clinton, left, speaks alongside Microsoft chairman Bill Gates during the Time Global Health Summit in New York, Wednesday, Nov. 2, 2005. (AP Photo/Gregory Bull)
Chairman and founder of Microsoft Corp., Bill gates, left, and Indian Minister of Communications and Information Technology, Dayanidhi Mara, wave at journalists in New Delhi, India, Tuesday, Dec. 6, 2005. They discussed various issues aimed at creating a more enabling environment for adoption of information technology across India. (AP Photo/Saurabh Das)
Microsoft chairman Bill Gates smiles while listening to Portuguese Prime Minister Jose Socrates address journalists following their meeting Wednesday Feb. 1 2006, at the Sao Bento palace, the premier's official residence in Lisbon. Gates is in Portugal to attend a leaders forum and the signing of several agreements between Microsoft and the Portuguese government. (AP Photo/Armando Franca)
Microsoft chairman Bill Gates stands while being introduced during a signing agreement ceremony that expands the strategic cooperation between Microsoft and Lenovo Group Ltd. at Microsoft headquarters, Monday, April 17, 2006, in Redmond, Wash. Seated from left are Scott Di Valerio, Bill Amelio, Steve Ballmer, Xu Qin, Yang Yuanqing, Ma Xin, Chen Shaopeng, Jin Xu. Microsoft's Windows operating system has long been popular in China, the problem has been getting Chinese users to pay for legitimate copies. On the eve of Chinese President Hu Jintao's visit Tuesday to Microsoft's Redmond campus, company officials hope things are changing. (AP Photo/Elaine Thompson)
Microsoft Corp. Chairman Bill Gates, left, is interviewed by CNBC's Donny Deutsch at the company's headquarters Wednesday, May 3, 2006, in Redmond, Wash. Most people probably dream of being the world's richest person--except, perhaps, the man himself. Gates told an online advertising conference that he'd prefer not to be the richest person in the world. (AP Photo/Elaine Thompson)
Microsoft chairman Bill Gates, center, smiles as he watches Team South Korea give a presentation on an exercise and diet software program during a demonstration by Imagine Cup finalists at the company's headquarters Wednesday, June 28, 2006, in Redmond, Wash. Team South Korea members include, from left, Haeri Lee, Wansang Park and Hyewha Jung. Gates spent an hour with some of the finalists of the company's Imagine Cup contest, in which students worldwide use Microsoft products to build a new technology. This year, the contest is focused on healthcare advances. More than 70 teams will vie for a $25,000 top prize at finals later this year in India. (AP Photo/Elaine Thompson)
Microsoft Chairman Bill Gates delivers a keynote speech at the Consumer Electronics Show in Las Vegas on Sunday, Jan. 7, 2007. (AP Photo/Jae C. Hong)
Microsoft Chairman Bill Gates adjusts his glasses during a ceremony at the Global Technological Support Center (GTSC) in Bucharest Romania Thursday Feb.1 2007. Bill Gates visits Bucharest to take part in celebrations marking ten years of Microsoft operations in Romania, and the announcement of the general availability in Romania of Microsoft Windows Vista, Microsoft Office 2007, and Microsoft Exchange Server 2007.(AP Photo/Vadim Ghirda)
Co-founder of Microsoft Bill Gates, center, laughs with Sen. John Kerry, D-Mass., right, as Boston Celtics legend Bill Russell, left, looks on before the start of commencement ceremonies at Harvard University in Cambridge, Mass., Thursday, June 7, 2007. (AP Photo/Michael Dwyer)
Microsoft Corp. founder Bill Gates is silhouetted during a launch announcement at the Unified Communications Server 2007 conference in San Francisco, Tuesday, Oct. 16, 2007. Microsoft Corp. launches programs that allow computer users to place calls right from Outlook and other Office applications, but analysts say the software maker must prove its tools are as reliable as those from established phone equipment makers. (AP Photo/Paul Sakuma)
Microsoft Corp. founder Bill Gates gestures in front of Microsoft's new video conference RoundTable during a launch announcement at the Unified Communications Server 2007 conference in San Francisco, Tuesday, Oct. 16, 2007. Microsoft Corp. launches programs that allow computer users to place calls right from Outlook and other Office applications, but analysts say the software maker must prove its tools are as reliable as those from established phone equipment makers. (AP Photo/Paul Sakuma)
Bill Gates, with the Bill and Melinda Gates Foundation, addresses the 63rd session of the United Nations General Assembly at UN headquarters, Thursday Sept. 25, 2008. (AP Photo/Richard Drew)
Google Chairman and CEO Eric Schmidt, left, jokes with Microsoft Corp. Chairman Bill Gates at the annual Allen & Co.'s media summit in Sun Valley, Idaho, Thursday, July 9, 2009. At right is Nathan Myhrvold, formerly Chief Technology Officer at Microsoft, and co-founder of Intellectual Ventures. (AP Photo/Nati Harnik)
Bill and Melinda Gates at the annual Allen & Co.'s media summit in Sun Valley, Idaho, Friday, July 10, 2009.(AP Photo/Nati Harnik)
Microsoft co-founder Bill Gates poses for photos at the "Get Schooled" conference and premiere hosted by the Bill & Melinda Gates Foundation and Viacom in Los Angeles, Tuesday, Sept. 8, 2009. (AP Photo/Jae C. Hong)
Former President Bill Clinton looks on as Bill Gates testifies on Capitol Hill in Washington, Wednesday, March 10, 2010, before the Senate Foreign Relations Committee hearing on global health. (AP Photo/Manuel Balce Ceneta)
The founder of the Microsoft Company, Bill Gates, smiles after he and German Development Minister Dirk Niebel met in Berlin, Germany, Wednesday, April 6, 2011. (AP Photo/Michael Sohn)
Melinda Gates, left, and husband Bill Gates laugh with Jeff Raikes following speaking at the opening reception of the Bill & Melinda Gates Foundation Thursday, June 2, 2011, in Seattle. The foundation formally opened the new headquarters Thursday evening, moving from scattered nondescript office buildings around Seattle to an architectural showcase in the center of its hometown. (AP Photo/Elaine Thompson)
FILE - This Oct. 24, 2011 file photo shows Microsoft Chairman Bill Gates participating in a panel discussion at the State Department in Washington. A trial accusing Microsoft of antitrust violations resumes in federal court in Salt Lake City Friday Nov. 18, 2011 with the software giant asking a judge to dismiss an the case brought by Utah's Novell Inc.(AP Photo/Manuel Balce Ceneta, File)
Microsoft's Bill Gates is watched by Berkshire shareholders as he uses an oversized bat to play against table tennis prodigy Ariel Hsing in Omaha, Neb., Sunday, May 6, 2012. Berkshire Hathaway is holding its annual shareholders meeting this weekend. (AP Photo/Nati Harnik)
Bill Gates, left, and Warren Buffett, right, at the Allen & Company Sun Valley Conference in Sun Valley, Idaho, Thursday, July 12, 2012. (AP Photo/Paul Sakuma)
Warren Buffett, right, and Bill Gates share a light moment during an interview with Liz Claman of the Fox Business Network, in Omaha, Neb., Monday, May 6, 2013. The Berkshire Hathaway shareholders meeting took place over the weekend. (AP Photo/Nati Harnik)
German Chancellor Angela Merkel, left, and Bill Gates, right, founder of the Bill and Melinda Gates Foundation, shake hands during a photo call prior to a meeting at the chancellery in Berlin, Germany, Thursday, Nov. 14, 2013. (AP Photo/Michael Sohn)
Bill Gates holds the Millennium Bambi trophy during the Bambi 2013 media awards in Berlin, Germany, Thursday, Nov. 14, 2013. (AP Photo/Gero Breloer)
Bill and Melinda Gates are interviewed in New York, Wednesday, Jan. 21, 2015. As the world decides on the most crucial goals for the next 15 years in defeating poverty, disease and hunger, the $42 billion Gates Foundation announces its own ambitious agenda. (AP Photo/Seth Wenig)
Microsoft co-founder and Berkshire Hathaway board member Bill Gates talks during an interview with Liz Claman on the Fox Business Network in Omaha, Neb., Monday, May 4, 2015. The annual Berkshire Hathaway shareholders meeting took place the previous Saturday in Omaha with over 40,000 in attendance. (AP Photo/Nati Harnik)
Bill Gates participates in the "Investing in Prevention and Resilient Health Systems" plenary session at the Clinton Global Initiative 2015 Annual Meeting at the Sheraton New York Times Square Hotel, on Sunday, Sept. 27, 2015 in New York. (Photo by Greg Allen/Invision/AP)
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The story serves as a reminder that the wealthiest and most successful people among us may have been exceptional from the start.
When I was an assistant professor at Harvard, Bill was a junior. My girlfriend back then said that I had told her: "There's this undergrad at school who is the smartest person I've ever met."
That semester, Gates was fascinated with a math problem called pancake sorting: How can you sort a list of numbers, say 3-4-2-1-5, by flipping prefixes of the list? You can flip the first two numbers to get 4-3-2-1-5, and the first four to finish it off: 1-2-3-4-5. Just two flips. But for a list of n numbers, nobody knew how to do it with fewer than 2n flips. Bill came to me with an idea for doing it with only 1.67n flips. We proved his algorithm correct, and we proved a lower bound—it cannot be done faster than 1.06n flips. We held the record in pancake sorting for decades. It was a silly problem back then, but it became important, because human chromosomes mutate this way.
Two years later, I called to tell him our paper had been accepted to a fine math journal. He sounded eminently disinterested. He had moved to Albuquerque, New Mexico to run a small company writing code for microprocessors, of all things. I remember thinking: "Such a brilliant kid. What a waste."
Thirty years later, other researchers found a sorting strategy that's 1% faster. But according to an NPR interview with Harry Lewis, another Harvard professor who taught Gates in the 1970s, those researchers had the help of powerful computers. The young Gates, on the other hand, relied solely on his own cognitive resources (and in fact he helped develop the computers that would find a faster solution).
It's easy to dismiss these reminiscences as exceptions to the rule — the rule that anyone can make it big without being a genius at age 20.
But a growing body of research suggests that intelligence is a remarkably good predictor of wealth and success later in life.
In 2013, Jonathan Wai, a professor at Duke University's Talent Identification Program, published a study that found the majority of Fortune 500 CEOs and billionaires had attended an elite academic institution either as an undergraduate or graduate student, putting them in the top 1% of cognitive ability. Even among the top 0.0000001% of wealth, Wai reported, those who earned more were generally better educated.
More recent research by Wai has found that about 40% of a sample of 1,991 CEOs attended elite schools, which presumably means they were in the top 1% of cognitive ability. Moreover, Wai found that companies run by more highly-educated CEOs tended to perform better. Wai equates admission to an elite institution with smarts because those schools admit only students with top SAT scores and SAT scores are generally related to intelligence.
Wai's methodology and conclusions have been criticized, for example by Steve Siebold, author of "How Rich People Think," and Wai admits that he would have preferred to gain access to people's SAT scores if that were possible. In an article on Business Insider, Wai acknowledged, "It might be that the power of the networks, brand name, and quality of education that come with elite school attendance is why so many of these people ended up in such positions of influence."
Another small study, conducted by researchers at Vanderbilt University, found that 320 students who had scored above the 1 in 10,000 level on the SAT before age 13 held more prestigious jobs at more prestigious companies by age 38 than the average population.
Bill Gates himself has acknowledged the potential link between intelligence and professional success. In 2005, he told Forbes: "Microsoft must win the IQ war, or we won't have a future."
That intelligence might play more than a minimal role in individual success is an uncomfortable idea to consider. But the takeaway from these studies and anecdotes isn't that, if you aren't off-the-charts intelligent (at least by standard measures of intelligence), you can't or won't get anywhere. It just seems to be statistically less likely you'll become the next Bill Gates.
Related: See more notable people who spent time at Harvard:
Notable Harvard University alumni
Professor who knew Bill Gates as a student at Harvard: He was the smartest person I'd ever met
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