In a restaurant in Kunshan, China, more than a dozen robots cook and deliver food to customers. Will robots replace every job? Find out what skill humans are better at than robots. Getty Images

As artificial intelligence advances, so does the human fear of being replaced by a computer. It's a fear that goes back to the Industrial Revolution, when textile workers protested new technology by destroying machines that could do their jobs quicker and more efficiently.

Now that robots (literally) walk the earth, there is an ever-more-pressing question of whether they will spell the end of employment for humans or actually just complement us and make us more productive. But even if it's the latter, some jobs have already vanished, and others are sure to follow. So what functions will these robots not be able to perform?

A Harvard Business Review article details a new National Bureau of Economic Research working paper, which finds robots have not been replacing jobs that require a quintessential human skill: social communication. The paper, by David J. Deming of the Harvard Graduate School of Education, explains:

While computers perform cognitive tasks of rapidly increasing complexity, simple human interaction has proven difficult to automate. Since 1980, jobs with high social skill requirements have experienced greater relative growth throughout the wage distribution. Moreover, employment and wage growth has been strongest in jobs that require high levels of both cognitive skill and social skill.

"The days of being able to plug away in isolation on a quantitative problem and be paid well for it are increasingly over," Deming tells HBR. "You need both types of skills."

According to Deming, jobs that require social skills grew by 24 percent from 1980 to 2012 while math-intensive jobs grew by only 11 percent. The jobs under the greatest threat of automation, he says, are routine-based positions like those of factory workers and filing clerks.

Deming took data from a longitudinal survey that tracked respondents from adolescence into their mid-50s through test scores, sports or club participation in high school, and adult employment and income, to compare wages of people who have high social skills with those who have low social skills.

While it's not a perfect study, the results are interesting. "People who have higher social skills, as measured by the survey, earn more money--even after controlling for things like their education, their cognitive skills (measured by standardized scores), what type of job they're in, etc.--than those with poor social skills," HBR writes. "There seems to be a positive return to social skills in the labor market, according to the data, and that return is relatively greater when people are in jobs that require more interaction with others."