The days of 30-year-old Nobel Prize winners like John Nash depicted in the 2001 film A Beautiful Mind are long gone, according to a study.

A century ago, scientists snapped up the majority of Nobel Prizes for work done before age 40, but now it takes longer for scientists to complete work that wins the most prestigious prize in science, researchers concluded.

Men and women make breakthrough scientific discoveries in their late 40s, according to Bruce Weinberg, an Ohio State University economics professor and the co-author of a paper published Thursday by the Proceedings of the National Academy of Sciences. The survey compared the ages of all Nobel Prize winners.

Today, the average age at which physicists do their Nobel Prize winning work is 48, Weinberg said in a statement Monday. Very little breakthrough work is done by physicists under 30.

The study found that in 1905 two thirds of all Nobel Prize recipients did their prize-winning work by age 40, and 20 percent of Nobel laureates earned the distinction before they turned 30.

The Nobel Prize, one of the most prestigious academic achievements, is an award won increasingly by people in their late 40s.

The time it takes to become a working scientist now compared to 1905 partly explains why award-winning achievements take longer, Weinberg said.

Weinberg and his co-author Benjamin Jones, a business professor at Northwestern University, analyzed 525 Nobel Prizes awarded between 1901 and 2008 in physics, chemistry and medicine.

The number of young scientists who produced Nobel Prize winning work peaked in 1923, the study found. By 1934, 78 percent of scientists did their best work by the time they were 40. The trend toward later-career achievement continued throughout the 20th century, Weinberg and Jones found.

The growth of scientific knowledge during the early 20th century partly explains the trend toward older high-achieving scientists. Discoveries in the scientific repertoire in the early 20th century had compounding benefits, as up and coming scientists in the mid-century cited them and built upon them, making new discoveries based more on advancing the state of the art than on sheer creativity.

If you take the view that science is a young person's game, then this aging trend is alarming, Weinberg said in the statement. But if scientists can be productive as they get older, as the study suggests, there may be less of a problem.