Accomplishment may be open to people of all ages, but discovery and innovation are the province of the young in the popular imagination. Whether you picture a starving poet pouring her soul onto paper in a garret or a startup innovator overturning whole industries, the face in your mind probably hasn't seen its 30th birthday.

Which, let's be honest, can be a little dispiriting for those who are some ways past it.

If you haven't made a major breakthrough in your chosen field, whether it's science, business innovation or the arts, by the time checkout clerks stop asking you for your ID when you buy beer, and you're worried that means you've missed the boat and aged out of the possibility of shaking up the world, stop fretting. Science has good news for you. The popular mythology in this case appears to be wrong.

According to a new working paper out of the National Bureau of Economic Research, the peak age for genius is actually 35 overall, and significantly later in some fields, like medicine.

Why Your Mid to Late-30s Are the Peak Years for Innovation

So why is it that innovation happens at older ages than many of us believe? It appears that the age at which creative breakthroughs happen has actually been rising over time. There is now so much to learn in many fields that it takes potential geniuses decades to gather the knowledge that is the necessary foundation for innovation.

One analysis of Nobel Prize winners illustrates this trend. Before 1905, 20 percent of great breakthroughs generally happened before scientists turned 30 and two-thirds before they turned 40. By 2000, prize-worthy work almost never happened before the age of 30 and in some areas, like chemistry, almost never happened before the scientist turned 40. In a more complicated world, age and experience apparently pay higher dividends.

Even in the humanities where few geniuses spend years getting their PhDs, the myth of the baby-faced genius may be overblown. "Over 40 percent of both Robert Frost's and William Carlos Williams' best poems were written after the poets turned 50. Paul Cézanne's highest-priced paintings were made the year he died," Quartz's Olga Kazan points out.

You, of course, are a business owner or aspiring to be one. Chances are you don't spend too much time penning poems or pondering theoretical physics. But if you've seen a few more birthdays than you hoped you would before you left your mark on the world, these studies are still good news for you. The principle that, these days, more learning and experience is needed to prepare the ground for true innovation applies in business as well.

The bottomline: don't think you're over the hill when it comes to major breakthroughs if you're closing in quickly on middle age -- your mid to late thirties are actually the peak years for innovation.