As daunting as such reform might be, it is far from impossible. A book called “Math Doesn’t Suck,” by the actress Danica McKellar (who starred as Winnie Cooper on “The Wonder Years” before earning her bachelor’s degree in math at U.C.L.A.), along with her follow-up books, “Kiss My Math,” “Hot X: Algebra Exposed” and “Girls Get Curves: Geometry Takes Shape,” may well have done more to encourage girls to stick with math than any government task force. McKellar’s math books might go a little far in pandering to adolescent girls’ stereotypical obsessions (the problems involve best friends, beads and Barbies rather than baseballs and speeding cars), but the wildly enthusiastic response they have received speaks to the effect that can be achieved by reworking the contents of standard math and science problems and countering the perception that boys won’t like girls who are smart.

The key to reform is persuading educators, researchers and administrators that broadening the pool of female scientists and making the culture more livable for them doesn’t lower standards. If society needs a certain number of scientists, Urry said, and you can look for those scientists only among the males of the population, you are going to have to go much farther toward the bottom of the barrel than if you also can search among the females in the population, especially the females who are at the top of their barrel.

In addition, she said, her colleagues need to recognize the potential of women who discover a passion for science relatively late. Studies show that an early interest in science doesn’t correlate with ability. You can be a science nut from infancy and not grow up to be good at research, Urry said, or you can come to science very late and turn out to be a whiz.

With a little practice and confidence, girls can even make up for an initial disadvantage working with machines, tools and electronic equipment. While boys consistently outperform girls in tests that measure the spatial skills essential for lab work and engineering, studies also show that spatial aptitude is a function of experience. At Olin College of Engineering in Massachusetts, the administration is dedicated to making sure that half the students in each entering class are women. All of Olin’s incoming students are required to take a machining course the first semester. According to Yevgeniya Zastavker, a faculty member who conducts research in biophysics and studies the role of gender in science: “Everyone is faced straight on with gender differences in the lab. We set them up in coed teams and ask them to design a tool or a product. If the gender dynamics get weird, we intervene, and that one intervention early on has a ginormous effect.”

Back at Yale, Urry laughed at my own stories of how inept I had been in lab — drizzling acid on my stockings, which dissolved and went up in smoke, getting hurled across the room by a shock from an ungrounded oscilloscope, not being able to replicate the Millikan oil-drop experiment. Even she had been a disaster in lab in college. Only when she took a more advanced lab and spent hours poring over a circuit diagram, figuring out that her fellow students had set up an experiment wrong, did she realize she knew as much as they did.

“I’m soldering things, and I’m thinking, Hey, I’m really good at this. I know the principles. It’s like an art. It took me years to realize I’m actually good with my hands. I have all these small-motor skills from all the years I spent sewing, knitting and designing things. We should tell young women, ‘That stuff actually prepares you for working in a lab.’ ”

As the Yale study laid bare — scientists of both sexes also need to realize that they can’t always see the way their bias affects their day-to-day lives. Abigail Stewart, director of the University of Michigan’s Advance program, which seeks to improve the lives of female and minority faculty members, told me in an e-mail that Handelsman’s study shakes the passionately held belief of most scientists that they are devoted to accurately identifying and nurturing merit in their students. “Evidence that we are not as likely to recognize and encourage talent (even modest talent, as in this study) shakes our confidence and (I hope) will make us more attentive to our limitations in recognizing talent where we don’t expect to find it.”