The bulk of attrition comes in engineering and among pre-med majors, who typically leave STEM fields if their hopes for medical school fade. There is no doubt that the main majors are difficult and growing more complex. Some students still lack math preparation or aren’t willing to work hard enough.

Other deterrents are the tough freshman classes, typically followed by two years of fairly abstract courses leading to a senior research or design project. “It’s dry and hard to get through, so if you can create an oasis in there, it would be a good thing,” says Dr. Goldberg, who retired last year as an engineering professor at the University of Illinois at Urbana-Champaign and is now an education consultant. He thinks the president’s chances of getting his 10,000 engineers is “essentially nil.”

The latest research also suggests that there could be more subtle problems at work, like the proliferation of grade inflation in the humanities and social sciences, which provides another incentive for students to leave STEM majors. It is no surprise that grades are lower in math and science, where the answers are clear-cut and there are no bonus points for flair. Professors also say they are strict because science and engineering courses build on one another, and a student who fails to absorb the key lessons in one class will flounder in the next.