REMEMBER the Dumb Kid in your math class who couldn’t understand what a square root was? Gone. Vanished from the earth like the stegosaurus. If your child is at an elite school, there are no dumb kids in his or her math class — only smart and smarter.

Even the most brilliant students have to work harder now to make their nut. The competition for places in the upper tier of higher education is a lot tougher than it was in the 1960s and ’70s, when having good grades and SAT scores in the high 1200s was generally sufficient to get you into a respectable college. My contemporaries love to talk about how they would have been turned down by the schools they attended if they were applying today. This is no illusion: 19 percent of applicants were admitted to my Ivy League school for the class of ’71; 6 percent were admitted for the class of ’15.

Graduate and professional school statistics are just as daunting. Dr. Bardes told me that he routinely interviewed students with perfect or near perfect grade point averages and SATs — enough to fill the class several times over. Last year 5,722 applicants competed for 101 places at Weill Cornell; the odds of getting in there are even worse than those of getting your 3-year-old into a New York City private school.

“Applicant pools are stronger and deeper,” concurs Stephen Singer, the former director of college counseling at Horace Mann, the New York City private school renowned for its driven students. “It used to be that if you were editor of the paper or president of your class you could get in almost anywhere,” Mr. Singer says. “Now it’s ‘What did you do as president? How did you make the paper special?’ Kids file stories from Bosnia or El Salvador on their summer vacations.” Such students are known in college admissions circles as “pointy” — being well-rounded doesn’t cut it anymore. You need to have a spike in your achievement chart.

AND it doesn’t hurt to be from an exotic foreign land. “Colleges are reaching out to a broader range of people around the world today,” says William R. Fitzsimmons, Harvard’s dean of undergraduate admissions. “They go to Africa and China. If you want first-class mathematicians, try looking in Bulgaria.” In case they miss someone, many colleges now have recruiting agents in other countries who are paid commissions — by both the parents and the college — to help “place” those students. Globalization comes to the college admissions world.

Just as the concentration of wealth at the very top reduces wealth at the bottom, the aggressive hoarding of intellectual capital in the most sought-after colleges and universities has curtailed our investment in less prestigious institutions. There’s no curricular trickle-down effect. The educator E. D. Hirsch Jr. has pointed to a trend he labels the Matthew Effect, citing the Biblical injunction: “ ‘For unto every one that hath shall be given and he shall have abundance: but from him that hath not shall be taken away even that which he hath.’ We’ve lifted up rich kids beyond their competence,” he says, “while the verbal skills of the black underclass continue to decline.”