After years of teaching, as well as writing and editing scores of research papers and books, I recently began to wonder if my SAT scores would be good enough to get into Princeton University, where I am now a faculty member. Based on my publication record and citations thereof, and my modest successes in the classroom, I think it is fair to say that the Princeton administration does not regret hiring me and promoting me to full professor. But if I were to apply to attend Princeton today, would I get in?

Without actually submitting an anonymous application, it was a hard question to answer. But I could try to obtain a dispassionate assessment of what my admission profile would look like by retaking the SAT —more than three decades after I first took it in high school. (I didn't apply for admission to Princeton back then, but selected the Rensselaer Polytechnic Institute over the Massachusetts Institute of Technology because RPI offered a better scholarship.)

I initially planned to take the test with a horde of students at the local high school. But that seemed difficult, both logistically and socially. Fortunately, the College Board Web site lets one download practice exams that are presumably equivalent to an actual test, along with instructions on how to administer and grade them.

So, some months ago, I blocked out a morning, cleared off my normally cluttered desk, locked my office door, and began the exam. My office assistant was stationed in the adjoining room and made sure I didn't run over time on any section.

How did I do? The math part of the exam was pretty easy. My Ph.D. is in mathematics, so that's not surprising. Still, there was the chance that I might have been tripped up by a trick question, as I was back in high school. I had already completed a year of trigonometry and calculus before taking the SAT then and was confident I had answered all of the quantitative questions correctly. I was surprised when I got a 780 on the math section.

This time, I did better. I got all those questions correct and scored 800.

The critical-reading section was harder. I was a slow reader in high school, and I'm a slow reader now. It was tough to pace myself properly. The hardest set of questions involved a pair of page-long essays on the Rev. Martin Luther King Jr. and whether or not a holiday in his honor is a good thing. One question asked something like, What would Author B say about the fourth paragraph in Author A's essay? Sheesh. Questions like that make my head spin. Anyway, I got a 680 on that part, significantly better than my corresponding score from 36 years ago, but probably not that good in the eyes of Princeton admissions officials.

I did better on the writing part, although it is hard to assess because the final score represents a combination of objective multiple-choice questions and a subjective essay. To help grade the essay, the Web site lets you download sample graded essays with which you can compare your own. The highest possible score, from each reader, on the essay is a six.

My essay question asked for one's opinion on privacy in America. Has American society become too open? I have an opinion on that question (openness is good), but I didn't, in the allotted 25 minutes, come up with any compelling anecdote to make my essay especially interesting. What I wrote was grammatically correct, logical, and used appropriate vocabulary. Compared with the sample essays, it wasn't as interesting as the ones that got a score of six, but it seemed logically tighter than those that received a score of five. The sample essays that received a score of four or lower seemed clearly inferior —both to me and to my office assistant. So, if I give myself a five on the essay, then my writing score is 710. If I give myself a six, it jumps up to 740.

What did I learn from the experiment?

For one, the scores seemed to be a good reflection of how I stand in comparison with when I was in high school. (In other words, I think I'm much closer to Princeton students verbally than I was then.) Also, it seems correct to me that I scored lower on the reading part than on the writing part and performed best on the quantitative part. But mainly what I learned is that the SAT is a challenging, well-thought-out exam.

Of course, the test is limited in scope, as it must be given that it requires only a few hours of one's time. It is simply impossible to measure every dimension of a secondary-school education in so short a time. For example, the math portion tests only the most elementary topics of algebra and geometry. With only 54 math questions, it simply can't assess all levels of mastery. Given the limited scope, however, the SAT raises a well-conceived set of questions.

For instance, some questions are really simple, whereas others are more subtle. A subtle question is one for which you can use multiple ways to get to the correct answer —some that are quick and easy, others that are tedious and time consuming. I take pride in my own exams when I come up with such questions. The SAT's math section has some questions like that.

One question, for example, gives several (x,y) pairs and asks which of five functions produces those pairs. You could start plugging x's into the functions to see if the correct y's are produced, but that is the long and tedious approach because two of the five functions are quadratic and one is cubic. The smart way is to graph the five data points, which quickly reveals that the function is linear with a certain obvious slope and intercept. Problem solved.

Many people ask whether the test really tests aptitude or achievement. Clearly, it tests some combination. A person needs to have attained a certain, rather minimal, level of achievement in math to score well on the analytical part, and he or she needs to have a fairly broad vocabulary and an understanding of English grammar to do well on the other two parts. But the exam also tests cleverness. For example, some math questions were nonstandard and required creative thought to determine the answer quickly.

So would I get into Princeton today? My score is probably borderline according to the university's admissions standards. But it is worth noting that admission to Princeton today is not the same as it was 36 years ago. My performance back then was sufficiently skewed to the geek side that I knew I had no chance to get into Princeton, so I didn't even apply. Today, however, my perception is that the admissions office has more geek-friendly policies —certainly we are attracting many brilliant students who in previous decades might have been destined for MIT.

The SAT itself does a fine job at what it sets out to do. The problem is that educators have gotten smart —in addition to educating, they teach to the test. That skews things; some school systems rightly shun that idea of teaching whereas others embrace it. Furthermore, the College Board itself embraces the notion of teaching to the test, evidenced by the fact that it encourages students to take practice tests and even the full SAT multiple times. If secondary-school educators could be kept in the dark about the content of the exam, and if all students were to take the test cold, I'm sure the SAT would provide valuable information to college admissions offices. But that is not the world we live in.

Finally, I have come up with an essay question that SAT test writers should consider for future SAT's: If 30 years from now you have the opportunity to retake the SAT exam, would you do it, and what would you hope to learn?

Robert J. Vanderbei is a professor in operations research and financial engineering at Princeton University.