One of my friends from West Point is a living testimonial to an Academy education. The story as I remember it goes something like this.

Joe graduated from high school with no particular plans. In his part of Pennsylvania, most high school grads got jobs. Very few went to college. Joe had been a standout high school football player and a more than adequate student, still it was unlikely that he would have gone to college if Army hadn't recruited him for football. He couldn't get into West Point out of high school, so he joined the Army and applied for the Military Academy Prep School.

From the prep school Joe got into West Point. He played plebe football and the next year moved up to the A Squad. He was doing great on A Squad and had just been promoted to first string when one of his knees got bent the wrong way at practice one day; I mean his leg now bent 90 degrees the wrong way. He could never play football again. Whether he could walk again was the main question.

Up until then Joe had been just getting by academically. The pain from his injury and the subsequent operation led to several weeks of heavy doses of morphine. He was in a hospital bed unable to attend classes and drugged to the point where he couldn't concentrate. At the end of that semester he was "found" in math. The Academy officials were concerned that he shouldn't be allowed to continue as a cadet in any case, since it was unlikely that he could be commissioned upon graduation. His future as a West Point Cadet looked bleak.

I'm going to pussyfoot a little with the next part of the story as I don't know what the NCAA rules were in those days and suspect that Army may not have played exactly by the rules in this case. Suffice it to say that the legendary football coach, Red Blaik, intervened, determined that Joe wanted to continue his cadet career, and made that possible. In the interim, Joe was "turned back" to the class of 1959 and would spend the next semester out of the Academy. Joe was directed to Brooklyn and a tutor or great renown. He went to the tutor for the time available and actually began to understand calculus and the more advanced math.

In those days (I don’t know how it's done now), instruction at West Point was minimal. Instructors briefly introduced new concepts, then asked if there were any questions, made assignments, and the class was over. The next class began with "recitation" in which all cadets were required to show how well they had learned the assignment for the day, grades were assigned, and then the next concept was briefly introduced. Cadets did most of the learning on their own. The opportunity to ask questions was a sham since the most obvious question, "I don't understand…", was officially off limits. Miss out on one concept and you were lost forever after. In the sections where Joe and I spent our days, many (all?) of us had gotten lost long ago.

After the intense tutoring in Brooklyn, though, Joe was not only caught up but, upon his return to West Point, he found himself well ahead of his new classmates. He actually understood what was going on in math and science courses and was soon in the advanced sections. That continued until his graduation.

Joe was commissioned and went off to serve in the Army, but he was worried about his bad knee. It bothered him on uneven ground, made it practically impossible for him to run, and was likely to fail him at the worst possible time. Joe resigned from the Army after 3 years and set out to find a civilian career.

Eventually his civilian jobs led him to industrial machinery, much of which suffered from vibration problems. Few if any of the industrial engineers in the plants had any understanding of the causes of or remedies for the vibration. Joe became the expert. He told me one day that he used differential equations to solve vibration problems in machinery. I asked, incredulously, if he actually solved differential equations and he said, "No, I write them."

In my own case, differential equations were where I hit the wall. They were black art as far as I was concerned. I know I'm not alone in my inability to master them. I believe that most engineers have no grasp of them. They may have passed a course, but from what they tell me, they got nothing out of it. Using differential equations in their business would be unthinkable for any but the most brilliant. Joe, the football player, is now a national expert on vibration abatement, called in by General Motors and Boeing to solve their vibration problems. He does it with differential equations.

The story should end here. If we go on we have to think about some heavy topics. If Joe, who wasn't understanding much math at West Point, could be made to understand it in a few months by a tutor, what does that say about the instructional method at the Academy? How much potential brilliance could have been unlocked in the minds of cadets with another instructional approach? An instructor once told us that we weren't being taught math, we were being taught to think. Could it be that we were also being taught to learn by ourselves? Were future learning and future thinking the real goals of West Point? See what I mean? The story should just end here.

Joe is "retired" now, lives at the beach, and only goes to work when he gets urgent calls from one of the major companies in the world. Which happens a lot.