I've never had the guts to learn how to perform proper archival research into 1900s West Point mathematics textbooks to confirm/see the solution, but I remember from biographies a famous anecdote from Dwight Eisenhower's days as a cadet involving integral calculus.
tl;dr: in that era students memorized step-by-step solutions from the textbook since it was the "right way" to do things. Eisenhower wasn't prepared, got called to the board and came to a creative solution back that didn't match the textbook. He got chewed out by the instructor for bluffing but then Major Bell an Associate Professor of Mathematics intervened and confirmed Eisenhower approach and insisted textbooks be updated to reflect the new solution.
From Page 77: https://www.google.com/books/edition/Eisenhower/RCeteK7LEiYC...
From: Page 10 of Eisenhower: Soldier and President by Stephen Ambrose
“Often the instructors knew little more than their students. In integral calculus one day, the teacher order Eisenhower to do a long, complicated problem on the blackboard. The insrturctor had previously explained the problem and supplied the answer, but since it had been obvious to Eisenhower that the instructor was doing it entirely by rote he had paid no attention. Thus, when called upon, he had ‘not the foggiest notion of how to begin.’ After struggling for almost a full hour, he finally tried a solution that, to his amazement, worked. He was asked to explain his solution; it was shorter and simpler than the rote answer. But the instructor interrupted him to charge that he had merely memroized the answer and then put down a lot of figures and steps that had no meaning.
Eisenhower could not abide being called a cheat. He began to protest so vehemently that he was soon in imminent danger of being expelled on a charge of insubordination. Just then, a senior officer from the Mathematics Department walked in. He inquried about the trouble, had Eisenhower go through the solution again, then pronounced it superior to the one being used in the department and ordered it incorporated into the Mathematics Department’s teaching”
From At ease: stories I tell to friends (written by Eisenhower -1967):
"About midway in our West Point course we began the study of integral calculus. The subject was interesting but the problems could be intricate. One morning after recitations the instructor said that on the following day the problem would be one of the most difficult of all. Because of this he was giving us, on the orders of the head of the Mathematics Department, an explanation of the approach to the problem and the answer.
The explanation was long and involved. It was clear that he was doing his task completely by rote and without any real understanding of what he was talking about. Because I was a lazy student, with considerable faith in my luck, I decided there was little use in trying to understand the solution. After all, with twelve students in the section, only one of us would get this problem to solve, the odds were eleven to one that I would not be tapped. The following morning I was chosen. Going to the board, on which I was required to produce the solution, and then explain it to the instructor, I had not the foggiest notion of how to begin. I did remember the answer given by the instructor and wrote it in the corner of the board.
I set to work. I had to make at least a good start on the problem, show something or receive a grade of zero which would do nothing for me in a course where my grades were far from high. Moreover, I could be reported to the disciplinary department for neglect of duty in that I had deliberately ignored the long explanation. With this in mind I sought in every possible way to jog my memory. I had forty-five or fifty minutes to solve the problem and I really concentrated. After trying several solutions that seemed to relate, at least remotely, to the one I dimly remembered from the morning before, I encountered nothing but failure. Finally, with only minutes left, I worked out one approach that seemed fairly reasonable. No one could have been more amazed than I when this line of action agreed exactly with the answer already written on the board. I carefully went over the work, sat down, and awaited my turn to recite. I was the last man in the section to be called upon. With some trepidation I started in. It took me a short time to explain my simple solution--indeed it had to be simple or I never would have stumbled upon it. At the end, the instructor turned on me angrily and said, "Mr. Eisenhower, it is obvious that you know nothing whatsoever about this problem. You memorized the answer, put down a lot of figures and steps that have no meaning whatsoever, and then wrote out the answer in the hope of fooling the instructor.
I hadn't been well prepared but this was tantamount to calling me a cheat, something that no cadet could be expected to take calmly. I reacted heatedly and started to protest. Just then I heard Major Bell, the Associate Professor of Mathematics (whom we called "Poopy," a name that was always applied to anyone at West Point who was above average in academic attainments) who had entered the room for one of his occasional inspections, interrupting. "Just a minute, Captain."
Of course, I recognized the voice of authority and shut up, although according to my classmates' description that night I was not only red-necked and angry but ready to fight the entire academic department. I would have been kicked out on a charge of insubordination if I had not been stopped. Major Bell spoke to the instructor, "Captain, please have Mr. Eisenhower go through that solution again."
I did so but in such an emotional state that it is a wonder that I could track it through. The long search for a solution and its eventual simplicity stood me in good stead. Major Bell heard it out and then said, "Captain, Mr. Eisenhower's solution is more logical and easier than the one we've been using, I'm surprised that none of us, supposedly good mathematicians, has stumbled on it. It will be incorporated in our procedures from now on." This was a blessing. A moment before, I had an excellent chance of being expelled in disgrace from the academy. Now, at least with one officer, I was sitting on top of the world."