I always liked mathematics.

Grade school math was mostly rote arithmetic and quite boring. We did some word problems in 5th and 6th grade, which were not hard, but not very interesting. Math did not become interesting until we started putting mathematical variables such as x, y, z, etc. into equations and then solved problems in terms of those variables. I think that is the point at which a lot of other students started losing interest in math - or, more precisely, arithmetic.

Compared to the boring math in grade school, math finally became interesting. We covered sets and set theory with union, intersection, complement (good through graduate school and beyond), number theory that included number bases, factoring, prime and composite numbers, etc.

Sometime in the middle of the year the teacher had a class contest. She picked out about 4 of the better students to sit in the front. The rest of the class had to come up with questions for the selected students. I was one of the 4 selected to sit in front. I did not know many students and they did not know me. The class came up with the hardest questions they could devise. I apparently did not appear to be very smart, so I got about the first four questions, such as "what is the 10th prime number". After answering each question without much delay, the rest of the class did not ask me another question, choosing instead to ask the other 3 students questions, where they more easily stump those students and get points in the contest.

In the spring we had a student or temporary teacher but I do not remember his name. I think our regular teacher was on maternity leave. We were covering division. I made a drawing of our teacher in class (I was always doodling or drawing). Some other students thought the drawing looked just like the teacher. But he might have been mad if he saw it, so I kept it to myself. Here it is. I did the face first, then added the rest (not to scale).

The teacher talked about addition, subtraction, multiplication, and then division. He said that in division, one takes a number x divides by a divisor d and gets a quotient q and remainder r such that when one multiplies the quotient q by the divisor d and adds the remainder r one gets the original x.

I almost never asked any questions nor made comments, but I thought about it, and then asked the following question.

If that is so, then why is 0 (zero) divided by 0 (zero) not 0 (with a remainder of 0) since when one multiplies 0 (zero) by 0 (zero) one gets 0 - which was exactly the rule he had just related to us.

He had no answer and was somewhat shaken (he went to pieces, so to speak). This was near the end of class. At the beginning of the next class, he tried to give an satisfying answer but it was not very enlightening.

Some 30 years later, after I had obtained a Ph.D. in computer science, I was looking through Donald Knuth's books on algorithms and discovered Knuth's answer, but only for real number arithmetic, not necessarily for integers. Knuth stated that if one takes the limit of x divided by y as that y approaches 0 (zero), then one gets a different limit (positive or negative infinity) when one approaches from the positive or negative side. Thus, the result of 0 divided by 0 is undefined. That is the best answer I have found to date - though the remainder appears to only have a defined meaning for integer arithmetic.

Mr. Clouser did a good job of teaching algebra.

This was beginning algebra, solving problems in terms of a mathematical variable such as x.

Mr. Clouser, again, did a good job of teaching algebra. He had contests whereby one said arithmetic problems in a sequence very fast and one had to try to come up with the answer. I did not really care for that, though RM and SH, among some others, really got into it.

We covered the quadratic equation, solutions, etc. Polynomial multiplication and division and factoring ended up being useful later on.

I liked geometry and the proofs. Our teacher Stanley Dotterer brought in a lot of math and logic puzzles that were very interesting. I do not think most students liked geometry and certainly they did not like the proofs.

Mr. Kreamer, who liked to do push-ups, etc., did a good job in this class.

This was about analytic geometry, trigonometry, and pre-calculus, including power series, transcendental numbers, etc. It was all very interesting.

We had covered functions such as cos, sin, etc., quickly at the end of 8th grade but no one did well at that time and it did not make sense. With analytic geometry, it all now made sense and could be used for many practical purposes. There ware a lot of practical applications of this mathematics in 12 grade physics.

I did well enough to get into advanced placement mathematics it West Point the next year. During the (quick) on-site interview, I was asked the derivative of a simple linear function. From this class, I was able to provide an immediate answer. That allowed me to take 4 semesters of mathematics and statistics in 3 semesters as part of advanced placement, giving me one additional elective course later in college.