"Much has been said by the students here in School about the lack of value and practical use of many things we teach in mathematics, physics and mechanics. Then too many of our graduates return and tell us they have never had need for this course or that in their practice. In most cases we find on investigation that they did not know enough about the subject to use it when opportunity arose so had to work around the matter in some other way and more often I suspect they knew so little of the subject that they failed to recognize the opportunity when it came up in the first place."
"There are two steps to the solution of any problem in mathematics - analysis which might be termed "headwork" and manipulation which is just what the term implies, "handwork." The first process, analysis or headwork, involves that seldom exercised process of human thought we call "reasoning." God alone endows you with the power to reason. No man is so good a teacher that he can give you the ability to think and reason. However, this God given trait may be developed both by individual effort and by that of the teacher. The second process, the "handwork" can be taught to anyone. Even a monkey can be taught to do tricks of this type. This involves for any given problem certain mechanical processes in arithmetic, algebra & calculus which we stress here at the School of Mines. We teach sufficient algebra, geometry, triginimetry and calculus for the student who is even below average to learn to manipulate the necessary mechanical processes that arise in any ordinary problem in engineering."
"This brings in the third element which one must contribute to the solution of problems - this has no part in the solution but is a mighty watchdog over the whole process. It is called common sense or judgement. One can know processes, methods & get results but if one's judgement is poor then these results may mean little or nothing ... Let me illustrate ...
W = wt of elephant [and] z = wt of flea.
Let W + z = 2x
W = 2x - z
W - 2x = -z
W2 - 2Wx = z2 - 2zx
W2 - 2Wx + x2 = z2 - 2zx + x2
(W - x)2 = (z - x)2
W - x = z - x
So W = z
__in ``Mathematics in Engineering,'' handwritten notes for a speech or presentation, Missouri School of Mines, c.1930-60. Rolfe Rankin was a Mathematics faculty member at MSM from 1922-1963 and was department chair from 1942-63. The above "proof" that a flea weighs the same as an elephant was the conclusion of Rankin's speech, and he left his audience with the task of figuring out where the rules of algebra were subtly violated to get a nonsensical conclusion, as I also leave this to the reader.