A Rigorous Comparison between Mathematicians and Engineers by Mason A. Porter You may have run into a mathematician or two and perhaps wondered how they got that way. The answer is actually quite simple. They were dropped by their parents when they were children-several times. In fact, according to a recent survey in _US News and World Report_, Ph. D. candidates in mathematics and applied mathematics were dropped an average of 7.2 times before their 13th birthdays, which undoubtedly did untold damage to their psyches. There are notable exceptions, however. I, for example, was dropped at least six dozen times as a child without any noticeable adverse effects. Such situations are rare, however, and it is rumored that these occur only in people whose heads express unusually high malleabilities. (I'm not sure, though. It's just a theory.) It has been said that mathematicians understand the way things function but can't actually get anything to work, while engineers can get things to work even though they can't figure out why. Although this paradigm is quite questionable-I doubt very strongly whether mathematicians truly know how a given object functions-one should notice that if it is true, applied mathematicians are placed in a rather enviable position. They do not know how things work _and_ they can't get them to work. I cannot speak for anybody else, but as a student in the Center for Applied Mathematics, I must say that I am quite proud of this distinction (although I'll insist until my dying day that I am not evidence of this phenomenon). There are perhaps more important distinctions between engineers and mathematicians. It is an indisputable fact that mathematicians get all the girls. (Empirical studies among graduate students at various universities have verified it.) It has been shown, moreover, that this result is independent of the gender of the mathematician. The mere utterance of the phrase "tensor analysis" drives women wild. Mathematics truly is the language of love. I have had classes, for example, in which I've studied curve fitting, lubrication theory, and even the Hairy Ball Theorem. Of course, several concepts (such as rigid rods and deformation of solids) actually encompass mathematics as applied to various engineering and scientific disciplines, but applied mathematicians are in a truly unique position, as they are familiar with more of this language than anybody who studies only one or two scientific areas in depth. I do not mean to say that mathematicians are more knowledgeable than engineers-they are not. They simply have been exposed to this romantic paradigm far more than the latter. Mathematicians and engineers are distinguishable in other ways as well. You might have witnessed an engineer (who, for the purpose of this example, dislikes mushrooms) complain about, say, the "high mushroom density" in his/her barley soup. Why must everything be some sort of density? Why not say simply that there are too many mushrooms in one's soup? As strange as engineers may often seem, mathematicians are truly curious beasts. If you have spent any appreciable amount of time with them, you must realize that the most apt comparison of your experiences are the interactions between Jane Goodall and her chimps. Have you ever seen mathematicians argue about the number of dimensions in the models they're studying? Nothing else matters--not the comprehensibility of their theory or the number of features of their system of choice their model has successfully emulated. Mathematicians simply care about whose system of equations has more dimensions. Though odd, this is easily explained--it is simply their version of penis envy. Additionally, these arguments are amusing to watch, but it really is no more complicated than two young boys comparing the relative size of Mr. Happy. Another oddity endemic to mathematicians is their fascination with the word "trivial." Things are not "difficult"; instead, they are "non-trivial." As a service to any engineers reading the present essay, I will now provide a brief glossary of various notions of difficulty in the language of mathematics. A "trivial" problem refers to a grungy calculation that can be assigned to graduate students for homework. It might take several days to complete, but the professor was able to do it. An "easy" problem is similar to a trivial one, except that the professor was unable to solve it when he was a graduate student. A "slightly non-trivial" problem is a single semester (or summer) project. A "non-trivial" problem is one about which somebody can write a thesis should he/she manage to solve it. A "very non-trivial" problem differs from a non-trivial one in that although it can in principle be a research project, it has gone unsolved for decades if not centuries. Fermat's Last Theorem, for example, was considered a very non-trivial problem until it was solved. (It has since been reclassified as having a difficulty residing somewhere between easy and slightly non-trivial.) Very non-trivial problems are occasionally also referred to as "not so easy" problems. (Mathematicians sometimes use the latter term when they suspect that ultimately it will be proven that the problem is unsolvable.) Lastly, a "hard" problem is one that has been shown can never be solved. For example, the problem of finding a general analytic solution to the n-body problem is considered hard. (Several problems that John Guckenheimer assigns in his classes also fit into this category.) A layperson would most likely substitute the word "impossible" to describe a problem at this level of difficulty. Since I have spent the last several paragraphs disparaging mathematicians, it is imperative that I explain why I became one. I assure you that I did not do so for the sole purpose of intellectual masturbation. (Of course, I willingly admit that that was _part_ of the reason.) Similarly, I did not simply join them because I could not beat them. The truth of the matter can be found in this essay. I did it for the women. Now that I have been indoctrinated, however, the only thing that remains to be said is "Oops!"