Have I ever mentioned that I have an undergraduate English degree? I do. Or – one of my undergraduate degrees is an English degree. I’m a social scientist. The English degree was pure consumption, knowledge for its own end. I should not have completed the requirements but rather spent that time studying German or French. Or I should have finished my math degree. No,no, the languages. I took plenty of math. One of those math classes was perhaps the most important I ever took.
It was Calculus III. I believe there were about fifteen of us at the beginning. Seven at the end. I think I was the only social scientist in that group. The rest were engineers, scientists, and maybe just one mathematician. This was the hardest undergraduate class I ever encountered, by far, by so far. I now know that it was a deliberate screen, driving off the insufficiently serious.
John Henry Newman devotes a chapter of The Idea of a University to “Knowledge Viewed in Relation to Professional Skill” – knowledge that is by no means for its own end. By the end of the speech, he has cleverly turned the argument back into a defense of a broad, liberal education, but he understands the necessity of professional training, too. How should a university engage in professional training?
[I]t is not mere application, however exemplary, which introduces the mind to truth, nor the reading many books, nor the getting up many subjects, nor the witnessing many experiments, nor the attending many lectures. All this is short of enough; a man may have done it all, yet be lingering in the vestibule of knowledge – he may not realize what his mouth utters; he may not see with his mental eye what confronts him; he may have no grasp of things as they are; or at least he may have no power at all of advancing one step forward of himself… (134-5)
That’s where I and my classmates were, on the vestibule of knowledge, Good At Math but unable to advance a step without assistance. I’m not sure how he did it – the difficulty of the class was necessary, but not sufficient to the task – but he taught us how to study math.
Six of us marched on to the same professor’s spring class (Differential Equations, I think), where we were joined by a new crop of recruits, all of whom found the course brutally difficult. Not the veterans, though. We thought it was a breeze. A powerful, difficult, laborious breeze, yes. But no big deal. We had already learned how to learn about math. I did not have another class so difficult, in math, or anywhere else, until I went to graduate school, which was a whole ‘nother ball game.
At this time last year, I was actually teaching a math class, to graduate students. Much of the material was exactly what we covered in that crucial Calculus III class, although I’m not sure that’s relevant. I was able to teach the class, I realized what my mouth uttered, because of Calculus III, twenty years in the past. I was able to finish my PhD because of Calculus III. I don’t want to guess how much of my professional success can be traced to this one course.
Newman argues that even professional training requires “the intellect” to be “disciplined for its own sake, for the perception of its own proper object, and for its own highest culture.” He calls this “the business of a University” (135). That’s what this math professor, a true practitioner of liberal education, did for us. I don’t remember his name.
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