The Art of Doing Science and Engineering: Learning to Learn

by Richard Hamming

Students are remarkably able to memorize their way through many math classes, and many do so. But when I get to analytic integration (I give the students a function and ask for its indefinite integral), there is no way they can memorize their way through the course the way I teach it. They must learn to recognize in an almost infinite number of disguises. For the first time in their career they are forced to learn to recognize forms independent of the particular representation—which is a basic feature of mathematics and general intelligence. To take analytic integration out of the course, or transfer it to routines in computers, is to defeat the purpose of a stage of learning something that is essential, in my opinion, unless something of equivalent difficulty is put in. The students must master abstract pattern recognition if they are to progress and use mathematics later in their careers.