Innumeracy: Mathematical Illiteracy and Its Consequences

by John Allen Paulos

One of Freud’s closest friends, a surgeon named Wilhelm Fliess, invented biorhythmic analysis, a practice based on the notion that various aspects of one’s life follow rigid periodic cycles which begin at birth. Fliess pointed out to Freud that 23 and 28, the periods for some metaphysical male and female principles respectively, had the special property that if you add and subtract appropriate multiples of them, you can attain any number. Stated a little differently: any number at all can be expressed as 23X + 28Y for suitable choices of X and Y. For example, 6 = (23 × 10) + (28 × –8). Freud was so impressed with this that for years he was an ardent believer in biorhythms and thought that he would die at the age of fifty-one, the sum of 28 and 23. As it turns out, not only 23 and 28 but any two numbers that are relatively prime—that is, have no factors in common—have the property that any number can be expressed in terms of them. So even Freud suffered from innumeracy.