Mar. 6, 1945
Germany
Darling,
Yesterday, there being no work to do, I slept late, and then spent a good part of the day studying "Mathematics & The Imagination." This book is extraordinarily interesting, and has opened a new field of thought to me, about which I have known nothing. I have drawn two conclusions from having read the book. (1) Everyone's (i.e. our children's) mathematical education should include differential & integral calculus, and (2) mathematics is taught all wrong in our schools.  We study the details to such an extent that we lose sight of the significance of the whole inquiry. Thus, in Euclidean geometry, we spend hour after hour following through the proof of all his theorems, whereas, I feel sure, we should spend perhaps half as long on that (since once you've done 6 or 8, you can do the rest easily enough), and the rest of the time should be spent analyzing axioms and postulates, relative geometry to thought, to reality, and to non-Euclidean geometries, such as Riemann's or Lobachensky's. In algebra, we study hours on the details of solving first and second degree equations. We should also spend hours analyzing the tools of algebra - roots, symbols, geometric analysis, numbers (real, prime, rational, irrational, transfinite, etc.) Thus algebra begins to have some meaning and ceases to be a tiresome exercise.
Then in the afternoon I tramped around and got a little exercise. Investigated a bomb shelter which the Heinies had built for the inhabitants of the town. It appears to have been well used!
Have you ever thought of the strange ways of thought of Americans as regards how we term our friends and our enemies? Thus, we call our allies Frogs, Dagos, Wops, and Limeys, while for our enemy we have our almost affectionate term - Jerry. These names are harmful, and connote, I believe, an underlying, deep, mental feeling of superiority and even contempt. In any case, it certainly doesn't make sense.
H