The best review of arithmetic consists in the study of algebra.

After examining the writings of Archimedes one can well understand how, in ancient times, an "Archimedean problem" came to mean a problem too deep for ordinary minds to solve, and how an "Archimedean proof" came to be the synonym for unquestionable certainty.

The miraculous powers of modern calculation are due to three inventions: the Arabic Notation, Decimal Fractions and Logarithms.

One of the most baneful delusions by which the minds, not only of students, but even of many teachers of mathematics in our classical colleges, have been afflicted with is, that mathematics can be mastered by the favored few, but lies beyond the grasp and power of the ordinary mind.

The history of mathematics is important also as a valuable contribution to the history of civilisation. Human progress is closely identified with scientific thought. Mathematical and physical reseaches are a reliable record of intellectual progress.