Commutative Quotes (2 quotes)
Please forget everything you have learned in school; for you haven’t learned it. … My daughters have been studying (chemistry) for several semesters already, think they have learned differential and integral calculus in school, and even today don’t know why x · y = y · x is true.
From 'Vorwort für den Lernenden', Grundlagen der Analysis (1930), vi. A later edition of the German text, published in the United States (1951, 1965), included Prefaces (only) translated into English by F. Steinhardt. In the latter text, the quote appears in English on pages 7-8, and in the original German on pages 15-16: “Bitte vergiß alles was Du auf der Schule gelernt hast; denn Du hast es nicht gelernt. … meine Töchter … schon mehrere Semester studieren (Chemie), schon auf der Schule Differential- und Integral-rechnung gelernt zu haben glauben und heute noch nicht, wissen, warum x · y = y · x ist.”
Quantity is that which is operated with according to fixed mutually consistent laws. Both operator and operand must derive their meaning from the laws of operation. In the case of ordinary algebra these are the three laws already indicated [the commutative, associative, and distributive laws], in the algebra of quaternions the same save the law of commutation for multiplication and division, and so on. It may be questioned whether this definition is sufficient, and it may be objected that it is vague; but the reader will do well to reflect that any definition must include the linear algebras of Peirce, the algebra of logic, and others that may be easily imagined, although they have not yet been developed. This general definition of quantity enables us to see how operators may be treated as quantities, and thus to understand the rationale of the so called symbolical methods.
In 'Mathematics', Encyclopedia Britannica (9th ed.).