The great Felix Klein urged us quite a number of years ago to join hands with our students and share the pleasures of “delightful and instructive walks through forests, fields, and gardens … without digging up the most profitable plants to replant them in prepared soil according to the principles of rational agronomy.” [1]

And he furthermore added: “Apart from the majority of enthusiastic students there are always a few students who are not entirely satisfied, who criticise and question. These are the ones dearest to my heart. For I see in them what I consider to be the true goal of all teaching: independent thought.” [2]

I feel that the intellectual mathematics philosophy is conceived in the spirit of these passages.

[1] Felix Klein, Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert. Teil I. Springer-Verlag, Berlin, 1928. Quoted from the English translation: Development of Mathematics in the 19th Century. Math. Sci. Press, Brookline, MA, 1979, page 152.

[2] Felix Klein, Über Aufgabe und Methode des mathematischen Unterrichts an den Universitäten. Jahresbericht der Deutschen Mathematiker-Vereinigung, 7, 126–138. Quotation from page 133, my translation.