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Section 5.1 of this chapter is written by Hans Niels Jahnke on the basis of his presentation at ICME 13. Michael Fried was invited to react to this presentation at ICME 13 and elaborated his reaction as Sect. 5.2 of this chapter. Although the authors are only responsible for their respective parts, the parts belong together and are therefore published here as a joint chapter. The first part analyzes the role of mathematics within the ideas on education of the neo-humanist movement. It refers to the period of around 1800–1850 and concentrates on the thinking of W. von Humboldt and the two catchwords of "anti-utilitarianism" and 'self-directed activity". From this general educational attitude resulted a certain preference for pure mathematics which had to be balanced against the daily needs of shopkeepers and workmen. A compromise on this issue was developed and implemented in the 1820s. Nevertheless, a strong emphasis on theoretical thinking, understanding and pure science remained for a long time the main stream of educational thinking In the eyes of the neo-humanists this was not a denial of the demands of practical life, but the best way to meet them. In his reaction entitled "Bildung, Paideia, and some undergraduate programs manifesting them," Michael N. Fried discusses how notions similar to that of Bildung are enshrined in the idea of paideia and the classical concept of the liberal arts. He shows that such ideas also work in modern times in the English speaking world by hinting at examples of prominent colleges in North America.

DOI: 10.1007/978-3-030-11069-7_5

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