Nascent function concepts in Nova Scientia

Abstract

The origin of the function concept is usually traced to Galileo's work on motion. We argue that specific proto-function concepts appeared in the work of Tartaglia a century before the publication of Galileo's Two New Sciences. The study of Tartaglia's ideas can be used in the classroom as a historical introduction to various function concepts, and certain modern extensions of Tartaglia's optimal range problem and inverse range problem are sources of enrichment for undergraduate courses in analysis, mathematical modeling and computation.

Acknowledgment

This work was supported in part by the National Science Foundation.

Notes

In the words of Salomon Bochner ‘Functions are a distinguishing attribute of modern mathematics, perhaps the most profoundly distinguishing of all’, ([1], p. 217).

Sarton remarks that ‘The history of instruments, we should remember, is one of the best approaches to the understanding of scientific progress, but it is full of difficulties; each instrument is developed gradually; none is created at one time for all time by a single man’. ([13], p. 44).

The mean radius rule of Gerard of Brussels ([14], p. 261) may also have affected Tartaglia's thinking.

In this regard see Duhem's criticism of Ubaldo's ‘narrow-mindedness’ and his defense of the intuitive approach versus Ubaldo's rigorous mathematics ([16], p. 149). E. H. Moore similarly faulted the deductive Euclidean programme for delaying the advent of modern science ([17], p. 411)