Das Unwahre des Resultatismus. Eine historische Fallstudie aus der Analysis. (The untrueness of resultatism. A historical case study relying on analysis)
The author argues that today mathematics is presented as a series of unquestionable results without any mention of the long process of doubting and searching which mathematicians have gone through to arrive at the results. Learners are forced to accept the final results as indubitable truths. Due to this many find mathematics boring and some develop an aversion towards it. The author illustrates his point by discussing the fundamental theorem of analysis that every continuous function f in a closed interval assumes every value between f(a) and f(b) within the closed interval. He shows how from 15th century onwards mathematicians never doubted the truth of it but tried to prove it in different ways; some through algebra, others through geometry and yet others through the concepts of functions and continuity. The modern approach is of course to explain the basic concepts of analysis through set theory and topology, assuming thereby that these disciplines are beyond any epistemological critique. Those who are aware of this type of critique by the different schools of constructive mathematics would no doubt support the view that historical development of mathematical ideas is very essential for a liberal and non-dogmatic presentation of mathematical concepts. This might make mathematics interesting to many who turn away from it.
scientific article; zbMATH DE number 4063048