Search for mathematical proof in the Web environment as a process of creative collective discovery

Abstract

Abstract. Although cooperation and collective efforts have always played an important role in the process of scientific discovery, recent technological innovations, such as the Internet, facilitate and encourage cooperation and collective effort to an unprecedented degree. This applies to all fields of science, even mathematics, where the process of mathematical discovery has traditionally been considered as an individual affair. This perspective requires new research on the theoretical level, and reveals the importance of various aspects of the process of scientific discovery in relation to the issues of problem solving, discovery and creativity, which have not been studied sufficiently.

Styles Of Mathematical Proving In East And West: Their Use In Teaching

“…over these objects. Reasoning is conducted over Based on the analysis of Polymath Web-based proof-event (Stefaneas & Vandoulakis 2012), we suggested a model for mathematics education, where mathematical learning is viewed as cooperative distributive discovery proof-event (Vandoulakis, 2016). This (sequence of) proof-event(s) can take place in a physical environment, i.e.…”

On The Significance Of Argumentation In Searching For Mathematical Proof

“…Proof-events are not considered infallible facts, until they are finally confirmed and validated by the relevant community. This allows one to examine episodes of erroneous approaches and purported proofs using the theory of argument put forward by Toulmin (1958) and Pollock (1992) (as arguments and counterarguments) and the concept of defeasible reasoning. Thus, the exchange of arguments and counterarguments between agents, aimed at clarifying possible gaps or implicit assumptions that occur during a proof, can be formally represented within this integrated framework (Almpani, Stefaneas, Vandoulakis, 2017).…”

“…2. Argumentation theory, notably Toulmin's model (Toulmin, 1958) and Pollock's logical theory of argument (Pollock, 1987;1992).…”

“…The methodology commonly used to study argumentation is based on Toulmin's model (Toulmin, 1958). Toulmin proposed a set of six interrelated components for the analysis of arguments:…”