The Web as A Tool For Proving

Abstract

The Web may critically transform the way we understand the activity of proving. The Web as a collaborative medium allows the active participation of people with different backgrounds, interests, viewpoints, and styles. Mathematical formal proofs are inadequate for capturing Web‐based proofs. This article claims that Web provings can be studied as a particular type of Goguen's proof‐events. Web‐based proof‐events have a social component, communication medium, prover‐interpreter interaction, interpretation process, understanding and validation, historical component, and styles. To demonstrate its claim, the article discusses the Kumo and Polymath projects, both of which employ Web‐based communication as part of proving. Web proving is a novel type of proving activity that may have a serious impact on the change in mathematical practices, despite the fact that it is not currently a universally acceptable methodology.

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.…”

“…The analysis of Web-based proof-events, in a sense similar to case of the Polymath project (Stefaneas & Vandoulakis, 2012).…”

Cognitive Strategies of Behavior of Primary School Children in the Digital Environment

“…The purpose of the study is to analyse the cognitive strategies of active and passive users in the digital environment. Stefaneas and Vandoulakis (2012) concluded that digital space had contributed to the formation of new cognitive formation. The usual system of proof is mathematical.…”

“…Brainstorming in the digital environment leads to success in the process of combination of the abilities and knowledge of its users (Stefaneas & Vandoulakis, 2012). Different users are specialists in distinct fields and can use a variety of scientific languages, which allows them not only to combine research values and standards but also to synthesize research methodologies and styles.…”

Toward a Philosophy of The Web

“…Thus, detailed domain‐specific studies of how the Web impacts particular domains of practice are critically part of the philosophy of the Web. Few areas can be considered seemingly more remote from mundan engineering considerations than proof‐proving in mathematics, yet in their remarkable contribution “The Web as a Tool for Proving” Petros Stefaneas and Ioannis Vandoulakis demonstrate the nature of the radical impact of the Web on this most formal and theoretical of domains (Stefaneas and Vandoulakis ). To move in the reverse direction, the communication and ubiquitous accessibility of the Web may alter our notion of embodiment.…”