doctoral_advisor birth_place nationality fields workplaces article_title name
moshé machover new york city british american philosophy of mathematics , mathematics education exeter university paul ernest
 paul ernest
paul ernest

paul ernest is a contributor to the social constructivist -lrb- see social constructivism -rrb- philosophy of mathematics .
ernest 's philosophical sources are the later works of ludwig wittgenstein and the fallibilism of imre lakatos .
this social constructivist philosophy claims that both the theorems and truths of mathematics , and the objects of mathematics , are cultural products created by humans .
furthermore the theorems and truths of mathematics always remain corrigible , revisible , and indeed fallible -- in principle at least .
this does not mean that mathematical knowledge is flawed or at risk .
however , the claim is that the belief that mathematical knowledge is infallible can not be demonstrated , it is an article of faith , even if the warrants for mathematical knowledge are the strongest warrants available to humankind for any knowledge claims .
ernest illustrates this position in his discussion of the issue of whether mathematics is discovered or invented .
his fullest exposition of the social constructivist position is given in the 1998 reference , although an earlier version is given in the 1991 reference .
ernest 's version of social constructivism is controversial and has led to strong criticism .
the principal criticism is that mathematical theorems are truths and truths by their nature are infallible .
in his account of social constructivism ernest links the worlds of research mathematics and that of school and college mathematics .
this link is achieved though the role of experts who as teachers communicate mathematical knowledge to learners and warrant their personal knowledge by means of testing and assessment .
as researchers experts both create new mathematical knowledge and warrant the productions of others .
through this linkage the personal knowledge of the experts is developed and itself warranted .
both explicit mathematical knowledge representations and personal mathematical knowledge circulate between the worlds of education and research , which are not themselves wholly disjoint .
the personal knowledge cycle is mutually refreshing for both education and research .
a criticism of this account is that if mathematical knowledge is socially constructed and accepted it might be accepted purely on the basis of group agreement .
however ernest argues that mathematical knowledge communication , creation and warranting take place in historical communities that respect traditions of mathematical practice with embedded and partly tacit criteria for acceptability .
such rules include accepted forms of presentation , reasoning , and consistency .
although these are historically contingent they are never arbitrary and in general conserve mathematical concepts , theories and rules of acceptance .
furthermore , the democratic , rational and critical elements of mathematical thinking and mathematical communities mean that errors are eliminated .
a criticism of this position is that it conflates the social institution of mathematics with objective mathematical knowledge .
paul ernest was born in new york city , new york in to parents john ernest and elna ernest -lrb- née adlerbert -rrb- .
however he has lived and worked in the uk since childhood , apart from two years of teaching at the university of the west indies , jamaica -lrb- 1982 -- 84 -rrb- .
he is currently emeritus professor of the philosophy of mathematics education at exeter university , uk .
originally a student of mathematics and philosophy up to phd level he became interested in educational issues through teaching school mathematics in london during the 1970s .
his main research interests concern fundamental questions about the nature of mathematics and how it relates to teaching , learning and society .
he has developed a semiotic theory of mathematics and education .
he is best known for his work on philosophical aspects of mathematics education and his contributions to developing a social constructivist philosophy of mathematics .
he is currently working on the ethics of mathematics .
