|Fields||Philosophy of mathematics, Mathematics education|
|Doctoral advisor||Moshé Machover|
|Doctoral students||Simon Goodchild|
Paul Ernest is a contributor to the social constructivist 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 cannot 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 (née Adlerbert). 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 (1982–84). 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.
- Ernest, Paul; Social Constructivism as a Philosophy of Mathematics; Albany, New York: State University of New York Press, (1998) 
- Ernest, Paul; The Philosophy of Mathematics Education; London: RoutledgeFalmer, (1991)