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S.: Passages of proof
 Bull. Eur. Assoc. Theor. Comput. Sci. EATCS
, 2004
"... Whether ’tis nobler in the mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles And by opposing end them? Hamlet 3/1, by W. Shakespeare In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs w ..."
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Whether ’tis nobler in the mind to suffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles And by opposing end them? Hamlet 3/1, by W. Shakespeare In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computerassisted proofs will be give a special attention. Finally, in a highly speculative part, we will anticipate the evolution of proofs under the assumption that the quantum computer will materialize. We will argue that there is little ‘intrinsic ’ difference between traditional and ‘unconventional ’ types of proofs. 2 Mathematical Proofs: An Evolution in Eight Stages Theory is to practice as rigour is to vigour. D. E. Knuth Reason and experiment are two ways to acquire knowledge. For a long time mathematical
Teachers' Conceptions of Mathematics and their Instructional Practices
"... this paper will discuss teachers' conceptions about the nature of mathematics and its influences on their teaching practices through the relevant literature. It will particularly refer to Hersh (1986)  focussing on the nature of mathematics, teachers' conceptions of nature of mathematics, and the ..."
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this paper will discuss teachers' conceptions about the nature of mathematics and its influences on their teaching practices through the relevant literature. It will particularly refer to Hersh (1986)  focussing on the nature of mathematics, teachers' conceptions of nature of mathematics, and the effects of teachers' conceptions of nature of mathematics on their instructional practice. Closing this paper, it will draw upon my own perceptions and experience of teaching mathematics in relation to Hersh (1986)
legitimise the conquests of intuition... J.
, 2008
"... The object of mathematical rigour is to sanction and ..."