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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
groupes?
"... D’après un exposé fait le 28 mars 2002 à la Journée de Mathématique et de Sciences de l’UMH ..."
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D’après un exposé fait le 28 mars 2002 à la Journée de Mathématique et de Sciences de l’UMH
Septembre/Octobre 2000 Shortcuts in Proof
"... How can we know if a proof is correct? People often imagine that it suffices for a mathematician to make the effort to read it carefully, line by line, after having taken note of the definitions and known results that might be of use. If certain questions are unresolved, as to be sure some are, we w ..."
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How can we know if a proof is correct? People often imagine that it suffices for a mathematician to make the effort to read it carefully, line by line, after having taken note of the definitions and known results that might be of use. If certain questions are unresolved, as to be sure some are, we would known precisely which ones, and the work of the researcher would consist uniquely of resolving these classified enigmas. Certainty would reign throughout mathematics. This situation, if it were true, would make mathematics categorically the opposite of physics. In physics, nothing can definitively establish a theory, which is nothing more than a hypothesis that can always be called into question by additional evidence. We know thus that one cannot prove a physical law, which is a general assertion based on observations and experiments which are no more than particular assertions. Logicians support the idealized vision of mathematics by maintaining that since the beginning of the century codified systems for writing proofs, called formal systems, have been available. If a proof is written with one of these systems a