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Mathematical proofs at a crossroad
 Theory Is Forever, Lectures Notes in Comput. Sci. 3113
, 2004
"... Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimen ..."
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Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psychological and social aspects, yesterday only marginal, but now changing radically the very essence of proof. In this paper, we try to organize this evolution, to distinguish its different steps and aspects, and to evaluate its advantages and shortcomings. Axiomaticdeductive proofs are not a posteriori work, a luxury we can marginalize nor are computerassisted proofs bad mathematics. There is hope for integration! 1
Academic Legitimacy of the Software Engineering Discipline
, 1992
"... Abstract: This article examines the academic substance of software engineering. It identifies the basic research questions and the methods used to solve them. What is learned during this research constitutes the body of knowledge of software engineering. The article then discusses at length what abo ..."
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Abstract: This article examines the academic substance of software engineering. It identifies the basic research questions and the methods used to solve them. What is learned during this research constitutes the body of knowledge of software engineering. The article then discusses at length what about software makes its production so difficult and makes software engineering so challenging an intellectual discipline. 1
Computing as engineering
, 2008
"... Abstract: Computing as a discipline is often characterized as a combination of three major traditions: theoretical, scientific, and engineering tradition. Although the three traditions are all considered equally necessary for modern computing, the engineering tradition is often considered to be usef ..."
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Abstract: Computing as a discipline is often characterized as a combination of three major traditions: theoretical, scientific, and engineering tradition. Although the three traditions are all considered equally necessary for modern computing, the engineering tradition is often considered to be useful but to lack intellectual depth. This article discusses the basic intellectual background of the engineering tradition of computing. The article depicts the engineering aims manifest in the academic field of computing, compares the engineering tradition with the other traditions of computing as a discipline, and presents some epistemological, ontological, and methodological views concerning the engineering tradition of computing. The article aims at giving the reader an overview of the engineering tradition in computing and of some open questions about the intellectual foundations and contributions of the engineering tradition in computing.
Database Theory Column
"... This paper is my onetime attempt to organize and register these thoughts. 2 Theory and its Function ..."
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This paper is my onetime attempt to organize and register these thoughts. 2 Theory and its Function
Theoretical Computer Science Proving and Programming
, 2007
"... There is a strong analogy between proving theorems in mathematics and writing programs in computer science. This paper is devoted to an analysis, from the perspective of this analogy, of proof in mathematics. We will argue that while the Hilbertian notion of proof has few chances to change, future p ..."
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There is a strong analogy between proving theorems in mathematics and writing programs in computer science. This paper is devoted to an analysis, from the perspective of this analogy, of proof in mathematics. We will argue that while the Hilbertian notion of proof has few chances to change, future proofs will be of various types, will play different roles, and their truth will be checked differently. Programming gives mathematics a new form of understanding. The computer is the driving force behind these changes. 1
Is “database theory ” an oxymoron? Or is ata platitude? Database Metatheory: Asking the Big Queries
"... What is the fitness measure that decides the surviva! of ideas (and areas) in mathematics, in applted science, and in computer science? Which ideas from database theory during the past twentyfive years have influenced research in other fields of computer science? How many were encapsulated in actua ..."
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What is the fitness measure that decides the surviva! of ideas (and areas) in mathematics, in applted science, and in computer science? Which ideas from database theory during the past twentyfive years have influenced research in other fields of computer science? How many were encapsulated in actual products? Was the relational model the on[y true paradigm sh @ m computer science? Is applicability the only and ultimate justification of theoretical research in an applied science? Are applicability pressures rea!ly exogenous and unwelcome? Are negattve results appropriate goals of theoretical research in an appiied science —or are they the on[y possibie such research goals? If scientific theories must be refutab!e, what are the “hard facts ” that provide the possibility of refutation in the case of database theory? 1