The QED manifesto revisited
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چکیده
We present an overview of the current state of formalization of mathematics, and argue what will be needed to make the vision from the QED manifesto come true. This short and intentionally provocative paper is dedicated to Andrzej Trybulec. When I first wrote about the Mizar system, Andrzej wrote to me: I have looked to pages that you have prepared. [. . . ] I advertise them, even if they are a bit enemical :-) I hope that Andrzej will enjoy this paper, and will not consider it to be too ‘enemical’. 1 Why the QED manifesto has not been a success (yet) One of the most interesting documents about the formalization of mathematics is the QED manifesto [2]. This anonymous pamphlet from 1994 paints a future in which most of mathematics will be put in the computer, even the proofs – especially the proofs – in such a way that the computer will be able to check it for correctness. The QED manifesto describes the development of a system, the QED system, that mathematicians will adopt for this purpose. The future that the QED manifesto sketches has not happened. There is no such system as the QED system in regular use by mathematicians today. There are two main reasons that the future from the QED manifesto currently is not much closer than it was in 1994: – The most important reason is that only very few people are working on formalization of mathematics. If there had been a larger research community interested in that subject, a system like the QED system would have been realized long ago. There are various reasons why not many people are working on the vision from the QED manifesto. For one thing formalization has no ‘killer application’. If one writes a formalization of a mathematical result, then one has 1 One of the main people behind the QED manifesto was Bob Boyer, but for idealistic reasons the authors of the QED manifesto were not identified in it.
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تاریخ انتشار 2007