QED manifesto explained

The QED manifesto was a proposal for a computer-based database of all mathematical knowledge, strictly formalized and with all proofs having been checked automatically. (Q.E.D. means Latin: quod erat demonstrandum in Latin, meaning "which was to be demonstrated.")

Overview

The idea for the project arose in 1993, mainly under the impetus of Robert Boyer. The goals of the project, tentatively named QED project or project QED, were outlined in the QED manifesto, a document first published in 1994, with input from several researchers.^[1] Explicit authorship was deliberately avoided. A dedicated mailing list was created, and two scientific conferences on QED took place, the first one in 1994 at Argonne National Laboratories and the second in 1995 in Warsaw organized by the Mizar group.^[2]

The project seems to have dissolved by 1996, never having produced more than discussions and plans. In a 2007 paper, Freek Wiedijk identifies two reasons for the failure of the project.^[3] In order of importance:

• Very few people are working on formalization of mathematics. There is no compelling application for fully mechanized mathematics.
• Formalized mathematics does not yet resemble real, traditional mathematics. This is partly due to the complexity of mathematical notation, and partly to the limitations of existing theorem provers and proof assistants; the paper finds that the major contenders, Mizar, HOL, and Coq, have serious shortcomings in their abilities to express mathematics.

Nonetheless, QED-style projects are regularly proposed. The Mizar Mathematical Library formalizes a large portion of undergraduate mathematics, and was considered the largest such library in 2007.^[4] Similar projects include the Metamath proof database and the mathlib library written in Lean.^[5]

In 2014 the Twenty years of the QED Manifesto^[6] workshop was organized as part of the Vienna Summer of Logic.

See also

• Formalism (mathematics)
• Mathematical knowledge management
• POPLmark, a more modest project in programming language theory

Further reading

• H. Barendregt & F. Wiedijk, The Challenge of Computer Mathematics, Transactions A of the Royal Society 363 no. 1835, 2351–2375, 2005
• Web site: A Special Issue on Formal Proof. Notices of the American Mathematical Society. December 2008. (open access issue)
• Richard A. De Millo, Richard J. Lipton, Alan J. Perlis, Social processes and proofs of theorems and programs, Communications of the ACM, Volume 22, Issue 5 (May 1979), Pages: 271 - 280
• John Harrison, Formalized Mathematics, Technical Report 36, Turku Centre for Computer Science (TUCS)
• Ittay Weiss, The QED Manifesto after Two Decades  Version 2.0, Journal of Software vol. 11, no. 8, pp. 803-815, 2016.

External links

• Freek Wiedijk, Formalizing 100 Theorems A page keeping track of the progress in the formalization of 100 common theorems.
• Freek Wiedijk, The Seventeen Provers of the World, a proof of the irrationality of the square root of two in seventeen different proof assistants.
• Formalized Mathematics a journal in which Mizar proofs are presented.
• The Archive of Formal Proofs a similar (refereed) repository of proofs in Isabelle/HOL.
• https://coq.inria.fr/opam/www/ A repository of proofs in Coq.
• UniMath "Coq library aims to formalize a substantial body of mathematics using the univalent point of view"

Notes and References

1. http://www.cs.chalmers.se/Cs/Research/Logic/TypesSS05/Extra/wiedijk_2.pdf The QED Manifesto
2. http://mizar.org/people/romat/qed95rep.pdf The QED Workshop II report
3. Freek Wiedijk, The QED Manifesto Revisited, 2007
4. Fairouz Kamareddine, Manuel Maarek, Krzysztof Retel, and J. B. Wells, Gradual Computerisation/Formalisation of Mathematical Texts into Mizar
5. mathlib libraryhttps://leanprover-community.github.io/mathlib-overview.html
6. https://www.cs.ru.nl/qed20/QED-index.html Twenty years of the QED Manifesto workshop