mathematics

QED manifesto

QED manifesto is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand QED manifesto rather than just read about it. In short: 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 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.

Key takeaways

QED manifesto belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect QED manifesto to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of QED manifesto from memory before moving on to harder problems.

Reference excerpt

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 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. 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. 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. 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 Rocq, 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. Similar projects include the Metamath proof database and the mathlib library written in Lean. In 2014 the Twenty years of the QED Manifesto 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

References

Further reading H. Barendregt & F. Wiedijk, The Challenge of Computer Mathematics, Transactions A of the Royal Society 363 no. 1835, 2351–2375, 2005 "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. [1] A repository of proofs in Coq. UniMath "Coq library aims to formalize a substantial body of mathematics using the univalent point of view"

Worked examples

Example 1 — a first encounter with QED manifesto

Start with the simplest possible case. Write down what QED manifesto claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to QED manifesto before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about QED manifesto ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of QED manifesto

In research: QED manifesto appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses QED manifesto in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: QED manifesto is common in secondary-school and first-year university syllabi. It links to neighbouring topics Educational projects, Formal methods, Mathematics literature, so understanding it makes those chapters shorter.
In everyday life: Look for QED manifesto outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study QED manifesto in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what QED manifesto means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain QED manifesto out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is QED manifesto in simple terms?

Why does QED manifesto matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study QED manifesto?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on QED manifesto.