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Mathgate is a website for learning logic and mathematics through formal proofs.

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The third motivation for the QED project is education. Nothing is more important than mathematics education to the creation of infrastructure for technology-based economic growth. The development of mathematical ability is notoriously dependent upon "doing" rather than upon "being told" or "remembering". The QED system will provide, via such techniques as interactive proof checking algorithms and an endless variety of mathematical results at all levels, an opportunity for the one-on-one presenting, checking, and debugging of mathematical technique, which it is so expensive to provide by the method of one trained mathematician in dialogue with one student. QED can provide an engaging and non-threatening framework for the carrying out of proofs by students, in the same spirit as a long-standing program of Suppes at Stanford for example. Students will be able to get a deeper understanding of mathematics by seeing better the role that lemmas play in proofs and by seeing which kinds of manipulations are valid in which kinds of structures. Today few students get a grasp of mathematics at a detailed level, but via experimentation with a computerized laboratory, that number will increase. In fact, students can be used (eagerly, we think) to contribute to the development of the body of definitions and proved theorems in QED. Let also us make the observation that the relationship of QED to education may be seen in the following broad context: with increasing technology available, governments will look not only to cut costs of education but will increasingly turn to make education and its delivery more cost-effective and beneficial for the state and the individual.
- The QED Manifesto, Anonymous, 1994


Proving Your First Theorems
(a video for theorem proving beginners)
September 13, 2014
Dependent Sums and Simple Products of Sets
September 6, 2014
Ordered Pairs as Sets
August 30, 2014
Disjoint Unions
Dependent Products and Simple Exponents of Sets (Proofs as Exercises)
Preamble Signature for Dependent Products and Simple Exponents of Sets
August 23, 2014
Introduction to Ordinals
Functions as Sets (Proofs as Exercises)
Preamble Signature for Functions as Sets
August 16, 2014
Universes and Infinity
Dependent Sums and Simple Products of Sets (Proofs as Exercises)
Preamble Signature for Dependent Sums and Simple Products of Sets
August 9, 2014
Arithmetic on the Natural Numbers
Ordered Pairs as Sets (Proofs as Exercises)
Preamble Signature for Ordered Pairs as Sets
August 2, 2014
Quotients
Disjoint Unions (Proofs as Exercises)

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