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Constructive Mathematics: Proof and Computation

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Building on mathematical method

Constructive proof is an important and highly regarded mathematical method. An EU-financed project sought to take this type of method to a new level.

Digital Economy

A constructive proof is a mathematical method that proves the existence of a mathematical object by providing a method for creating the object. Such constructive proofs have long been held in high regard by mathematicians. However, it is only in recent decades that mathematicians and programmers have devoted considerable effort to developing deep mathematics constructively. Building on this, the EU-backed 'Constructive mathematics: Proof and computation' (CONSTRUMATH) project aimed to develop mathematics with intuitionistic logic and some appropriate set–theoretic or type–theoretic foundation. Financed by the EU's Seventh Framework Programme (FP7), the project focused on three main areas. The first was constructive analysis, algebra and topology. The second was the extraction and implementation of programmes from constructive proofs. The third was constructive reverse mathematics. In addition to the cutting-edge work CONSTRUMATH carried out in constructive mathematics, it also organised a training trimester and workshop. The workshop helped raise the profile of perhaps the most promising recent development in mathematical logic, the initiative to link homotopy and type theories. CONSTRUMATH enabled researchers in constructivity to keep abreast of recent developments in the field, facilitated existing contacts, and fostered new research collaborations between the participating groups.

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