
Big Math and the OneBrain Barrier A Position Paper and Architecture Proposal
Over the last decades, a class of important mathematical results have re...
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A Survey of Languages for Formalizing Mathematics
In order to work with mathematical content in computer systems, it is ne...
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Discovering Mathematical Objects of Interest – A Study of Mathematical Notations
Mathematical notation, i.e., the writing system used to communicate conc...
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Exploration of Neural Machine Translation in Autoformalization of Mathematics in Mizar
In this paper we share several experiments trying to automatically trans...
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Mathematical Reasoning via Selfsupervised Skiptree Training
We examine whether selfsupervised language modeling applied to mathemat...
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Computational Logic: Its Origins and Applications
Computational Logic is the use of computers to establish facts in a logi...
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The Space of Mathematical Software Systems – A Survey of Paradigmatic Systems
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of increasingly powerful but also diverging systems. To give researchers a guide to this space of systems, we devise a novel conceptualization of mathematical software that focuses on five aspects: inference covers formal logic and reasoning about mathematical statements via proofs and models, typically with strong emphasis on correctness; computation covers algorithms and software libraries for representing and manipulating mathematical objects, typically with strong emphasis on efficiency; concretization covers generating and maintaining collections of mathematical objects conforming to a certain pattern, typically with strong emphasis on complete enumeration; narration covers describing mathematical contexts and relations, typically with strong emphasis on human readability; finally, organization covers representing mathematical contexts and objects in machineactionable formal languages, typically with strong emphasis on expressivity and system interoperability. Despite broad agreement that an ideal system would seamlessly integrate all these aspects, research has diversified into families of highly specialized systems focusing on a single aspect and possibly partially integrating others, each with their own communities, challenges, and successes. In this survey, we focus on the commonalities and differences of these systems from the perspective of a future multiaspect system.
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