Abstract. This paper reports on refinements and extensions to the MathLang framework that add substantial support for natural language text. We show how the extended framework supports multiple views of mathematical texts, including natural language views using the exact text that the mathematician wants to use. Thus, MathLang now supports the ability to capture the essential mathematical structure of mathematics written using natural language text. We show examples of how arbitrary mathematical text can be encoded in MathLang without needing to change any of the words or symbols of the texts or their order. In particular, we show the encoding of a theorem and its proof that has been used by Wiedijk for comparing many theorem prover representations of mathematics, namely the irrationality of √ 2 (originally due to Pythagoras). We encode a 1960 version by Hardy and Wright, and a more recent version by Barendregt. 1 On the way to a mathematical vernacular for computers Mathematicians now use computer software for a variety of tasks: typing mathematical texts, performing calculation, analyzing theories, verifying proofs. Software tools like

We propose a proof representation format for human-oriented proofs at the assertion level with underspecification. This work aims at providing a possible solution to challenging phenomena worked out in empirical studies in the DIALOG project at Saarland University. A particular challenge in this project is to bridge the gap between the human-oriented proof representation format with under-specification used in the proof manager of the tutorial dialogue system and the calculus- and machine-oriented representation format of the domain reasoner.