Toward Mechanical Mathematics

Wang, Hao

doi:10.1147/rd.41.0002

Cited by 229 publications

(27 citation statements)

References 11 publications

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“…In line with McCarthy [29], Wang [41], and deBruijn [13], we envision a mathematician-machine communication, where the human presents a mathematical proof-one that could equally be communicated succinctly between experts, and where the machine then tries to "understand" the language and reasoning of such mathematical arguments to construct a corresponding formal proof that satisfies correctness. If existent proof environments, which are strong on the reasoning side, could be extended to allow for more expressive proof representation languages, their usability would be greatly improved.…”

Section: Discussion and Future Workmentioning

confidence: 99%

Supporting the formal verification of mathematical texts

Zinn¹

2006

Journal of Applied Logic

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The formal verification of mathematical texts is one of the most interesting applications for computer systems. In fact, we argue that the expert language of mathematics is the natural choice for achieving efficient mathematician-machine interaction. Our empirical approach, the analysis of carefully authored textbook proofs, forces us to focus on the language and the reasoning pattern that mathematician use when presenting proofs to colleagues and students. Enabling a machine to understand and follow such language and argumentation is seen to be the key to usable and acceptable math assistant systems. In this paper, we first perform an analysis of three textbook proofs by hand; we then describe a computational framework that aims at mechanising such an analysis. The resulting proof-of-concept implementation is capable of processing simple textbook proofs and constitutes promising steps towards a natural mathematician-machine interface for proof development and verification.

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Section: Discussion and Future Workmentioning

confidence: 99%

Supporting the formal verification of mathematical texts

Zinn¹

2006

Journal of Applied Logic

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“…The work of Qian Baocong can be consulted for detailed introduction. (Wu 1977: 515) At the same time, he developed a grand vision of "mechanization of mathematics," a term created by the Harvard-based mathematical logician Hao Wang 王浩 (1921 -95) after his computer proof of Bertrand Russell and Alfred North Whitehead's Principia Mathematica (Wang 1960). Wang had visited China in 1972 and1973 -74 and met Wu Wen-Tsun.…”

Section: Tradition Serving Modernization: Wu Wen-tsun's Methods Of "Mementioning

confidence: 99%

Ancient Chinese Mathematics in Action: Wu Wen-Tsun's Nationalist Historicism After the Cultural Revolution

Hudeček

2012

East Asian Science, Technology and Society: An International Jo

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The article attempts to theoretically explain the origins of the nationalist and historicist turn of the Chinese mathematician Wu Wen-Tsun (born 1919). Wu returned to China from France in 1951 as an internationally recognized expert on algebraic topology, but his career was frustrated by political disruption and isolation from international research, especially during the Cultural Revolution (1966 -76). After he studied ancient Chinese mathematics during the 1974 campaign against Confucianism (Pi Lin Pi Kong 批林批孔), he defended its relevance for modern mathematics and set out to demonstrate it in his own work. This coincided with Wu's reorientation from algebraic topology to mechanization of geometric proofs. Wu claimed that ancient Chinese mathematics inspired the method he developed, both by its general style and by specific techniques. His use of ancient Chinese mathematics was connected to his calls for an independent mathematical tradition in China. I argue that he turned to nationalism to protect himself from the "uneven development" of mathematics, in analogy to Ernest Gellner's theory of nationalism. The early success of his method of mechanization, however, resulted in more dependence on world mathematics, and a revival of ancient Chinese mathematics has not occurred.

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“…Note that our hypothesis, (9), says: the result after arrival at LP with x set to A and Y set to (CONS Al B) is equal to some expression. Our conclusion, (2), says: the result after arrival at LP with x set to (CONS Al A) and Y set to B is equal to some (other) e~ression.…”

Section: Accumulatorsmentioning

confidence: 97%

Introducing iteration into the Pure Lisp theorem prover

Moore

1975

IIEEE Trans. Software Eng.

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It is shown how the Lisp iterative primitives PROG, SETQ, GO, and RETURN may be introduced into the Boyer-Moore method for automatically verifying Pure Lisp programs. This is done by extending some of the previously described heuristics for dealing with recursive functions. The resulting verification procedure uses structural induction to handle both recursion and iteration. The procedure do~s not actually distinquish between the two and they may be mixed arbitrarily. For example, since properties are stated m. terms of user-defined functions, the theorem prover will prove recursively specified properties of iterative functions. Like its predecessor, the procedure does not require user-supplied inductive assertions for the iterative programs.

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Toward Mechanical Mathematics

Cited by 229 publications

References 11 publications

Supporting the formal verification of mathematical texts

Supporting the formal verification of mathematical texts

Ancient Chinese Mathematics in Action: Wu Wen-Tsun's Nationalist Historicism After the Cultural Revolution

Introducing iteration into the Pure Lisp theorem prover

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