# Realization of a geometry theorem proving machine

@inproceedings{Gelernter1995RealizationOA, title={Realization of a geometry theorem proving machine}, author={Herbert L. Gelernter}, booktitle={IFIP Congress}, year={1995} }

Introduction Few of those who have seen a modern high-speed digital computer digest and transform a mass of data in less time than it takes to follow the process in the mind can suppress a certain amount of speculation concerning the future of such machines. Under the assumption that the computer is operating at the mere threshhold of its capacity in performing the tasks we have thus far delegated to it, a long-range program directed at the problem of "intelligent" behavior and learning in…

## 432 Citations

### Empirical explorations of the geometry theorem machine

- MathematicsIRE-AIEE-ACM '60 (Western)
- 1960

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- 1988

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- 2014

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### The heuristic of George Polya and its relation to artificial intelligence

- Computer Science
- 1981

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### Automated Theorem Proving and Its Prospects

- Mathematics
- 1995

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### Solving Geometric Construction Problems Supported by Theorem Proving

- Mathematics, Computer Science
- 2014

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### Algebraic methods for geometric reasoning

- Computer Science
- 1988

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### Handbook of satisfiability

- Computer Science
- 2009

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