NDLI: Computer-encouraged serendipity in pure mathematics

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Computer-encouraged serendipity in pure mathematics

Content Provider	ACM Digital Library
Author	Strauss, C. M.
Abstract	Computer applications to research in pure mathematics during the past several years have concentrated on using the data processing and logical capabilities of computers to carry out exhaustive and exhausting combinatorial or logical manipulations. Computers can also be used to suggest entirely new theorems and results, but this sort of application has not yet been particularly widely investigated.The addition of an interactive graphics terminal to even a small to medium-sized computer enables one to construct "n-dimensional blackboard." On this device a mathematician can display and manipulate two-dimensional projections of n-dimensional geometrical constructs with much greater speed and accuracy than he can bring to his usual blackboard sketches. This sort of facility can be particularly helpful to the type of mathematician who thinks geometrically, and who relies a great deal on geometrical visualizations to suggest new theorems and proofs. Using control dials, joysticks, and other analog input devices, a mathematician can get immediate portrayal of the geometric effect of continuously varying parameters. He also has finger-tip control over the current values of these parameters, encouraging the development of a visceral feeling for the effect of these parameter variations.Early experience with such an "n-dimensional blackboard," implemented in a prototype version on the microprogrammed mini-computer BUGS system at Brown University, is extremely promising. This BUGS blackboard, used in the area of singularities of algebraic curves in complex two-space, has suggested several new theorems and areas for further investigation.A description is given of the facilities of the BUGS blackboard. Also, the observed interaction between the physical facilities available on the BUGS system is mentioned, as well as the sorts of mathematical results that the use of these facilities in the BUGS blackboard seems to encourage.
Starting Page	89
Ending Page	89
Page Count	1
File Format	PDF
ISSN	00978930
DOI	10.1145/988026.988040
Journal	ACM SIGGRAPH Computer Graphics (COMG)
Volume Number	8
Issue Number	3
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1988-08-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Computer Science Computer Graphics and Computer-Aided Design

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