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Mathematical Reasoning: The History and Impact of the DReaM Group pp 1–35Cite as

The History of the DReaM Group

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Abstract

I describe the history of the DReaM Group (Discovery and Reasoning in Mathematics), which I created after my arrival at the University of Edinburgh in 1971. The group has been characterised by its diversity of approaches to the representation of and reasoning with knowledge, including: deduction; meta-level reasoning; learning, especially of new reasoning methods; representation creation and change; as well as applications to problems as diverse as formal verification, analogical blending and computational creativity. From 1982, we have been supported first by a series of EPSRC rolling grants and then, when this funding mechanism ceased, platform grants. Now that the latter mechanism has also ceased, we felt it was time to take stock, celebrate our achievements, assess our strengths and plan our future research. This history lays the bedrock for that self-analysis. Inevitably, space restrictions have forced me to be highly selective in what research I cover. I apologise to those whose excellent research I have had to omit or only hint at. My selection has been mainly influenced by my desire to illustrate our methodological and application diversity. I hope that the other chapters in this book will fill some of those gaps.

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Fig. 1.1
Fig. 1.2
Fig. 1.3

Notes

  1. 1.

    “2” because it was a second year course.

  2. 2.

    Later to become SERC and then EPSRC.

  3. 3.

    Now Palmer.

  4. 4.

    AKA—the Mathematical Reasoning Group.

  5. 5.

    Climbing the highest peaks in each of seven continents.

  6. 6.

    https://en.wikipedia.org/wiki/Alvey. Accessed 26.8.19.

  7. 7.

    https://en.wikipedia.org/wiki/Fifth_generation_computer. Accessed 26.8.19.

  8. 8.

    http://dream.inf.ed.ac.uk/events/CIAO/.

  9. 9.

    Recall that we are reasoning backwards from the goal.

  10. 10.

    The metaphor is of ripples on a pond. Initially, they obscure the reflection of the surrounding countryside, but as the ripples move out, the reflection is restored.

  11. 11.

    These axioms follow Peano’s spirit but have been modified according to modern practice.

  12. 12.

    If you are concerned with the direction of the rewrite arrow, recall that we are reasoning backwards, so the direction of implication is right to left.

  13. 13.

    Pronounced “new \(\mathbb {T}\)”.

  14. 14.

    https://cryptosense.com/.

  15. 15.

    https://www.ed.ac.uk/cyber-security-privacy.

  16. 16.

    theorymine.co.uk.

  17. 17.

    https://en.wikipedia.org/wiki/Limit_(category_theory) accessed 15.7.19.

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Acknowledgements

The research reported in this paper was mainly supported by a succession of EPSRC rolling and platform grants. Thanks to Greg Michaelson, Kwabena Nuamah, Predrag Janičić and two anonymous referees for feedback on earlier versions.

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    Alan Bundy

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    Dr. Gregory Michaelson

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Bundy, A. (2021). The History of the DReaM Group. In: Michaelson, G. (eds) Mathematical Reasoning: The History and Impact of the DReaM Group. Springer, Cham. https://doi.org/10.1007/978-3-030-77879-8_1

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