skip to main content
10.1145/345542.345555acmconferencesArticle/Chapter ViewAbstractPublication PagesissacConference Proceedingsconference-collections
Article

Representing and handling mathematical concepts by humans and machines (invited talk abstract)

Published: 01 July 2000 Publication History

Abstract

The following claims will be made.
There is a language L that is sufficiently powerful that most mathematics can be formulated in it, sufficiently natural that mathematicians can use it easily and sufficiently formal that computers can deal with it. For example in L one can state that ƒ is the primitive of the continuous function g on the reals (whereby explicit forms of ƒ and g can be given), that α is the largest eigenvalue of the symmetric matrix M, or that {x1, …, xk} is the basis of the Hilbert-space H (where again the x's and H can be described explicitly).
There are computer systems that can answer the following queries for substantial parts of mathematics.
Does statement A hold?
Give me an object x such that A(x) holds. (Now the computer has the responsibility of giving the explicit form of x.)
Give me evidence for the answers in (i) and (ii).
It will be argued that it is possible and desirable to construct such a language L and such computer systems.

Cited By

View all

Index Terms

  1. Representing and handling mathematical concepts by humans and machines (invited talk abstract)

      Recommendations

      Comments

      Information & Contributors

      Information

      Published In

      cover image ACM Conferences
      ISSAC '00: Proceedings of the 2000 international symposium on Symbolic and algebraic computation
      July 2000
      309 pages
      ISBN:1581132182
      DOI:10.1145/345542
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Sponsors

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      Published: 01 July 2000

      Permissions

      Request permissions for this article.

      Check for updates

      Qualifiers

      • Article

      Conference

      ISSAC00
      Sponsor:

      Acceptance Rates

      ISSAC '00 Paper Acceptance Rate 40 of 98 submissions, 41%;
      Overall Acceptance Rate 395 of 838 submissions, 47%

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • Downloads (Last 12 months)0
      • Downloads (Last 6 weeks)0
      Reflects downloads up to 15 Sep 2024

      Other Metrics

      Citations

      Cited By

      View all

      View Options

      View options

      Get Access

      Login options

      Media

      Figures

      Other

      Tables

      Share

      Share

      Share this Publication link

      Share on social media