Hilbert's Twenty-Fourth Problem View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2002-03

AUTHORS

Ruediger Thiele, Larry Wos

ABSTRACT

For almost a century, a treasure lay hidden in a library in Germany, hidden until a remarkable discovery was made. Indeed, for most of the twentieth century, all of science thought that Hilbert had posed twenty-three problems, and no others. In the mid-1990s, however, as a result of a thorough reading of Hilbert's files, a twenty-fourth problem was found (in a notebook, in file Cod. ms. D. Hilbert 600:3), a problem that might have a profound effect on research. This newly discovered problem focuses on the finding of simpler proofs and criteria for measuring simplicity. A proof may be simpler than previously known in one or more ways that include length, size (measured in terms of the total symbol count), and term structure. A simpler proof not only is more appealing aesthetically (and has fascinated masters of logic including C. A. Meredith, A. Prior, and I. Thomas) but is relevant to practical applications such as circuit design and program synthesis. This article presents Hilbert's twenty-fourth problem, discusses its relation to certain studies in automated reasoning, and offers researchers with varying interests the challenge of addressing this newly discovered problem. In particular, we include open questions to be attacked, questions that (in different ways and with diverse proof refinements as the focus) may prove of substantial interest to mathematicians, to logicians, and (perhaps in a slightly different manner) to those researchers primarily concerned with automated reasoning. More... »

PAGES

67-89

References to SciGraph publications

  • 1998-10. Automating the Search for Elegant Proofs in JOURNAL OF AUTOMATED REASONING
  • 2001-08. Solving Open Questions and Other Challenge Problems Using Proof Sketches in JOURNAL OF AUTOMATED REASONING
  • 2001-08. Finding Shortest Proofs: An Application of Linked Inference Rules in JOURNAL OF AUTOMATED REASONING
  • 1996-06. Using hints to increase the effectiveness of an automated reasoning program: Case studies in JOURNAL OF AUTOMATED REASONING
  • 2001-08. Missing Proofs Found in JOURNAL OF AUTOMATED REASONING
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1020537107897

    DOI

    http://dx.doi.org/10.1023/a:1020537107897

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1018594741


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0802", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Computation Theory and Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "name": [
                "Karl-Sudhoff-Institut fur Geschichte der Medizin und Naturwissenschaften, Universit\u00e4t Leipzig, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Thiele", 
            "givenName": "Ruediger", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Argonne National Laboratory", 
              "id": "https://www.grid.ac/institutes/grid.187073.a", 
              "name": [
                "Mathematics and Computer Science Division, Argonne National Laboratory, 60439, Argonne, IL, U.S.A. e-mail"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Wos", 
            "givenName": "Larry", 
            "id": "sg:person.014212155341.71", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014212155341.71"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1023/a:1010639725972", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002278623", 
              "https://doi.org/10.1023/a:1010639725972"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00252178", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006042548", 
              "https://doi.org/10.1007/bf00252178"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00252178", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006042548", 
              "https://doi.org/10.1007/bf00252178"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1010695827789", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013635039", 
              "https://doi.org/10.1023/a:1010695827789"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1010635625063", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021478966", 
              "https://doi.org/10.1023/a:1010635625063"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s1355-2198(99)00035-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036851331"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1005847113370", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036997145", 
              "https://doi.org/10.1023/a:1005847113370"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1305/ndjfl/1093891799", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064915675"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1305/ndjfl/1093957574", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064916090"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2002-03", 
        "datePublishedReg": "2002-03-01", 
        "description": "For almost a century, a treasure lay hidden in a library in Germany, hidden until a remarkable discovery was made. Indeed, for most of the twentieth century, all of science thought that Hilbert had posed twenty-three problems, and no others. In the mid-1990s, however, as a result of a thorough reading of Hilbert's files, a twenty-fourth problem was found (in a notebook, in file Cod. ms. D. Hilbert 600:3), a problem that might have a profound effect on research. This newly discovered problem focuses on the finding of simpler proofs and criteria for measuring simplicity. A proof may be simpler than previously known in one or more ways that include length, size (measured in terms of the total symbol count), and term structure. A simpler proof not only is more appealing aesthetically (and has fascinated masters of logic including C. A. Meredith, A. Prior, and I. Thomas) but is relevant to practical applications such as circuit design and program synthesis. This article presents Hilbert's twenty-fourth problem, discusses its relation to certain studies in automated reasoning, and offers researchers with varying interests the challenge of addressing this newly discovered problem. In particular, we include open questions to be attacked, questions that (in different ways and with diverse proof refinements as the focus) may prove of substantial interest to mathematicians, to logicians, and (perhaps in a slightly different manner) to those researchers primarily concerned with automated reasoning.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1023/a:1020537107897", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136522", 
            "issn": [
              "0168-7433", 
              "1573-0670"
            ], 
            "name": "Journal of Automated Reasoning", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "29"
          }
        ], 
        "name": "Hilbert's Twenty-Fourth Problem", 
        "pagination": "67-89", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "58987ff99cdf2c88124fc89a2b5fc8866f4b195cb88d023b1220f66556147802"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1023/a:1020537107897"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1018594741"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1023/a:1020537107897", 
          "https://app.dimensions.ai/details/publication/pub.1018594741"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T14:03", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8660_00000487.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1023/A:1020537107897"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1023/a:1020537107897'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1023/a:1020537107897'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1020537107897'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1020537107897'


     

    This table displays all metadata directly associated to this object as RDF triples.

    98 TRIPLES      21 PREDICATES      35 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1023/a:1020537107897 schema:about anzsrc-for:08
    2 anzsrc-for:0802
    3 schema:author Ncc8ce31709434bdca96cf1b9855a7d1c
    4 schema:citation sg:pub.10.1007/bf00252178
    5 sg:pub.10.1023/a:1005847113370
    6 sg:pub.10.1023/a:1010635625063
    7 sg:pub.10.1023/a:1010639725972
    8 sg:pub.10.1023/a:1010695827789
    9 https://doi.org/10.1016/s1355-2198(99)00035-0
    10 https://doi.org/10.1305/ndjfl/1093891799
    11 https://doi.org/10.1305/ndjfl/1093957574
    12 schema:datePublished 2002-03
    13 schema:datePublishedReg 2002-03-01
    14 schema:description For almost a century, a treasure lay hidden in a library in Germany, hidden until a remarkable discovery was made. Indeed, for most of the twentieth century, all of science thought that Hilbert had posed twenty-three problems, and no others. In the mid-1990s, however, as a result of a thorough reading of Hilbert's files, a twenty-fourth problem was found (in a notebook, in file Cod. ms. D. Hilbert 600:3), a problem that might have a profound effect on research. This newly discovered problem focuses on the finding of simpler proofs and criteria for measuring simplicity. A proof may be simpler than previously known in one or more ways that include length, size (measured in terms of the total symbol count), and term structure. A simpler proof not only is more appealing aesthetically (and has fascinated masters of logic including C. A. Meredith, A. Prior, and I. Thomas) but is relevant to practical applications such as circuit design and program synthesis. This article presents Hilbert's twenty-fourth problem, discusses its relation to certain studies in automated reasoning, and offers researchers with varying interests the challenge of addressing this newly discovered problem. In particular, we include open questions to be attacked, questions that (in different ways and with diverse proof refinements as the focus) may prove of substantial interest to mathematicians, to logicians, and (perhaps in a slightly different manner) to those researchers primarily concerned with automated reasoning.
    15 schema:genre research_article
    16 schema:inLanguage en
    17 schema:isAccessibleForFree false
    18 schema:isPartOf N4f2e5b5aeea9458ab2f129c251d727cd
    19 N9529f642474b4cf4a9741df93cb4868c
    20 sg:journal.1136522
    21 schema:name Hilbert's Twenty-Fourth Problem
    22 schema:pagination 67-89
    23 schema:productId N48bf3161bcec44b5b772703799868257
    24 Na6c3c1cb04d0478a8b911190f20eb755
    25 Nbe23d4a03f5f49f2aba2ef002833aca1
    26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018594741
    27 https://doi.org/10.1023/a:1020537107897
    28 schema:sdDatePublished 2019-04-10T14:03
    29 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    30 schema:sdPublisher N79ad1e2b4f9d4dd99095a558f7c63318
    31 schema:url http://link.springer.com/10.1023/A:1020537107897
    32 sgo:license sg:explorer/license/
    33 sgo:sdDataset articles
    34 rdf:type schema:ScholarlyArticle
    35 N0b719231d280465f850a19a0c9ab5ec1 schema:affiliation Na9f324ca891d4b99b002bf51badc9323
    36 schema:familyName Thiele
    37 schema:givenName Ruediger
    38 rdf:type schema:Person
    39 N48bf3161bcec44b5b772703799868257 schema:name doi
    40 schema:value 10.1023/a:1020537107897
    41 rdf:type schema:PropertyValue
    42 N4f2e5b5aeea9458ab2f129c251d727cd schema:issueNumber 1
    43 rdf:type schema:PublicationIssue
    44 N661b2e1424d64e76b02764f8dea36852 rdf:first sg:person.014212155341.71
    45 rdf:rest rdf:nil
    46 N79ad1e2b4f9d4dd99095a558f7c63318 schema:name Springer Nature - SN SciGraph project
    47 rdf:type schema:Organization
    48 N9529f642474b4cf4a9741df93cb4868c schema:volumeNumber 29
    49 rdf:type schema:PublicationVolume
    50 Na6c3c1cb04d0478a8b911190f20eb755 schema:name dimensions_id
    51 schema:value pub.1018594741
    52 rdf:type schema:PropertyValue
    53 Na9f324ca891d4b99b002bf51badc9323 schema:name Karl-Sudhoff-Institut fur Geschichte der Medizin und Naturwissenschaften, Universität Leipzig, Germany
    54 rdf:type schema:Organization
    55 Nbe23d4a03f5f49f2aba2ef002833aca1 schema:name readcube_id
    56 schema:value 58987ff99cdf2c88124fc89a2b5fc8866f4b195cb88d023b1220f66556147802
    57 rdf:type schema:PropertyValue
    58 Ncc8ce31709434bdca96cf1b9855a7d1c rdf:first N0b719231d280465f850a19a0c9ab5ec1
    59 rdf:rest N661b2e1424d64e76b02764f8dea36852
    60 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    61 schema:name Information and Computing Sciences
    62 rdf:type schema:DefinedTerm
    63 anzsrc-for:0802 schema:inDefinedTermSet anzsrc-for:
    64 schema:name Computation Theory and Mathematics
    65 rdf:type schema:DefinedTerm
    66 sg:journal.1136522 schema:issn 0168-7433
    67 1573-0670
    68 schema:name Journal of Automated Reasoning
    69 rdf:type schema:Periodical
    70 sg:person.014212155341.71 schema:affiliation https://www.grid.ac/institutes/grid.187073.a
    71 schema:familyName Wos
    72 schema:givenName Larry
    73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014212155341.71
    74 rdf:type schema:Person
    75 sg:pub.10.1007/bf00252178 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006042548
    76 https://doi.org/10.1007/bf00252178
    77 rdf:type schema:CreativeWork
    78 sg:pub.10.1023/a:1005847113370 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036997145
    79 https://doi.org/10.1023/a:1005847113370
    80 rdf:type schema:CreativeWork
    81 sg:pub.10.1023/a:1010635625063 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021478966
    82 https://doi.org/10.1023/a:1010635625063
    83 rdf:type schema:CreativeWork
    84 sg:pub.10.1023/a:1010639725972 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002278623
    85 https://doi.org/10.1023/a:1010639725972
    86 rdf:type schema:CreativeWork
    87 sg:pub.10.1023/a:1010695827789 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013635039
    88 https://doi.org/10.1023/a:1010695827789
    89 rdf:type schema:CreativeWork
    90 https://doi.org/10.1016/s1355-2198(99)00035-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036851331
    91 rdf:type schema:CreativeWork
    92 https://doi.org/10.1305/ndjfl/1093891799 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064915675
    93 rdf:type schema:CreativeWork
    94 https://doi.org/10.1305/ndjfl/1093957574 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064916090
    95 rdf:type schema:CreativeWork
    96 https://www.grid.ac/institutes/grid.187073.a schema:alternateName Argonne National Laboratory
    97 schema:name Mathematics and Computer Science Division, Argonne National Laboratory, 60439, Argonne, IL, U.S.A. e-mail
    98 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...