## A Review of Mathematical Knowledge Management ⋆

Citations: | 1 - 0 self |

### BibTeX

@MISC{Carette_areview,

author = {Jacques Carette and William M. Farmer},

title = {A Review of Mathematical Knowledge Management ⋆},

year = {}

}

### OpenURL

### Abstract

Abstract. Mathematical Knowledge Management (MKM), as a field, has seen tremendous growth in the last few years. This period was one where many research threads were started, and the field was defining itself. We believe that we are now in a position to use the MKM body of knowledge as a means to define what MKM is, what it worries about, etc. In this paper, we review the literature of MKM and gather various metadata from these papers. After offering some definitions surrounding MKM, we analyse the metadata we have gathered from these papers, in an effort to cast more light on the field of MKM and its evolution.

### Citations

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Citation Context ...odern logic. In Hilbert’s hands, this became his famous Program, while Russell and Whitehead produced the Principia Mathematica [31], to which we owe type theory. While Gödel’s incompleteness theorem =-=[17]-=- certainly put an understandable damper on4 these developments, luckily many nevertheless persevered. Of course, one must mention the Bourbaki project as extolling the virtues of a formal library of ... |

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Citation Context ...n would be well advised to read Cajori’s monumental 1929 A History of Mathematical Notations [9]. For the ones more concerned with interactivity, watching Douglas Engelbart’s 1968 Mother of All Demos =-=[13]-=- is humbling. For those most interested in mechanizing mathematics, it is well worth revisiting the early pioneers like Turing and von Neumann (in particular [29] ). Completely indispensable is a thor... |

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Citation Context ...ne important milestone is Frege’s Begriffsschrift [16], to whom we owe modern logic. In Hilbert’s hands, this became his famous Program, while Russell and Whitehead produced the Principia Mathematica =-=[31]-=-, to which we owe type theory. While Gödel’s incompleteness theorem [17] certainly put an understandable damper on4 these developments, luckily many nevertheless persevered. Of course, one must menti... |

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Citation Context ...ted in mechanizing mathematics, it is well worth revisiting the early pioneers like Turing and von Neumann (in particular [29] ). Completely indispensable is a thorough reading of the Automath papers =-=[11, 27]-=-—some recent MKM work just “rediscovers” some of de Bruijn’s early insights. Similarly, the QED Manifesto [5] has helped frame the discussion around formalized mathematics for a very long time (see [3... |

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Citation Context ... only recently, its history goes back much further at least to Euclid’s great and extraordinarily influential Elements. For the formalist, certainly one important milestone is Frege’s Begriffsschrift =-=[16]-=-, to whom we owe modern logic. In Hilbert’s hands, this became his famous Program, while Russell and Whitehead produced the Principia Mathematica [31], to which we owe type theory. While Gödel’s incom... |

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Citation Context ... relating to these. 2 Although we believe the extraction of important topics was objective, the grouping and labeling is inevitably somewhat more subjective. 3 Especially naïve as both of us had read =-=[28]-=-.6 Document Library Formal Digital Interactive Process 5.1 Views Fig. 1: The 6 views of MKM In our investigation of the MKM literature we identified six major lenses through which researchers view MK... |

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Citation Context ...tues of a formal library of mathematics. But Bourbaki was hardly the first to try to design such a library. Leibnitz, frequently credited as having founded both library science and information theory =-=[10]-=-, deserves first-mover credit here. The issues of managing large amounts of information (including substantial parts of mathematics) were already brough to the fore by Denis Diderot’s Encyclopédie ou ... |

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Citation Context ...atical knowledge management have a similarly extended history. Those interested in mathematical presentation would be well advised to read Cajori’s monumental 1929 A History of Mathematical Notations =-=[9]-=-. For the ones more concerned with interactivity, watching Douglas Engelbart’s 1968 Mother of All Demos [13] is humbling. For those most interested in mechanizing mathematics, it is well worth revisit... |

13 | Specifying strategies for exercises
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Citation Context ...ion. This view emphasizes the central role of mathematical knowledge in how mathematics is learned, produced, and applied. The MKM 2008 paper “Specifying Strategies for Exercises” by B. Heeren et al. =-=[18]-=- exhibits an interactive view. It investigates the specification of strategies for use in exercise-solving systems. 6. Process. Another major view of mathematics is that it is a process in which mathe... |

13 |
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Citation Context ...ulum Search for Intergeo” by P. Libbrecht [30] takes a library view of MKM. It describes how a library of interactive geometry resources is organized so that it facilitates search. Other examples are =-=[40, 44]-=-. 3. Formal. Mathematical knowledge is highly structured and interrelated. In the formal view of MKM, mathematical knowledge is managed according to how it is structured and interrelated. Deduction an... |

11 |
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Citation Context ...M 2007 paper “Methods of Relevance Ranking and Hit-Content Generation in Math Search” [45] takes a digital view. It proposes techniques for searching digital mathematics libraries. Other examples are =-=[1, 24]-=-. 5. Interactive. Mathematical knowledge is created, discovered, and communicated by human-to-human and human-to-tool interaction. The basis of the interactive view of MKM is that mathematical knowled... |

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Citation Context ... Horozal and C. E. Brown [26]. It studies the relationship between an informal presentation of introductory real analysis and a formal presentation of it in the Scunak type theory. Other examples are =-=[13, 15]-=-. 4. Digital. Like almost all other kinds of knowledge, there is a strong impetus to digitize mathematical knowledge so that it can be handled by computer and communication systems. The digital view o... |

8 |
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Citation Context ...er “Specifying Strategies for Exercises” by B. Heeren et al. [25] exhibits an interactive view. It investigates the specification of strategies for use in exercise-solving systems. Other examples are =-=[32, 5]-=-. 6. Process. Another major view of mathematics is that it is a process in which mathematical models are created, explored, and interconnected. The process view of MKM focuses on how mathematical know... |

6 |
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Citation Context ...ticular [29] ). Completely indispensable is a thorough reading of the Automath papers [11, 27]—some recent MKM work just “rediscovers” some of de Bruijn’s early insights. Similarly, the QED Manifesto =-=[5]-=- has helped frame the discussion around formalized mathematics for a very long time (see [32] as an enlightening and readable example). The more recent history of many parts of MKM have been covered e... |

5 |
Geuvers and R. de Vrijer (eds
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Citation Context ...ted in mechanizing mathematics, it is well worth revisiting the early pioneers like Turing and von Neumann (in particular [29] ). Completely indispensable is a thorough reading of the Automath papers =-=[11, 27]-=-—some recent MKM work just “rediscovers” some of de Bruijn’s early insights. Similarly, the QED Manifesto [5] has helped frame the discussion around formalized mathematics for a very long time (see [3... |

5 | Methods of relevance ranking and hit-content generation in math search
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(Show Context)
Citation Context ...articular, is concerned with how mathematical knowledge can be put on and accessed via the web. A. S. Youssef’s MKM 2007 paper “Methods of Relevance Ranking and Hit-Content Generation in Math Search” =-=[33]-=- takes a digital view. It proposes techniques for searching digital mathematics libraries. 5. Interactive. Mathematical knowledge is created, discovered, and communicated by human-to-human and human-t... |

5 | A framework for interactive proof
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(Show Context)
Citation Context ...er “Specifying Strategies for Exercises” by B. Heeren et al. [25] exhibits an interactive view. It investigates the specification of strategies for use in exercise-solving systems. Other examples are =-=[32, 5]-=-. 6. Process. Another major view of mathematics is that it is a process in which mathematical models are created, explored, and interconnected. The process view of MKM focuses on how mathematical know... |

5 |
An exploration in the space of mathematical knowledge
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Citation Context ...M 2008 paper “ Automated Signature Evolution in Logical Theories” [12]. It argues that logical theories evolve over time and, as a consequence, their signatures need to be managed. Other examples are =-=[8, 28]-=-. 78 Representation Case-study Extraction Markup Presentation Mechanized Interactivity Search Practice Web Translation Organization Library Usability Document Education Environment Integrity Process ... |

4 | MKM: A new Interdisciplinary Field of Research
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(Show Context)
Citation Context ...d data analysis methodology. In the following section, we lay out the raw results we have obtained, and in section 6 we analyze them. We close with a conclusion. 2 What is MKM? In 2004 in the article =-=[14]-=-, we described MKM as follows: MKM is a new interdisciplinary field of research in the intersection of mathematics, computer science, library science, and scientific publishing. The objective of MKM i... |

4 | The QED manifesto revisited
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Citation Context ...7]—some recent MKM work just “rediscovers” some of de Bruijn’s early insights. Similarly, the QED Manifesto [5] has helped frame the discussion around formalized mathematics for a very long time (see =-=[32]-=- as an enlightening and readable example). The more recent history of many parts of MKM have been covered elsewhere (although a unified treatment is still missing), and we will not repeat that here. H... |

3 |
Grzegorz Bancerek, and Andrzej Trybulec, editors
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(Show Context)
Citation Context ...rg, Austria. The MKM 2001 workshop, attended by 60 or so participants from 10 countries, launched the field of Mathematical Knowledge Management (MKM) 1 and was the first in a series of international =-=[6, 7, 2, 1, 21, 4, 20, 3]-=- and regional [23–26] conferences and workshops on MKM. Since its inception, the MKM community has struggled with questions like “What does it mean to manage mathematical knowledge?”, “What should the... |

3 | Roles of math search in mathematics
- Youssef
(Show Context)
Citation Context ...ulum Search for Intergeo” by P. Libbrecht [30] takes a library view of MKM. It describes how a library of interactive geometry resources is organized so that it facilitates search. Other examples are =-=[40, 44]-=-. 3. Formal. Mathematical knowledge is highly structured and interrelated. In the formal view of MKM, mathematical knowledge is managed according to how it is structured and interrelated. Deduction an... |

2 |
Mathematical Knowledge Management
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(Show Context)
Citation Context ...thematical knowledge possesses several characteristics that sharply distinguish it from other kinds of knowledge, MKM also has a nontrivial intersection with the field of general knowledge management =-=[15]-=-. MKM is indeed a new field of research, but mathematicians have been concerned with managing mathematical knowledge for hundreds, if not thousands, of years. A short history of mathematical knowledge... |

2 | Cross-curriculum search for Intergeo
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(Show Context)
Citation Context ...athematical library works is the primary concern; what is held in a library and how it is represented are secondary concerns. The MKM 2008 paper “Cross-Curriculum Search for Intergeo” by P. Libbrecht =-=[22]-=- takes a library view of MKM. It describes how a library of interactive geometry resources is organized so that it facilitates search. 3. Formal. Mathematical knowledge is highly structured and interr... |

2 |
Practical forms of type theory
- Turing
- 1948
(Show Context)
Citation Context ... Engelbart’s 1968 Mother of All Demos [13] is humbling. For those most interested in mechanizing mathematics, it is well worth revisiting the early pioneers like Turing and von Neumann (in particular =-=[29]-=- ). Completely indispensable is a thorough reading of the Automath papers [11, 27]—some recent MKM work just “rediscovers” some of de Bruijn’s early insights. Similarly, the QED Manifesto [5] has help... |

2 |
Digitisation, Representation and Formalisation
- Adams
(Show Context)
Citation Context ...M 2007 paper “Methods of Relevance Ranking and Hit-Content Generation in Math Search” [45] takes a digital view. It proposes techniques for searching digital mathematics libraries. Other examples are =-=[1, 24]-=-. 5. Interactive. Mathematical knowledge is created, discovered, and communicated by human-to-human and human-to-tool interaction. The basis of the interactive view of MKM is that mathematical knowled... |

2 |
Copyright issues for MKM
- Adams, Davenport
(Show Context)
Citation Context ...ment view is “On Correctness of Mathematical Texts from a Logical and Practical Point of View” by K. Verchinine et al. [41]. It is concerned with formalized mathematical documents. Other examples are =-=[37, 2]-=-. 2. Library. One major view of mathematics is that it is a huge body of mathematical facts. According to the library view of MKM, the main objective of MKM is to design and implement libraries, repos... |

1 | Available at http://www.risc.uni-linz.ac.at/about/ conferences/MKM2001/Proceedings - RISC-Linz |

1 |
Automating signature evolution in logical theories
- Bundy
(Show Context)
Citation Context ...y of mathematicians, scientists, and engineers who produce mathematical knowledge. Process is the dominant view taken in A. Bundy’s MKM 2008 paper “ Automated Signature Evolution in Logical Theories” =-=[8]-=-. It argues that logical theories evolve over time and, as a consequence, their signatures need to be managed. 7 5.2 Topics A great many topics have been addressed in the MKM literature. From the topi... |

1 |
Formal representation of mathematics in a dependently typed set theory
- Horozal, Brown
(Show Context)
Citation Context ...wledge is created, discovered, and communicated. A formal view is taken in the MKM 2007 paper “Formal Representation of Mathematics in a Dependently Typed Set Theory” by F. F. Horozal and C. E. Brown =-=[19]-=-. It studies the relationship between an informal presentation of introductory real analysis and a formal presentation of it in the Scunak type theory.4. Digital. Like almost all other kinds of knowl... |

1 | Web site at http://imps.mcmaster.ca/na-mkm-2004 - North - 2004 |

1 |
Andrey Paskevich, and Anatoly Anisimov. On correctness of mathematical texts from a logical and practical point of view
- Verchinine, Lyaletski
(Show Context)
Citation Context ...sing theorem provers. An example of a recent MKM 2008 paper written from the document view is “On Correctness of Mathematical Texts from a Logical and Practical Point of View” by K. Verchinine et al. =-=[30]-=-. It is concerned with formalized mathematical documents. 2. Library. One major view of mathematics is that it is a huge body of mathematical facts. According to the library view of MKM, the main obje... |

1 |
Managing digital mathematical discourse
- Borwein, Stanway
(Show Context)
Citation Context ...M 2008 paper “ Automated Signature Evolution in Logical Theories” [12]. It argues that logical theories evolve over time and, as a consequence, their signatures need to be managed. Other examples are =-=[8, 28]-=-. 78 Representation Case-study Extraction Markup Presentation Mechanized Interactivity Search Practice Web Translation Organization Library Usability Document Education Environment Integrity Process ... |

1 |
From proof-assistants to distributed libraries of mathematics: Tips and pitfalls
- Coen
(Show Context)
Citation Context ... Horozal and C. E. Brown [26]. It studies the relationship between an informal presentation of introductory real analysis and a formal presentation of it in the Scunak type theory. Other examples are =-=[13, 15]-=-. 4. Digital. Like almost all other kinds of knowledge, there is a strong impetus to digitize mathematical knowledge so that it can be handled by computer and communication systems. The digital view o... |

1 |
Specifying strategies for exercises. In Autexier et al
- Heeren, Jeuring, et al.
(Show Context)
Citation Context ...ion. This view emphasizes the central role of mathematical knowledge in how mathematics is learned, produced, and applied. The MKM 2008 paper “Specifying Strategies for Exercises” by B. Heeren et al. =-=[25]-=- exhibits an interactive view. It investigates the specification of strategies for use in exercise-solving systems. Other examples are [32, 5]. 6. Process. Another major view of mathematics is that it... |

1 |
On the roles of LaTeX and MathML in encoding and processing mathematical expressions
- Padovani
(Show Context)
Citation Context ...ment view is “On Correctness of Mathematical Texts from a Logical and Practical Point of View” by K. Verchinine et al. [41]. It is concerned with formalized mathematical documents. Other examples are =-=[37, 2]-=-. 2. Library. One major view of mathematics is that it is a huge body of mathematical facts. According to the library view of MKM, the main objective of MKM is to design and implement libraries, repos... |