Mathematical knowledge management

Periodic Pattern of Human Knowing (Part #5)

[Parts: First | Prev | Next | Last | All] [Visuals] [Links: To-K | From-K | From-Kx | Refs ]

Corfield's expression of concern has been powerfully reinforced by the challenge of managing the volume of mathematical knowledge as articulated in the keynote speech to a Mathematical Knowledge Management meeting in 2003 by Michiel Hazewinkel (Mathematical knowledge management is needed) who notes:

• total number of pages published in mathematics so far makes up a stack of about 60km height.
• how much redundancy there is in all that is anybody's guess; at present there not even preliminary ideas how to estimate that.
• the universally used Mathematics Subject Classification scheme is a tree with some 5500 leaves; most of these are large enough to drown a whole (super)specialism in.
• there were some 25,000 mathematical articles published in 2001.
• the number of new theorems (as defined by their authors) published per year has been estimated at 200,000, this does not include lemmas, propositions, scholia, constructions, definitions, etc

Hazewinkel's framing of the situation is that: "We don't even know how much we know that we don't know we know"?? This is reminscent of the preoccupation of the notorious "poem" of Donald Rumsfeld, as discussed separately (Unknown Undoing: challenge of incomprehensibility of systemic neglect, 2008).

The meeting was associated with the Mathematical Knowledge Management Network, funded for a year as a project under the Knowledge Technologies action line of the European Union's Fifth Framework. That event has been associated with a series of conferences (Austria, 2001; Italy, 2003; Poland, 2004; Germany, 2005; UK, 2005; Austria, 2007; UK, 2008) assembling valuable contributions. However it is difficult to detect much preoccupation with any overarching "overview" (as stressed by Corfield) as opposed to improving "access".

• James Harold Davenport and Bruno Buchberger (Eds.). Mathematical knowledge management: second international conference (MKM 2003, Bertinoro, Italy, 2003). Springer, 2003
• Andréa Asperti, Grzegorz Bancerek, Andrzej Trybulec. Mathematical knowledge management: third international conference, MKM 2004 ... Mathematical knowledge management: third international conference, MKM 2004. Springer, 2004

A MKM Interest Group (Mathematical Knowledge Management) has since been created as a loose network to focus on the intersection of mathematics and computer science. Specifically it focuses on the need for efficient, new techniques - based on sophisticated formal mathematics and software technology - for deriving benefit from the enormous knowledge available in current mathematical sources and for organizing that knowledge in a new way. On the other side, due its very nature, the realm of mathematical information would seem to be the best candidate for testing innovative theoretical and technological solutions for content-based systems, interoperability, management of machine understandable information, and the Semantic Web.

The challenge is also recognized, and variously addressed, as for example:

• a proposal submitted to the NSF Cyber-enabled Discovery and Innovation (CDI) Program (Jim Pitman, et al., Bibliographic Knowledge Network, 2008)
• a proposal for for a wiki for mathematical knowledge by Christoph Lange (A Semantic Wiki for Mathematical Knowledge Management, 2006; SWIM : A Semantic Wiki for Mathematical Knowledge Management, 2007).
• the Open Archives Initiative, as explained by Antonella De Robbio and Dario Maguolo (Mathematics Subject Classification and related schemes in the OAI framework, 2002)

With respect to the argument here, however, there seems to be little concerted effort to focus on the order implied by the field of mathematical knowledge as a whole, as previously considered (Is the House of Mathematics in Order? -- are there vital insights from its design, 2000). One such attempt by Dave Rusin (The Mathematical Atlas: a gateway to modern mathematics, 2000) does indeed offer a modest map providing links into the Mathematics Subject Classification (MSC), discussed below. This offers a visual index to the subfields of mathematics. The question is whether more is possible -- benefitting from the sophisticated understandings of mathematics.

[Parts: First | Prev | Next | Last | All] [Visuals] [Links: To-K | From-K | From-Kx | Refs ]