[Date Index] [Thread Index] [FOM Postings] [FOM Home]

*To*: <fom@math.psu.edu>*Subject*: FOM: ``thoughts on the future of FOM''*From*: "Matt Insall" <montez@rollanet.org>*Date*: Wed, 22 Dec 1999 21:54:44 -0800*Importance*: Normal*Sender*: owner-fom@math.psu.edu

> FOMers, what are your thoughts on the future of f.o.m. over the next > 100 or 1000 years? I'm new to the list, so I hope I'm not speaking out of turn. (Also, I will make my comments brief, in the interest of not overloading email inboxes with too many long messages on this interesting topic.) I predict that, among other things, FOM will develop much more fully its ``applied'' perspectives, in light of the development of the science of computation in the past century. The more we work on fragments of set theory, and variations on first and second order logic, the more computer scientists and computer engineers try to adapt the new ideas to their craft. I predict that the ideas developed from the interaction between researchers in FOM and computer scientists and computer engineers will lead to a highly sophisticated form of simulated intelligence. Moreover, the ideas and solutions will not only flow from ``pure'' FOM to ``applied'' FOM, but in both directions. This is already begun, with projects such as QED, the Consequences of the Axiom of Choice Project, and others. These currently take the form of fairly huge searchable databases with sophisticated search machinery, but I expect this will change significantly in the not-so-distant future. Directions of research in ``applied'' FOM will (I predict) include 1. A rigourous development of automated program verification unlike anything seen in the past century 2. An extended development of the foundations of ``fuzzy'' mathematics (One might call this FOFM, i.e. the ``Foundations Of Fuzzy Mathematics''.) 3. A growing number of researchers working on ``fuzzy'' fragments of set theory, first-order logic, etc. (One might call this FFOM, i.e. the `` Fuzzy Foundations Of Mathematics''.) 4. Significant developments in the foundations of and applications of temporal (and modal) logic; for instance, temporal models of set theory which will model the FACT that (currently, at least) many practicing mathematicians do not consider a statement (in or out of their area of expertise) to be ``true'' until it has been proved, published and ``undergone the test of time'', in some sense. (This type of development may provide a model for one aspect of Professor Friedman's recent post where he asks if all statements considered by mathematicians, either up to now or for all time, have some heretofore undisclosed ``special property''. Even if such ``special properties'' are discovered for all of mathematics up to the present, it may be theoretically impossible to determine an appropriate such property for all mathematics for all time. The very idea sounds terribly self-referential to me. But then, appropriate models of the resulting development of mathematics as a whole may come in the form of an application of temporal logic to FOM, with the ``special properties'' being time-dependent.) Matt Insall http://www.rollanet.org/~montez montez@rollanet.org

[Date Prev] [Date Next] [Thread Prev] [Thread Next]

[Date Index] [Thread Index] [FOM Postings] [FOM Home]