Name
Abstract | ||
|---|---|---|
Since approximately 1960, symbolic computation added algebraicalgorithms (polynomial algorithms, simplification algorithms forexpressions, algorithms for integration, algorithms for theanalysis of algebraic structures like groups etc.) to numerics andprovided both numerical and algebraic algorithms in the frame ofpowerful integrated mathematical software systems like Macsyma,Reduce,..., Mathematica, Maple,... Various wonderful tools likegraphics, notebook facilities, extensible two-dimensional syntaxetc. greatly enhanced the attractivity of these systems formathematicians, scientists, and engineers. Over the recent decades,sometimes based on very early work in the 19th century, new anddeep research results in various branches of mathematics have beendeveloped by the symbolic computation research community which ledto an impressive variety of new algebraic algorithms.In parallel, in a different community, based on new and deepresults in mathematical logic, algorithms and systems for automatedtheorem proving were developed. In the editorial for the Journal ofSymbolic Computation (1985), I tried to offer this journal as acommon forum for both the computer algebra and the computationallogic community and for the interaction and merge of the twofields. In fact, in some specific theorem proving methods (as, forexample, decision methods for the first order theory of real closedfields and decision methods for geometry), algebraic techniquesplay an important role. However, we are not yet at a stage whereboth worlds, the world of computational algebra (thealgorithmization of the object level of mathematics) and the worldof computational logic (the algorithmization of the meta-level ofmathematics) would find there common frame in terms of integratedmathematical software systems.In the talk, I will sketch a view on future symbolic computationthat hopefully will integrate numerics, computer algebra, andcomputational logic in a unified frame and will offer softwaresystems for supporting the entire process of what could be called"mathematical theory exploration" or "mathematical knowledgemanagement". In this view, symbolic computation is not only aspecific part of mathematics but, rather, will be specific way ofdoing mathematics.This will have drastic effects on the way howresearch, education, and application in mathematics will bepossible and the publication, accumulation, and use of mathematicalknowledge will be organized. We envisage a kind of "Bourbakism ofthe 21st century", which will be very different --- and partly inopposition to --- the Bourbakism of the 20th century. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1145/1073884.1073885 | ISSAC |
Keywords | Field | DocType |
symbolic computation,computer algebra,mathematical logic,algebraic algorithm,algebraic structure,mathematical software system,simplification algorithms forexpressions,mathematical knowledgemanagement,future symbolic computationthat,decision method,first order,computational logic,theorem proving,software systems | Computational logic,Symbolic-numeric computation,Computer science,Automated theorem proving,Mathematical theory,Symbolic computation,Software system,Theoretical computer science,Mathematical software,Mathematical logic | Conference |
ISBN | Citations | PageRank |
1-59593-095-7 | 0 | 0.34 |
References | Authors | |
1 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bruno Buchberger | 1 | 847 | 168.26 |