Oct 30, 2001 Richard Fateman1 Do Math Making Computers Do Math Prof. Richard Fateman Fall, 2001 University of California, Berkeley

Oct 30, 2001 Richard Fateman2 What could we possibly mean? Solve applied mathematics problems –Convert math statements to effective algorithms (programs) –Follow specific commands to perform algebraic transformations Prove theorems – or Search for counter-examples Prove programs correct (combine previous ideas!) Read (and write!) texts and handbooks to produce indexed re-usable math knowledge

Oct 30, 2001 Richard Fateman3 Brute force algebra...

Oct 30, 2001 Richard Fateman4 Is Math an AI problem?

Oct 30, 2001 Richard Fateman5 Is Math an AI problem? Can we build a math expert? –Must we build an artificial intelligence? –Can we teach math with or without other interactions? –Obvious success in limited domains. –All of math? Not so easy!

Oct 30, 2001 Richard Fateman6 Complex domains, representation problems?

Oct 30, 2001 Richard Fateman7 Is doing Math a GUI Problem? Plot3D[Sin[x*y],{x,0,4},{y,0,4}]

Oct 30, 2001 Richard Fateman8 Can the world-wide web do what a single computer cannot do?

Oct 30, 2001 Richard Fateman9 Yes, in some ways Access the library to get printed or on-line data about a topic Answer specific questions using education-level appropriate approaches on topics from elementary school arithmetic through calculus to advanced math (Distributed Expert) Search in on-line databases for relevant articles, programs, formulas to help solve problems. Fix, update central repository of know-how

Oct 30, 2001 Richard Fateman10 What else ? Communicate among active servers: can we have networked solvers cooperating or competing to solve problems? Encode math formulas so that multiple programs (CAS, TeX, Editor, numeric compiler) can communicate with a common channel MathML/XML ?

Oct 30, 2001 Richard Fateman11 Tools Computer algebra systems, general or special purpose – Mathematica, Maple, Macsyma, GAP, PARI, Interactive computer systems for scientific calculation – Matlab, Octave, MathCad Library research systems – NEC ResearchIndex – California Digital Library

Oct 30, 2001 Richard Fateman12 Very specific topics

Oct 30, 2001 Richard Fateman13 TILU, Table of Integrals LookUp Building the world's most expert (human or non- human) symbolic indefinite and definite integration program, on-line. –Algorithms –Tables –Generation of new solutions –Archiving newly found information

Oct 30, 2001 Richard Fateman14 Code generation The generation of highly specific and maximally efficient programs for certain numerical computations, e.g. approximate solution of differential equations tuned to specific equations or specific computers or specific memory configurations. Numerical routines based on difficult-to-program symbolic approximations such as Taylor series.

Oct 30, 2001 Richard Fateman15 “Expert” shells / Search The building of expert shells for stating and solving problems. Assisting NEC's ResearchIndex project to decode postscript specifications of journal article pages tofind math, and encode the math in (say) TeX. Allowing it to be indexed.

Oct 30, 2001 Richard Fateman16 Graphical User Interfaces Building universal front ends that understand math typing and even handwriting (Biscotti, Texmacs, Livemath, Graphing Calculator)...and that talk to everyone else. –Naive vs. skilled humans: –Who knows that xsinx is the same as x sin(x)?

Oct 30, 2001 Richard Fateman17 Macsyma / open source Re-building the Macsyma computer algebra system as open-source: an opportunity to re-engineer in current technology; convert to a tool-based orientation; combine with other programs Octave, Texmacs, Pari, advanced algorithms

Oct 30, 2001 Richard Fateman18 Current Funding 1+ funded new research assistantships (NSF) for projects related to computer algebra/ scientific environments (possible) additional funding for digital library related activity.