Math-Aware Search Engines: Physics Applications and Overview

New search engines exist which take equations as their query, and return results which match either the query’s mathematical meaning or its structural presentation. These results are drawn from scientific papers, online encyclopedias, and math discussion forums. Their scope includes some of physics, a lot of math, and some content from other natural sciences. Development of math-aware search engines has progressed far in the decade or so that the field has been alive. The engines are able to parse some equivalencies of mathematics such as commutativity and to find similar (in addition to equivalent) formulae to the query. Their math interpretation abilities, excepting one encyclopedia-based engine (Wolfram Alpha), do not yet reach that of Computer Algebra Systems (CAS) like Mathematica. Developments are proceeding for journal-based engines to include the mathematical meaning-comparison features of CASs; hopefully, in time, the math rules encompassed by CASs will grow past their present limitations in this application as well. Physics uses math to encode systems’ evolutions. Sometimes, mathematical roadblocks are encountered in physics: a math problem is encountered for which no-one who knows about the problem also knows of a solution. Searching across disciplines, using equations, might help the researchers to locate a solution. The fact that jargon is avoided in the search phase allows this cross-disciplinary research to be efficient. Pre-made solutions are not the only thing which might be found: good approximations, worked-out work-arounds to using that equation, and analogous systems from which to improve understanding (or design experiments) might be found. To bridge the gap between developers’ publications on their search engines, and potential users’ awareness of those same engines, this paper reviews their applicability to physics and presents the current math-aware search engines.