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mathsteps

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Step by step math solutions

github.com/socraticorg/mathsteps

socraticorg/mathsteps

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## Resources If you would like to add something to this list, please submit a pull request or email mathsteps@socratic.org ### Existing open source step-by-step solvers - [PRESS PRolog Equation Solving System](https://github.com/maths/PRESS) A computer algebra system for solving symbolic, transcendental, non-differential equations. The equations in the PRESS test suite have largely been taken from English A-level examination papers from the years 1971-1979. The system has four different top-level modules: one for solving single equations, one for sets of simultaneous equations, one for inequalities, and one for proving identities. The procedure for solving single equations is the central core of the program. The other top-level modules are largely interfaces to the relevant parts of the single equation code. (See below for more information on PRESS.) - [MathPiper](http://mathpiper.org) A conventional computer algebra system that has been modified to support step-by-step mathematics. The step-by-step equation solver in MathPiper (which is based on PRESS) has not been officially released yet, so if you would like to experiment with it contact [Ted Kosan](https://github.com/tkosan). The following tutorial provides a brief explanation of how this equation solver works: - [Parsing and the Language of Expression Trees](http://patternmatics.org/temp_1/mathfuture/lesson4/) - [Tree Pattern Matching and Transformation Rules](http://patternmatics.org/temp_1/mathfuture/lesson5/) - [The Hidden Rules Mathematicians Use to Solve Elementary Algebra Equations](http://patternmatics.org/temp_1/mathfuture/lesson6/) ### Reading - [Michael Beason and the “MathXpert” system](https://www.helpwithmath.com/) - [Structure in algebra research paper](http://pat-thompson.net/PDFversions/1987StrucInAlg.pdf) - [2015-AuditedAlgebra.pdf](https://github.com/socraticorg/mathsteps/files/723419/2015-AuditedAlgebra.pdf) - On the following website is a file named moses-simp.pdf that contains a paper titled "Algebraic Simplification a Guide for the Perplexed": [https://groups.csail.mit.edu/mac/users/gjs/6.945/readings/simplification/](https://groups.csail.mit.edu/mac/users/gjs/6.945/readings/simplification/). It describes the various ways simplification is typically used in a CAS. - PRESS (PRolog Equation Solving System) research papers. PRESS was created by a team of researchers lead by Dr. Alan Bundy at the University of Edinburgh's Department of Artificial Intelligence during the 1970s and 1980s. In 2014 Marvin Minsky (who was one of the pioneers of the field of artificial intelligence) stated that much of current AI research was years behind the AI research that was being done in the 1970s, and the PRESS research is a good example of this. Most of Dr. Bundy's research papers are available on his [research outputs website](http://www.research.ed.ac.uk/portal/en/persons/alan-bundy%28bfb547ed-a4df-4a6c-b1be-8ecd9b13419f%29/publications.html?pageSize=all&page=0). The following papers are the ones on this website that are directly related to PRESS. - [Analysing Mathematical Proofs (or Reading between the Lines)](http://www.research.ed.ac.uk/portal/en/publications/analysing-mathematical-proofs-or-reading-between-the-lines(73c17f1f-acc9-491a-a1b0-845149769bbe).html) 1975 - [A treatise on elementary equation solving](http://www.research.ed.ac.uk/portal/en/publications/a-treatise-on-elementary-equation-solving(735e584b-8d45-41e5-b530-910ed2967844).html) 1979 - [Using meta-level inference for selective application of multiple rewrite rule sets in algebraic manipulation](http://www.research.ed.ac.uk/portal/en/publications/using-metalevel-inference-for-selective-application-of-multiple-rewrite-rule-sets-in-algebraic-manipulation(aeed06b9-a6cc-4d57-8801-8a07bda98e95).html) 1981 - [Using Matching in Algebraic Equation Solving](http://www.research.ed.ac.uk/portal/en/publications/using-matching-in-algebraic-equation-solving(dd8c9205-12f6-4512-a79e-325c2d9d6420).html) 1981 - [Meta-level inference in Algebra](http://www.research.ed.ac.uk/portal/en/publications/metalevel-inference-in-algebra(13ca87c0-3025-4adf-8fc1-8ecf7973e3f6).html) 1981 - [Homogenization: Preparing Equations for Change of Unknown](http://www.research.ed.ac.uk/portal/en/publications/homogenization-preparing-equations-for-change-of-unknown(42be6027-6add-46c3-ad69-0a03324a4e33).html) 1981 - [Solving Symbolic Equations with PRESS](http://www.research.ed.ac.uk/portal/en/publications/solving-symbolic-equations-with-press(40cf51b3-fae3-4ebc-b4b6-c02111db4f49).html) 1982 - [The Computer Modelling of Mathematical Reasoning (Book)](http://www.research.ed.ac.uk/portal/en/publications/the-computer-modelling-of-mathematical-reasoning(1ddb87c0-1de3-402b-9dce-986b72bf9a65).html) 1983 - [Discovery and Reasoning in Mathematics](http://www.research.ed.ac.uk/portal/en/publications/discovery-and-reasoning-in-mathematics(cbc8b80d-90cb-4cf9-a5f9-1de6fd8c1bbc).html) 1985 ### Existing closed-source step-by-step solvers - PhotoMath for [iOS](https://itunes.apple.com/ca/app/photomath-camera-calculator/id919087726?mt=8) and [Android](https://play.google.com/store/apps/details?id=com.microblink.photomath&hl=en) - [Cymath](https://www.cymath.com/) - [MathPapa](https://www.mathpapa.com/algebra-calculator.html) - [MathCraft](http://www.cyc.com/mathcraft/) An AI math tutor which is based on the [Cyc](https://en.wikipedia.org/wiki/Cyc) human-like reasoning system (think HAL 9000 and the Star Trek computer). Doug Lenat (who founded the Cyc project in 1984 and who still leads it) recently estimated that Cyc contains around 5 percent of the common-sense knowledge a typical human has, but it is around 97 percent of the way to accumulating the remaining 95 percent automatically because it understands natural language. ### Open source software related to step-by-step math - [Expression tree structure app](http://patternmatics.org/test/expression_structure.html)