Introducing Plurimath
Background
Many math representational languages are in current use, and they all do a great job of representing math in formulas.
The commonly used presentational math languages include:
While they mostly can achieve the same presentational output, these languages are based on different data models on how they understand math syntax. A formula represented in one of them cannot be easily converted into each other in a roundtrip fashion.
Note

Asciimath is a math input language created to output MathML, so while it easily converts into MathML, the reverse is not always straightforward. 
Note

There is "AsciiMath" (capital "M"), the original implementation of AsciiMath, and "Asciimath" (lowercase "M"), the AsciiMath implementation in Ruby by the Asciidoctor project. The syntaxes they support are slightly different and their behaviors are incompatible. A topic for another blog post. 
Need for math conversion
Backtracking a bit — the Plurimath project was created due to the need from the Metanorma standards authoring suite.
Metanorma is widely used by standardization bodies to create standards, and the accurate representation of math is a foremost priority in these standards.
One interesting fact in math publication, is that different publication formats are bound different math presentational languages, lending to different challenges in rendering math:

PDF: MathML is typically used to render math into graphics. PDF 2.0 specifically accepts MathML 2 as input, but doesn’t render them.

HTML: MathML is now increasingly the default choice due to growing native browser support. However, many people still use LaTeX math with MathJax.

Word: Word only supports OMML, Microsoft’s version of math presentation.

LaTeX: Only LaTeX math input is supported, and is typically rendered into PDF.
Different bodies create publications using different workflows and standardize on different publication formats.
Since Metanorma has to produce an identical math presentation across multiple formats, we created Plurimath to solve this problem.
Consolidated math representation model
Wait… isn’t that just Content MathML?
True, a complete semantic model for math, such as Content MathML, and OpenMath, can technically be the answer.
However, notice that all the math representation languages we listed out are presentation math languages, which means that they are meant to only represent the look of the math formula, not provide the underlying meaning of a math formula.
This is easiest illustrated by the multiplication operator. In a formula "ab", two variables placed adjacent to each other typically mean a multiplied by b, but could also take on other meanings depending on the context. In a semantic math language, this issue is resolved by directly encoding the desired mathematical operator to the variables, such as illustrated as "times(a, b)".
In order to allow conversion between these various presentational math languages, we have to first create a data model that accommodates the most complex features of this language collection, and then link this data model back to each presentational language. This is the consolidated math representation model that we have created for Plurimath.
Journey
Math was never an afterthought in Metanorma. Fortuitously, in a way that fortune favors the prepared, we already have created a set of unidirectional converters for selected pairs of languages.
These include:

omml2mathml (converts OMML into MathML)

mathml2asciimath (converts MathML into AsciiMath)

latexmath (converts LaTeX math input into MathML)

html2asciimath (converts HTML "fake math" into AsciiMath)
This previous portfolio, though, clearly did not cover all language pairs and conversion directions. Based on these implementations, we embarked on the Plurimath project that consolidates all functionality of these libraries into a unified implementation.
Availability and usage
Plurimath is currently published as a Ruby library (plurimath at Rubygems) that provides a central interface for conversion of multiple math representation languages, including:

Presentational MathML 3.0

Microsoft Office Math Markup Language

AsciiMath

LaTeX math

HTML math
And it’s available today.
Moving forward
There are many more topics about interoperability of math representations, such as Unicode coverage of math symbols, font coverage of Unicode math, and rendering ambiguity. The Plurimath team shall address them in a future series of posts.
In the meantime, try Plurimath out — any feedback would be greatly appreciated!
Note

A Javascript version of Plurimath will soon be available… 