searching for math

At the meeting today, Deyan brought up that it is not possible to clearly
write about potential solutions for searching math (something in our
charter) when we haven't defined what we mean by 'math search'. We agreed
that people would post opinions and/or links to papers that reflect their
opinions.To start things off, here's my take....

I think the most common math search is to search for some topic to learn
about that topic. For example, someone might search for geometric
progressions, Fibonacci numbers, or Bessel functions of the second kind.
All of these types of searches seem well handled today because the text in
documents that discuss them mention those words.

The second kind of search is where I have an expression or equation and I
want to know something about it. For example suppose I am reading something
and it has the expression
[image: image.png]

Maybe some in this group recognize this, but I don't. I think this is where
I would want to be able to do a search where I paste this in so I get
results that help me to understand it, its properties, and its relationship
to various areas.

For this particular expression, I doubt many people would write it
differently other than maybe using a different variable of integration or
possibly using something other than 'x' (unlikely). However, in other
searches, there are many equivalent expressions that might reverse the
order of a sum or distribute a factor into a term. I believe dealing with
all these issues (and many others) have been addressed in various research
papers and specialized mathematical search engines.

A quick search turns up the following math search engines:
1. wolframalpha.com
2. searchonmath.com
3. https://approach0.xyz/search/
4. https://www.google.com/imghp  (google image search)

I would not normally classify Wolfram Alpha as a search engine, but it was
the first hit on google for "math search engine". Also, I believe it is
used by bing.

Of these, only '3' returned a result that came back with the content
related to the topic I grabbed the expression from. So clearly work remains
to be done on math search engines. On the other hand, I'm not sure what
there is for the WG to do. The input to these systems (TeX, calculator
math, images) can all be derived from MathML (presentation or content).

Interestingly, I tried using the TeX for this as part of a google search --
nothing very close on the first page. I also tried bing -- the first hit
was close and the second hit was on topic.

From this very limited experiment, my take is that the WG doesn't need to
work on augmenting MathML for search (but search engines themselves need
improvements). I'll leave it to those who have actually worked on search to
contradict me and provide examples where augmenting presentation MathML
would result in better search in the real world.

    Neil


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