Maths notation is needlessly complex [video]
This presentation misses a more fundamental point.  It&#x27;s not about the <i>notation</i> at all, it&#x27;s about understanding that EXPT, SQRT and LOG are <i>functions</i> with a particular relationship to each other.  That relationship can be expressed using a two-dimensional spatial notation, but that doesn&#x27;t really help you understand the concept at all because there are a lot of <i>different</i> relationships that are naturally described by putting three things in a triangle.<p>What you <i>really</i> want students to understand is that expt, log, and nth-root are <i>functions</i> that are related in the following way:<p><pre><code>  expt(b, n) = x
  log-x-base-b(x, b) = n
  nth-root(x, n) = b
</code></pre>
It&#x27;s really that simple.  No fancy notation needed.  In fact, fancy notation <i>always</i> gets in the way of understanding because people naturally think in words, not in spatial relationships.  Mathematical notation was invented not because it aids understanding, but because when you&#x27;re writing math with pen and ink it&#x27;s faster and uses less paper to use Greek letters and spatial relationships than full words.  But when you&#x27;re on a computer, it&#x27;s easier to write out the names of functions, and that is actually a better impedance match to people&#x27;s natural mental processes, which involve <i>language</i>.<p>[UPDATE] I would like to revise this: not everyone thinks in language.  But everyone <i>communicates</i> in language.  For <i>communicating</i> mathematical concepts, language is the best tool we have.  There&#x27;s a reason that the symbology in math papers is invariably wrapped in natural language.  It&#x27;s the same reason that the video has a narration.  It wouldn&#x27;t make any sense otherwise.