This smartphone app solves a recognized equation written
down by capturing and translating a picture of it into a solver,
like Wolfram Alpha for instance.

[+] For equations, a keyboard is still less
convenient than pen-and-paper. Handwriting-
recognition for mathematical symbols would be
needed, but that's feasible, especially since the
usefulness of this would
motivate compromises (e.g. modify one's
handwriting).

Might require an interface like predictive text,
where the software guessed at what you meant,
and you accepted/rejected its guess. Since this
will use online equation solvers, it can also use an
online handwritten math-symbol-recognizer <link>

The linked Android app screenshots don't show
equations, rather expressions. Those do, however
have a simple correspondance
with a subset of trivial equations.

In defense of this idea, the distinction between
trivial and nontrivial equations
bears on whether this idea is baked. Because
the problems it solves are trival, the
computational engine of that
app isn't an equation solver, and doesn't need to
be online -- it's just a 4(?)-function calculator.
The idea proposed here is to harness the power of
a real online equation solver, like Wolfram Alpha:
a significant difference, IMO.

Even the OCR part of that app, which is where it
comes closest to baking this idea, is a long way
from reading nontrivial
equations. The spatial arrangement in
*two* dimensions, of math symbols has
significance unlike conventional
OCR. Size of symbols also carries meaning. Not to
mention "Where" or "Let" clauses, or
equation systems.

<tongue in cheek>
While this is definitely a good idea, unfortunately most mathematicians equation 'writing' is more akin to chicken scratching, so the recognition part will need to be VERY clever, to turn said mess into a coherent equation, that the maths part of the software can deal with.
</t i c>
I would suspect, as [mouseposture] noted, that 'proper' equation recognition (output compatible with some maths software) would be a far harder task than ordinary handwriting recognition.

At their simplest, mathematical equations are dificult to read, frequently with arbitrary or ambiguous symbols. Whoever started teaching basic multiplication using an x as the operator symbol has a lot to answer for, the difference between a manually written mu and u is often invisible even for people with neat handwriting, and I had at least one text book that used N for at least 5 different variables depending on context (admittedly in different equations, but still). In addition, the difference between 1+x/5 and (1+x)/5 is frequently hard to determine in hand written equations, per [mouse]'s second anno above.

Getting this to work on printed equations would eliminate some, but not all of these problems, as simple font differences can still confuse symbols, and it won't help with symbol ambiguity.

Actually, turns out Windows 7 does mathematical
handwriting recognition from tablet or touchscren
input <link>, and there's 3rd party software that'll do
it on
OSX. Judging by the quantity of technical literature
on the subject, though, it appears that doing this
really *reliably* is not yet a solved problem

I'm still waiting for the app that will look at a picture of an
object and tell me what the hell it is. Strangely, I think
these two apps might turn out to be remarkably similar in
design.