# PhotoMath, NOT the end of math education as we know it . . . yet

PhotoMath is a new app you can use on your iOS device or Windows phone/tablet (Android version coming in 2015) which can solve math equations for you!! But before all you math students think you won’t have to learn algebra and before all you math teachers decide to quit teaching and set up that ebay shop selling all your old LPs let’s have a look at the iOS version.

First off, there have been computer algebra systems publicly available for a couple of decades now. Derive (one of my favourites, now sadly defunct) was a good, easy to learn program for Windows machines (and it was also a great graphing utility). Additionally there have been handheld calculators which will solve pretty complicated stuff since the mid 90s. These systems had two major hurdles that some could not jump over: their expense and having to learn how to enter the equations into the system. In some cases the second hurdle could be quite high. I remember just giving up on trying to learn MatLab; I couldn’t see the point when most of the stuff I was doing I could solve faster by hand. A friend of mine who works in the automotive industry says there is a real demand for experienced MatLab users so maybe I should try again. In my copious free time. Even earlier than that there were computer programs that would give you numerical approximations of solutions for certain kinds of equations. But the gold standard is: if the answer is the square root of two then that’s what I want to see.

So, what makes PhotoMath more of (or at least a different) threat? It’s dead easy. On the iOS version anyway you just fire up the ‘app’, centre the equation you want to solve in an onscreen box (much like you would do with a UPC code reader) and, after a pause while the app parses the equation, a solution magically appears. You can, if you wish, see the steps involved. This sounds like a blessing to all algebra students and a boon for all math teachers. Except . . .

For the moment, at least, it’s severely limited. According to Photomath’s website it can currently handle arithmetic expressions, fractions and decimals, powers and roots, and simple linear equations. Let me tell you what that actually means in practice.

Arithmetic equations: PhotoMath will evaluate a calculation for you involving addition, subtraction, multiplication and division. So, for example, if you give PhotoMath the expression:

$\left( 3+5 \right)\div 7$

you get the answer: 1.142857 (which disappears off the screen pretty quickly after you stop focusing on the expressions but PhotoMath does keep track of everything you asked it to do and the solutions, you just have to go to the right menu). In this way, PhotoMath is acting like a calculator, saving you the effort of keying in the expression.

Fractions: I couldn’t get PhotoMath to parse

$\frac{5}{17}$

but it was happy with

$5\div 17$

and it gave me an answer of 0.294118. That’s not really handling fractions as far as I’m concerned but I suspect that will be ‘fixed’ soon. Maybe it was just my way of testing PhotoMath. I’m using software much like Equation Editor in Word to create onscreen mathematical expressions for PhotoMath to read.

Powers and roots: Again, as a calculator, PhotoMath is fine . . . sort of. Here’s some examples with PhotoMath’s results:

$\begin{array}{l}\sqrt{49}=7\\\\\sqrt{50}=7.071068\\\\\sqrt[3]{27}=140.296115\\\\\sqrt[3]{30}=164.something\end{array}$

Oh dear, I guess PhotoMath isn’t that good at cube roots. I also tried

$\sqrt{-4}$

which gave me no results at all. So PhotoMath doesn’t do imaginary numbers either.

$\begin{array}{l}{{3}^{4}}=81\\\\{{3}^{2.5}}=9\\\\{{3}^{-2}}=0.111111\\\\{{3}^{{{2}^{3}}}}=6561\\\\{{3}^{\tfrac{1}{2}}}=1.732015\end{array}$

So, mostly good except for the decimal exponent. For the last one, PhotoMath did a good job of showing sensible steps for evaluating the expression.

Simple linear equations: Linear equations means things like the following (PhotoMath’s solution included):

$\begin{array}{l}3x-5=8\to x=\frac{13}{3}\\\\2y-4=5y+3\to y=-\frac{7}{3}\end{array}$

Interesting how Photomath’s solutions involve fractions. I quite like that as it makes it easier to back-step through the steps if you wish.

But Photomath cannot yet handle things like:

$\begin{array}{l}\frac{2x}{3}-5=0\\\\\frac{x-3}{x+2}=4\\\\\frac{x}{2}-3=6\end{array}$

But it did manage:

$\begin{array}{l}\frac{x-2}{5}-7=0\\\end{array}$

but if you want to know the solution . . . my rates are quite competitive.

PhotoMath didn’t like inequalities at all. And when I gave it

${{x}^{2}}-x-6=0$

it gave me

${{x}^{2}}-x=6$

Which isn’t even the best way to deal with the problem.

A few other things I noticed: if the math expression is fuzzy or you don’t hold your iDevice still enough you can get an incorrect answer. That alone would make me very reluctant to even suggest it to one of my students. And, very annoyingly, it won’t go into landscape mode. This means that in order to fit lengthy equations into the box you have to pull further and further back which not only may then start to pick up things that are not part of the equation but the equation itself may become too out of focus for an accurate evaluation. That really should be changed. Finally, when I was checking some of the exponential equations, PhotoMath would sometimes flip back-and-forth between a correct and an incorrect answer. I think it was having trouble because I was not holding my phone perfectly steady. I knew which was the correct answer but would a student?

I’d say that PhotoMath is currently useful as a limited calculator replacement, saving you the trouble of keying in an expression or checking yourself. What will be interesting to see is whether or not its equation solving capacities grow more powerful. Unless that happens PhotoMath will remain a interesting side note of math education.