Graphical interfaces emerged long before digital devices and even before the devices became electric. Early examples can be traced back to the 19th century.
There are two main reasons that demanded the use of interface icons. As mechanical devices became more complex in the 19th century, there was no longer enough room to show the explanations of each button and lever in a written form. Secondly, as these devices were mass produced and sold abroad, the interfaces could no longer be restricted to a single language. There was a demand for a new global language that could be understood by anyone. Both of these changes date back to the second industrial revolution.
W. T. Odhner invented his version of the Arithmometer in 1873. It was a pinwheel calculator that was industrially produced in Russia. On its front panel you can see the plus and minus symbols with arrows pointing which way you should crank the handle in order to add or substract numbers.
Another example of the use icons in a graphical interfaces, are mechanical typewriters. Mostly the buttons of typewiters would only contain letters and words as labels for functions. However the plus and minus symbols are also present in some typewriters. Take the Royal portable typewriter for instance, which was produced in the 1930's. It had a horizontal lever in its frontpanel with the plus and minus symbols on its opposing ends and a label "Touch control" beneath it. The lever apparently was used to control the stiffness of the typewriters buttons.
It's not surprising that the first interface icons were symbols whose meaning was already known to users from mathematics or another context. This way the users could easily deduce their meaning with a low cognitive load.
Reel-to-reel tape recorders
Reel-to-reel tape recorders have been manufactured since the beginning of the 20th century. In the 1950's and 60's models became more widely available for home and recreational use. In the first recorders the buttons were simply labeled with words: "play", "stop", "rewind" and so on, but as buttons got smaller words needed to be replaced with icons. You can find a good resource about early recoders and playback buttons at: www.pushclicktouch.com/blog/?p=57.