Photoshop, the Adobe program for manipulating images, has become the symbol of a digital generation – for some, its use is a feminist issue, for others, a post-truth one. It has also been the means behind plenty of hilarious Twitter threads. (For those who prefer their software free, there have been many similar programs developed such as GIMP which provide some of the important functionality without the investment).

But Photoshop – as you might expect – is also extremely mathematical. It’s a beautiful mash-up of creativity and science, with a necessary side-effect of becoming a whizz at maths through a whistle-stop tour of it, even for those who might otherwise claim maths is too challenging or esoteric for them. As a former maths teacher, that sounds like an innovative way to explore some of the visual applications of mathematical concepts that pupils might find both intuitive and appealing. Here are just a few of the most basic ones:

- A good understanding of ‘inverse’ and ‘to invert’. When we first teach this concept, far too often is it a brief stop on the ‘multiplying and dividing fractions’ train; a terminology issue rather than a conceptual one. But anyone who has studied art to a reasonable level can tell you that colours can be inverted too – as can areas in Photoshop. The visual information contained in inverting the colours in an image and asking pupils what they notice, or lassoing an area and switching between this and its inversion (all the area not captured by the lasso) would be an excellent way to get students questioning the term and its meaning. Interestingly, the term
*complement*is also used for the colour that Photoshop switches to when inverting (it’s the colour opposite the original on the colour wheel), which could be a lovely way in to introducing set theory. You could also discuss other colour theory concepts such as*monochromatic*,*analogous*,*triadic*and*tetradic*, which are terms referring to the way the colour scheme is located on the colour wheel.

- In Blend Mode, using the Multiply function, if you multiply any colour by black, you get black. Gently exploring this an example of an absorbing element in a set (in fact a zero element) and making the analogy with multiplying by zero in the set of integers could be a powerful way of demonstrating the way in which axioms can translate across sets of very disparate ideas. Similarly, as you’d expect anything white will ‘disappear’ after the Multiply Blend Mode is applied, making white the identity element. You could even make some nice ‘equations’ like this:

- A very visual use for percentages. When we teach percentages in school, we often push the financial applications of them as a way to engage pupils. But in later life, the likelihood is they will use a calculator or computer program to find these – and that their understanding of the principles behind percentages are pretty shaky in any case. But percentages as a dynamic visual, especially in the case of transparency/opacity, help to explore percentage powerfully as a continuous variable. Using the zoom function also helps to illustrate percentage as used in scale and area, with the added advantage that values over 100% can be visualised too.

- Combinations: in Photoshop as in any image creator, the bit depth determines how much colour information is available for each pixel. A bit depth of one allows for two possible values; eight gives 2
^{8}, or 256. Then colour modes determine the number of colour channels available – for example, RGB (Red, Green, Blue) there are three colour channels; for CMYK (Cyan, Magenta, Yellow, Key) there are four. Depending on both the bit depth and the colour channels, the number of possible colours displayed is then calculated. For eight-bit RGB, then, there are over 16 million possible colours. Allowing pupils to investigate these possibilities would be a fantastic lesson with plenty of important mathematics – including the limits of accuracy (and human eyesight) in the real world!Of course, there is much, much more to Photoshop mathematics – this is just the beginning. Comment below with your ideas!