We're going to take a quick look at one of the most long lived paint producers in the world, Windsor and Newton.
Winsor and Newton was first established in 1832, by William Winsor (described by their website as a chemist) and Henry Newton (described by their website as an artist) (X). They had identified a hole in the arts market, notably, paints with reliable colours.
Notice that Winsor was a chemist. All of these colours don't just appear out of no-where, they have to be created, and they are largely created by chemists. That is because artists colours have to have several properties beyond being applicable by a brush, including consistent colour across batches, consistent colour before and after dying, and to stand up against the ravages of time. Although these may seem simple at first, they require precise measurements, precise sourcing, and an understanding of how chemical compounds change and break down over time.
Before the early 1800s artists would be expected to purchase pigments and mix them to create paint themselves, a time consuming, and often irregular process, that required all painting to be done indoors, as there was no stable way to transport the paint long distances. Artists would make studies or sketches of the landscape, and then try and translate those onto a canvas once back at their studio, reliant on their own memory for things like colour and distance.
Often, a painter's apprentice would take on the task of mixing the artist's pigment into paint at the artist's specification, and according to their measurements and recipes. However, smaller disciplines, or single artists who could not afford to keep apprentices, often mixed their own.
Let us look momentarily at the Mona Lisa.
The absence of eyebrows is often remarked upon by art scholars and there are a number of different theories as to why her eyebrows are absent here. In fact, she was originally painted with eyebrows, as discovered using infra-red imaging by Pascal Cotte (a photographer and, key to the orignal poster's point, an engineer) (X). One of the leading theories is that the pigment used to paint her eyebrows has faded to near invisibility over time, an idea for which there is significant precedence.
In fact, Da Vinci has made this mistake before, in his brief but illustrious career as an artist in the Last Supper. Da Vinci's Last Supper used an experimental technique of oil paints on dry plaster, rather than the well established tempera on wet plaster. (X) As a direct result, the Last Supper is under extreme conservational restrictions. The room in which the Last Supper stands is hermetically sealed in order to prevent mold growth and environmental damage. (X) Additionally, no flash photography is allowed. This is because the painting is literally so delicate that the light from flash photography damages it. (X)
Let us look now at contemporary pigments. One of the first lessons I had in my art classes was 'never put red or yellow paint on your face'. This is oddly specific, but it was quickly explained to us that mid- and high-quality red and yellow paint are often given their colour using cadmium. Those of you with science backgrounds might note that cadmium is highly toxic.
Despite the danger, cadmium is easy to acquire, and easy to process into pigment. Perhaps more importantly, and certainly more importantly for artists, cadmium does create a vibrant colour, and an opaque paint that, crucially, does not degrade over time.
Similar chemically or geographically interesting pigments can be found both contemporarily and through out history. Take ultramarine blue, which was initially made using crushed lapis lazuli, available from only one mine in the world during the renaissance era. As such it was more expensive by weight than gold. (X)
Imagine for a moment the immense wealth that went into Giotto's Scrovegni Chapel, the immense distance and cost that went into that very colour of blue.
I would be remiss not to flag the Forbes Pigment Collection. The Forbes Pigment collection has more than 2,500 specimens, and is dedicated to preserving examples of rare or interesting pigments. (X)
An interesting, if horrifying example is that of 'Mummy Brown', made from the crushed remains of mummified corpses. Obviously, this colour is no longer standard, and its use was disputed even at the time, but it is a relevant point in history.
The continued presence of these well catalogued pigments allows a great deal of insight, both for the soft sciences (when did we have access to this pigment, was that pigment sourced from off continent, and if so, how did it get here?), and the hard sciences (where was this chemical sourced, how was that chemical treated to result in this vibrant colour?)
Finally, (and thank you all for sticking with me this far) is a pigment some of you may be familiar with. Vantablack, one of the worlds blackest substances, was originally developed to 'coat satellite camera openings, absorbing stray light from he sun and moon so distant stars can be seen better'. (X)
Although Vantablack was originally designed in pursuit of a strictly scientific discipline, it did not remain so. Anish Kapoor in 2016 bought the rights to vantablack's 'use as an art material' (X). Although this is not the only time that a pigment has been copyrighted, it was an extremely public display, and one that the art world rebelled against.
(X) Anish Kapoor - Gathering Clouds (2014)
Stuart Semple began the intense process of creating a rival 'blackest black'. He eventually succeeded. Although his recipe for the blackest black remains a guarded secret, a tube of the most recent edition of the paint is available on the artist's website for an extremely reasonable price, and smelling of fresh coffee. (X)
Although this is all fairly niche, it is still a fantastic example of how art and science intersect, to say nothing of feats of architecture like Brunelleschi's Dome, GFP Bunny by Eduardo Kac, Renissance perspective, or Pig Wings by Oron Catts, Ionat Zurr, and Guy Ben-Ary.
(Much of this information was first introduced to me at school. The links provided here are not comprehensive, nor have they been well vetted by me. My information comes largely from textbooks and professors I no longer have access to, and wouldn't know how to cite even if I did.)