Here is the myth about the relationship between science and engineering:
Science explores the universe to gain knew knowledge, then engineering comes along later and applies the new knowledge to create technology.
That myth is false and backwards. The way things have always happened in history is that engineers have invented new technologies and then scientists came along to theorize about it and take credit afterwards. Steam engines, internal combustion, electric engines, electric transmission, light bulbs, radio, the airplane... it was all created by mining engineers, mechanics, instrument makers and inventors, mostly with no scientific input.
Now that I’ve got your attention, let me back up a bit and clarify my terms. Science is concerned with discovering the secrets of the universe--what the universe is made of, how it is put together, where it came from, where it is going, what causes underlie the things we experience, and similar concerns. Engineering, by contrast, is concerned with accomplishing things. It has objective, observable, measurable goals, and reliable, predictable methods for achieving those goals.
I'll admit that my definition of engineering includes things like modern medicine, chemistry, and navigation that are not traditionally considered part of engineering, but there isn't a word that really works here. I picked “Engineering” because, used as a verb, it comes close. That is, “engineering a solution” refers to a solution that is measurable, predictable and reliable, regardless of what field it is in.
We can go all the way back to Classical Greece to see how science follows engineering rather than leading it. The first scientists were philosophers in the Ionian colony of Greece on the coast of Turkey about 600 BC. They were quickly followed by other Greeks, most notably the Pythagoreans, atomists, and Plato and Aristotle (about 400 BC). They used arithmetic, geometry, and astronomy to theorize about the universe. But arithmetic, geometry, and astronomy were engineering disciplines that predated the Classical Greeks by thousands of years.
Some form of arithmetic predates writing (invented around 3200 BC), as we know from the existence of pottery tokens found in ancient Sumer going back to 9000 BC . Arithmetic was invented for the purely practical purpose of trade. It provided a solution to trading multiples of items that was measurable, predictable, and reliable. It was an early form of engineering.
The roots of geometry likewise predate writing. We can't know exactly what methods were used in building the megalithic structures that go back to 9000 BC (Stonehenge was fairly late at around 3000 BC), but they must have had basic surveying tools such as measuring lines to lay out the foundations. The canal builders must have had sighting instruments to dig in proper straight lines. Those who built walls with one stone atop another, must have had something like a plumb bob to keep the walls straight vertically. We don't know how far back these sorts of engineering tools go, but we have evidence that they were in common use in Egypt before writing was invented. These tools and methods developed into true geometry millennia before Euclid was even born. There are tablets from ancient Mesopotamia that show the use of the Pythagorean Theorem thousands of years before Pythagoras. Geometry was a purely practical engineering discipline used for surveying, building, and calculating container volumes for shipping and trade.
Astronomy is a bit harder to date because enthusiasm tends to outrun rationality in the study of ancient observatories (after all, archaeology is a branch of science, not engineering). There are many astronomical events that could be indicated by sight lines, and many sight lines in a megalithic structure, so the birthday paradox practically guarantees that you are going to find some astronomically significant site lines in any ancient megalith. Still, we do know that astronomical observations were very advanced in both Mesopotamia and Egypt long before Classical Greece. Astronomy, too, was a form of engineering because it provide a measurable and reliable way to predict the movements of the planets.
From these early forms of engineering, the Classical Greeks came up with all kinds of weird and wrong scientific theories. Thales who is often called the first scientist taught that the earth floated on an infinite sea of water and that all things come from water.
Philolaus who is often credited with inspiring the heliocentric universe of Copernicus proposed a cosmology based on the tradition of a hearth, with a central fire around which all the heavenly bodies rotated. But in the cosmology of Philolaus, the central fire was not the sun; the sun was just another body rotating about the center. The reason that denizens of the earth never see the central fire is because the earth orbits with its inhabited face always outwards away from the central fire.
In the next circle up from the earth was the moon, in the next one up was the sun, then Mercury, Venus, and the other planets. Last was the circle of the fixed stars which did not rotate. Beneath the circle of the earth was one more circle, that of the counter earth, which rotates always between the earth and the central fire so that we never see it. However, the shadow of the counter earth could explain lunar eclipses that could not be explained as a shadow of the earth.
The cosmology of Philolaus was scientific in the sense that it was naturalistic and based on observation. It used a clever solution to the problem of explaining lunar eclipses. And to add power to the explanation, it explained mythological things as well. The counter earth could be the realm of the dead and the central fire could be the prison that held the titans. Philolaus apparently understood the scientific principle of explanatory power, the idea--popular among modern scientists--that to choose between two theories, you should choose the one that explains more things.
Eurytus was another early scientist. He believed that numbers contained the deep truth about things and looked for a way to find the number of man. He worked from the analogy of geometrical figures and the way that a figure was classified by the number of vertices in it. For example, a triangle has three vertices and a quadrilateral has four. Eurytus attempted to find the number associated with other things by counting vertices. For example, he would draw the outline of a man by laying out pebbles at what he took to be the corners, and count the number of pebbles to determine the number of man.
What is striking about this from the point of view of an engineer is how useless it is. There is some value in classifying triangles and quadrilaterals by their number of vertexes. The value is that there are important properties that apply to all triangles and to all quadrilaterals. But how likely is it that any important geometrical properties will apply to whatever figure Eurytus comes up with? Even assuming that his identification of the number of vertexes in the human figure is unique, what difference does it make what the properties of such a polygon are?
What we see over and over in history is academic scientists taking the practical tools and results developed by engineers, and indulging themselves in flights of fancy, trying to explain or unify or just say something that will impress other scientists. Common histories of science and technology obscure this trend by moving certain branches of engineering into the science category in order to boost the reputation of science. Newton's theory of gravity is considered science, but it had no speculation about underlying causes. In fact, Newton specifically repudiated such speculation.
Newton's theory was a purely practical exercise in celestial and terrestrial mechanics. It was a mathematical theory that combined Galileo's laws of ballistics with Kepler's laws of orbits to form a more concise law that included both. It's purpose was to make measurable and reliable predictions, not to explain anything or to shed light on the nature of the universe. Scientists then took this result and began to speculate about the nature of gravity, action-at-a-distance and other things of the sort that concern scientists, but none of that has stood the test of time like Newton's basic engineering did.
There are a lot more examples that I've been collecting. I'll post some more here if there is any interest in the topic.