"Alison Wolf of King's College London and author of a provocative book called Does Education Matter? has argued elsewhere, that maths and science education are something fun and desirable that countries spend more on as they get richer, rather than being the engine of economic growth."
This citation is from an ongoing debate on The Economist web site concerning innovation. If you argue that the pursuit of science is searching for God in a materialistic pantheism and that this is the goal of mankind, it is of great interest to know how to optimize it. Is it driving the economy at the same time or is it a byproduct of the economy?
What is rather clear from history is that the scientific revolution starting during the 17th century stimulated the development of philosophy most of the time. It also leads to a secularization that freed the minds of people. However, would this have happened without the development of trade and business and a middle class? Francis Bacon became the "trumpeter of a new era" by extrapolating from the invention of the compass, gun powder and the movable type, all pre-17th century events, all tools for subduing Nature.
73% of the people voting on the motion in the Economist debate think math and science are important for innovation but the remainder believes that management skills are limiting as well as venture capital. Looking at the AngloAmerican history there is a correlation of a wave of inventions after the introduction of public schools, with the light bulb and the areoplane as examples. Then there is a new wave after the creation of armies of PhDs in the mid 20th century with the transistor and DNA helix as prime examples. America has, though, always been very good at making products out of ideas which would also speak for managerial skills.
It is not easy to determine which is the hen or the egg between science and management but it would be very good to know. Truly brilliant scientists might make stimulating breakthroughs even if society is not well to do around them but to get a scientific revolution probably requires prosperity in the environment.