Role of Science, Maths, and Technology in Progress

The role of science, maths and technology in progress has always been assumed to be related but, no one actually gave a precise understanding, I am trying to give one, using a quote:

Let, there be 3 types of knowledge, which span all that is to know in this universe:

Type 1 : "There are known knowns; there are things we know we know" 

Type 2 : "We also know there are known unknowns; that is to say, we know there are some things we do not know" 

Type 3 : "There are also unknown unknowns, the ones we don't know we don't know.” 

The primary roles of science, maths, and technology can be explained as follows: 

The primary role of science is to take elements of type 3 and convert them to type 2, because this deals with unknown elements to begin with we need imagination, curiosity and creative thinking to do scientific original research.

The primary role of maths is to take elements from type 2 and convert them to type 1, because these deals with handling known elements it need application of logic, systematic thinking and reductions to known elements.

The primary role of technology is to take abstract elements of type 1 and make them useful and implement it.

Few examples to help convey my idea:
Example 1: Discovering gravity and its cause is science, knowing how exactly to model the effects is maths, and using those models to make geostationary satellites is wonder of technology.

Example 2: An algorithm to test if a given number is prime, it is a known unknown element or piece of a big number theory puzzle. The primality testing algorithm might have needed great creativity and imagination but, the algorithm is finally mathematical tool and maths played it's role to give us a tool to solve that piece of puzzle. The algorithm is not a piece of scientific discovery but a mathematical breakthrough.

Example 3: Using technology to take elements from type 3 to type 2, is still called as scientific research. For example, CERN Large Hadron Collider facility is a technology used for scientific research and even a simple microscope or exploratory telescopes are other examples. The technology (i.e, the accelerator or the microscope) was developed after it was already made into a concept of type 1, but the technology itself aids in new discoveries by extending our senses and abilities to see more and grasp more.  

Important Note: These roles are defined in terms of necessity and not sufficiency. 

Example: One might need mathematics to pen down imagination in concrete words and mathematical solution to a problem might dictate the existence of a concept which was initially of type 3 to be of type 2.