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.  

What is the purpose of education?

Seems to be a very difficult question, but I believe, it has a very simple answer.

The purpose of education is not just to help you just do experiments, understand nature, be a good person, and/or make thoughtful decisions, but it is to inculcate the following 3 abilities:

1) Ability to learn: No one cares to remember the details of things taught in school or college, but the ability to learn things which would help us on our way in life, is supposed to be developed by the system of education. In other words, this is the ability to create, write and edit new documents.

2) Ability to unlearn: This is an important ability in today's age of information. Once you are given exposure to several fields and you understand, that there are things you do not like or things you learnt, but it does not seem to be of any immediate use. This also includes things you learnt and liked, but it is proven to be untrue later. Then the ability which helps you to keep that knowledge aside in reserve or in recycle bin is the ability to unlearn. Note: There is no "Delete Permanently" option in reality.

3) Ability to relearn: The world is dynamic in nature. Things which are unimportant today, might be very important tomorrow. The ability to restore a file from the recycle bin and edit it suitably, in other words, the ability to learn something long forgotten is the ability to relearn.

Inculcating these abilities in every individual is the responsibility of high school and undergraduate education with suitable help from parents. Helping interested people master these abilities should be the role played by institutes of higher education.

(Original idea based on “The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn. ” ― Alvin Toffler)

Let me know your views in comments!