Let us now consider synthetic-a-priori-based creative knowledge. Here, a new concept or parameter is injected to establish a relationship among existing concepts/parameters using deduction. A classic example of synthetic-a-priori-based creative knowledge is presented by the concept map depicted in Figure 7. It boils down to following statements—(1) Euler’s number e can be expressed as ex= 1 + (x /1!) + (x 2/2!) + (x 3/3!) + ….; (2) Sine function can be expressed as sin(x ) = x - ((x 3)/(3!)) + ((x 5)/(5!)) - ((x 7)/(7!)) + ….; (3) Cosine function can be expressed as cos(x ) = 1- ((x 2)/(2!)) + ((x 4)/(4!)) - ((x 6)/(6!)) + ….; (4) Functionsex , sin(x ), and cos(x ) yieldeix = cos(x ) + i *sin(x ), wherein “i ” equals the square root of -1; that is,\(i=\sqrt{-1}i\); (5) An imaginary number can be represented using\(i=\sqrt{-1}\); (6) The relation eix = cos(x ) + i *sin(x ) yieldsei π + 1 = 0 if x = π (pi = π); and (7) Euler’s identity impliedei π + 1 = 0. The first three statements represent pieces of knowledge classified as secondary relations of ideas, because these can be derived via deduction from respective primary relations of ideas and definitional knowledge. For the same reason, statement (6) is also a secondary relation of ideas. Statements (5) and (7) are pieces of definitional knowledge, whereas statement 4 is a piece of synthetic-a-priori-based creative knowledge, since it entails a new concept (imaginary number \(i=\sqrt{-1}\)) that was not known before Euler introduced it to deduce a relationship between the Euler’s number, sine function, and cosine function. It is remarkable that synthetic-a-priori-based creative knowledge has a temporal dimension. As a result, it may transform into definitional knowledge at a later time. For example, nowadays, an imaginary number is a piece of definition knowledge; however, at the time of its inception, it was a piece of synthetic a-priori-based creative knowledge.