PurposeThe purpose of this paper is to bring out with analytical argumentation and mathematical treatment the central problem of Islamic economics, finance, institutionalism and socio‐scientific thought as it is being practiced today and for some time now. The problem arises from the failure of contemporary Islamic intellection to formulate its methodology according to the cardinal principle, and the singularly central and minimal axiom of all its inferences. This is the precept of the oneness of God explained in terms of the epistemology of unity of divine knowledge and the unity of the consequential knowledge‐induced world‐system.Design/methodology/approachThe objective is achieved by mathematical theorems for pointing out the impossibility problem of Islamic economics and finance. The analytical alternative in the epistemological framework of unity of knowledge, or the functional law of oneness of God in its functional ontological functioning in economics and finance are formalized.FindingsA number of Impossibility Theorems of Islamic economics and finance are stated and solved. Alternative epistemological premise and its functional nature are presented in the light of unity of knowledge or what is known as the law of oneness of God and its application to the unified world‐system.Research limitations/implicationsThis is a theoretical paper based on analytical argumentation and mathematical formalism to bring out the theorems that state and resolve the problem of impossibility of attaining the goals of Islamic economics and finance under their present pursuit.Practical implicationsAlthough the paper is of a theoretical nature it has profound practical extensions. The principal ones are in the direction of developing the structure of Islamic economy and financing within a globally interactive, integrative and evolutionary system of practical interrelations. Such a structuring will embed the economy, finance, business and society in an organic model of unity of interrelations.Social implicationsThe paper presents a new social and ethical meaning to the present exogenous treatment of Islamic economics that proceeds on by an exogenous treatment of morality, ethics and their functioning in an unsustainable economic, finance, and social order.Originality/valueThis paper is emphatically original. It questions the entire premise and methodological orientation of the prevailing nature of Islamic economics and finance. The intellection and its application based on the absence of unity of knowledge as the divine mooring of Islamic intellection in everything has been distanced or treated as an exogenous still‐born axiom having no dynamics in the analytical and functional system otherwise.