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Wilhelm Launhardt (1832‐1918) is a founder of mathematical economics. His main work, Mathematical Foundations of Economics, published in 1885, was translated into English in 1993. As an engineer, he contributed to the field of not only engineering, but also of economics and, in particular, to those parts in economics which can be treated fruitfully with mathematics. Launhardt developed his work independently from the French engineers, but based it squarely on the work of the agricultural engineer von Thünen. He made references to the economists Sax, Walras and Jevons. His main economic contribution lies in founding location theory but, beyond that, he contributed to the mathematical treatment of economics, labor economics, monetary economics and technology economics with a special emphasis on railway issues from a locational point of view. Hence, it is the purpose of this paper to show how Launhardt used mathematics in his engineering‐based approach to the economics of location and technology.

Rice’s Theorem is a notorious stumbling block in Computer Science. We review some previous work of us that shows that we can extend Rice’s result to large segments of everyday mathematics, so that similar stumbling blocks appear in many areas of mathematics, as well as applied areas such as mathematical economics; one of its applications (Koppl’s conjecture) is discussed in some detail. Note: this paper has been written in an informal style.

Nobody concerned with political economy can neglect the history of economic doctrines. Structural changes in the economy and society influence economic thinking and, conversely, innovative thought structures and attitudes have almost always forced economic institutions and modes of behaviour to adjust. We learn from the history of economic doctrines how a particular theory emerged and whether, and in which environment, it could take root. We can see how a school evolves out of a common methodological perception and similar techniques of analysis, and how it has to establish itself. The interaction between unresolved problems on the one hand, and the search for better solutions or explanations on the other, leads to a change in paradigma and to the formation of new lines of reasoning. As long as the real world is subject to progress and change scientific search for explanation must out of necessity continue.

The purpose of the study is to explore contributions made in Islamic economics methodology, particularly in the use of mathematical models used to build Islamic economic theories.

The methodology adopted is a survey by means of literature review.

Overuse of mathematical models in economics has it apparent weakness in simplifying complex realities and use of impracticable assumptions. But, that notwithstanding, they have a role to play in the development of Islamic economics. Empirical analysis in Islamic economics has weaknesses, including the very fact that moral phenomenon in Islamic economics is difficult to quantify, but its contribution, just like mathematics, is needed to develop the field. Islamic economics adopt mathematical models that do not cause obstacles in achieving the aim of Islamic economics, which is Falah. Where it is harmful, it is discarded. Islamic economics has yet to have a universally accepted research methodology; instead, numerous methodologies are used today. The poor use of mathematics in Islamic economics by new researchers, among other factors, may be due to young researchers’ poor background in mathematics.

The paper is unique in looking at the topic of Islamic economic methodology from the angle of application of mathematical models.

Attempts to prove, in this second chapter of the author’s monograph, that with a new research programme, it is possible to build a methodological bridge between economics and all other natural sciences and the scientists should address this challenge. Reviews basic principles that govern nature, including Einstein’s findings along with such luminaries as Copernicus, Newton, Galileo and Jeans. Concludes that the future is safe, as a new generation of scientists is now emerging in the East and the West, and that the new methodology should provide enough space for new roads, ideas and interpretations, which may occur in the future. Closes by saying a new spirit should be initiated in economics and transplanted into natural sciences.

There is a double crisis in modern science and in particular in physics and mechanics. Among others Einstein and Stephane Lupasco, in the 1930s, warned about this crisis. The Quantum Theory cannot be reconciled with the Relativity Theory. Specifically there is a gap (cleavage) between micro – and macro‐physics and mechanics. Parallel or beneath there is also a second crisis derived from a discontinuity (again a cleavage) between classical and modern science, that is between two previous revolutions. A new research programme of a simultaneous equilibrium versus disequilibrium approach, initially applied in economics has now been extended to include natural sciences. It is the question of a new, more comprehensive methodology which is actually a sui generis synthesis between classical and modern heritage. The rigorous application of the new research programme leads to the organisation of an Orientation Table, that is, a methodological map of all possible combinations (systems). The Table shows, without any exaggeration, a few revolutionary results. For instance, with the help of the Table, modern science or the second revolution (Einstein, Bohr, Heisenberg) does not appear contradictory but rather complementary to classical science or the first revolution (Newton, Lavoisier). The Kuhnian thesis to the contrary is disproved and the second crisis is solved. With the help of the Universal Hypothesis of Duality (the basis of the Orientation Table), matter and energy, at the micro – and macro‐level, appear in a double form (the Principle of Duality): stable (equilibrium) particles and unstable (disequilibrium) waves. The strong interactions from modern physics are associated with the law of gravitation (attraction) or stable equilibrium which governs stable matter and energy. The weak interactions are associated with the law of disgravitation (dispersion or repulsion) including entropy or unstable equilibrium which governs unstable matter and energy. In this way the first crisis is also solved.

The first Principia Mathematica (1686) by Sir Isaac Newton with reference to natural philosophy and his system of the world has largely contributed to the first revolution in scientific thinking in modern times. It has created the conceptual basis of modern science in the classical tradition by providing the tools of analysis and the technique of reasoning in terms of stability—from—within or, as we would say today, the model of stable equilibrium conditions.

The purpose of this chapter is to study the mathematisation of finance – excessive use of mathematical models in finance – which has been widely blamed for the recent financial and economic crisis. We argue that the problem might actually be the financialisation of mathematics, as evidenced by the gradual embedding of branches of mathematics into financial economics. The concept of embeddedness, originally proposed by Polanyi, is relevant to describe the sociological relationship between fields of knowledge. After exploring the relationship between mathematics, finance and economics since antiquity, we find that theoretical developments in the 1950s and 1970s lead directly to this embedding. The key implication of our findings is the realization that it has become necessary to disembed mathematics from finance and economics, and proposes a number of partial steps to facilitate this process. This chapter contributes to the debate on the mathematisation of finance by uniquely combining a historical approach, which chronicles the evolution of the relation between mathematics and finance, with a sociological approach from the perspective of Polyani’s concept of embedding.

The equation of unified knowledge says that S = f (A,P) which means that the practical solution to a given problem is a function of the existing, empirical, actual realities and the future, potential, best possible conditions of general stable equilibrium which both pure and practical reason, exhaustive in the Kantian sense, show as being within the realm of potential realities beyond any doubt. The first classical revolution in economic thinking, included in factor “P” of the equation, conceived the economic and financial problems in terms of a model of ideal conditions of stable equilibrium but neglected the full consideration of the existing, actual conditions. That is the main reason why, in the end, it failed. The second modern revolution, included in factor “A” of the equation, conceived the economic and financial problems in terms of the existing, actual conditions, usually in disequilibrium or unstable equilibrium (in case of stagnation) and neglected the sense of right direction expressed in factor “P” or the realization of general, stable equilibrium. That is the main reason why the modern revolution failed in the past and is failing in front of our eyes in the present. The equation of unified knowledge, perceived as a sui generis synthesis between classical and modern thinking has been applied rigorously and systematically in writing the enclosed American‐British economic, monetary, financial and social stabilization plans. In the final analysis, a new economic philosophy, based on a synthesis between classical and modern thinking, called here the new economics of unified knowledge, is applied to solve the malaise of the twentieth century which resulted from a confusion between thinking in terms of stable equilibrium on the one hand and disequilibrium or unstable equilibrium on the other.