Some Upstream Research Programs for Muslim Mathematicians: Operationalizing Islamic Values in the Sciences through Mathematical Creativity

Abstract

This article is inspired to a large extent by my reading and understanding of the works of Roshdi Rashed (1) and Imre Lakatos. (2) In my opinion their works, among those of others, (3) are very important for creative (4) Muslim mathematicians who want to reflect deeply on the meaning, scope, and goals of mathematics as well as on the nature of the truth and certainty (5) sought by mathematicians when they do, or rather, create mathematics. The foundational conceptual, meta-mathematical starting point here is to see mathematical creativity as "a human activity, a meta-process, which acts upon and generates new mathematics." (6) Although my discussion shall focus for the most part on Islamic mathematics, (7) Malay-Islamic mathematics, (8) and the Islamization of mathematics, (9) I believe that the underlying, more general thrust of this article will be of some relevance to all non-western mathematicians (10) who wish to develop philosophies, methodologies, and practices of mathematics that are more in line with their respective religious beliefs, cultural traditions, and value systems. (11) If mathematics, like science in general, is value-and culture-laden, (12) then, ipso facto, any theories, methods, and models developed in mathematics will accordingly also be value-and culture-laden. (13) As argued by Brian Martin, the Platonic conception of mathematics as value-free is itself a value-laden conception which only serves to hide from most people the intimate links between mathematics as such and the belief systems of its practitioners. (14) Or, in the words of Rev. Richard S. Kirby, who argues for a "theology of mathematics": The future math, like the past, cannot be value free. It has always been a radically human activity. It serves human purposes. It may be rigorous, but its objectivity is subject to human values, including the [evolving] ideology of 'objectivity'. It is also one of the most vibrant areas for human creativity, as new fields emerge in areas such as vector analysis, topology, calculus, set theory, and many other fields. (15) Similarly, in his important inaugural professorial address the eminent Malaysian mathematician Shaharir bin Mohamed Zain shows in some detail through a selection of mathematical topics that: ... the development of each topic was indeed first started by appealing to a value system and belief on the basic nature of the issue. Then, the mathematical results obtained were used to confirm and strengthen the value system or belief. More often than not, this [i.e., the results obtained] became a new value system and belief on which further development of mathematical science was based ... [hence] mathematical science is not as objective as it is commonly believed ... not purely quantitative and logical ... mathematical truth is shown here as many-valued and relative to a particular agreed paradigm. Its acceptance is not purely based on rationalism, logic and consistency, but also based on pragmaticism, aestheticism, rigour, sophistication, belief and personality of scholars. (16) From the above conclusion that mathematics is value-laden, Shaharir then draws the attention of Malay-Muslim mathematicians to the idea (quite novel at the time) of the rationality and the imperative of the Islamization of mathematics as a "symbiosis" between mathematics and the Islamic value-system, namely, a mathematics whose objective, quantitative results embody the cognitive and ethical values of Muslim mathematicians who care deeply about understanding and living the Islamic vision of truth and reality (17) in both their personal and professional lives. (18) Upstream and Downstream Research What is meant here by "upstream" research (19) is research that is motivated by a high sense of critical self-awareness on the part of the researcher of his personal identity and purpose in life, in line with his understanding of, and commitment to, the worldview and value-system he is embracing or declares himself to be embracing, and includes the understanding of the real problems he has identified to be tackled as a result of that critical self-awareness. …