In this article, we try to present a potential plan or crude design, and perspective for promoting mathematics-for-industry. Since the mid-1990s, the drastic improvements in computer performance have forged a much closer link of mathematics to science (including social science), technology and industry. Getting such high performance computer, we have now a new feature of applications of mathematics to industrial-scientific technology (through several software). Those applications may also provide an impact and new development on mathematics itself, and then, again be able to develop further the world of mathematical science.

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This document gives a brief explanation for what is “Statistical Mathematics,” and describes how its notion has been expanding to a wide variety of research fields. The recent interests of statistical mathematics are focused on generating more flexible mathematical models for describing complex phenomena in terms of data generation mechanism and/or its function. Such efforts demand collaborative works with the machine learning community in a big data era which we are now faced with.

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The authors review the historical and current perspectives of development, application and its supporting communities of statistics particularly in the field of official statistics, biometrics, psychometrics and technometrics to clarify their similarities and differences from the viewpoints of the roles in the society.

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Mathematical science is expected to be one of the most fundamental research fields that promote the next-generation scientific and technological innovation. Mathematical science is not staying within the traditional academic nutshell, but is crossing the other scientific and technological fields and industry. Great expectations are put on the industrial applications that enable the Japanese industry to fight the global competition employing the advanced mathematical tools. In this paper, the industry-academia collaboration is discussed in terms of application of computer simulation.

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The author clarifies the position of mathematical sciences in trans-disciplinary sciences and technologies after he reviews typical roles of classical mathematical sciences as the method of fluxions by Newton and historical efforts to explain mathematical sciences to non-mathematicians by Clifford and Pearson. He also tries the classification of the function of mathematical scientific methods from the viewpoints of their objects and operations.

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This paper introduces activities of Reliability Engineering Association of Japan (REAJ). REAJ is a volunteer group of professionals who engages in assuring reliability and safety of various products, system, and human systems. REAJ organizes some symposiums and forums to encourage for academic and industrial developments, and publishes scientific journal to introduce the latest research. Some study groups are contributing to mutual communications of members who have similar challenges.

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