Many areas in academia and industry depend on mathematical sciences to open up new frontiers and advance discovery. Research in mathematics contributes to advances in areas such as medicine, cyber security, weather prediction, digital data compression and mining, aeronautics and computing, to name a few. Today’s challenges faced by academia and industry are so complex that they can only be solved through the help and participation of mathematical scientists
The role of Mathematical Sciences in Civilization has been of central importance for centuries. The current trend to a global economy and a knowledge society has placed information and innovation technologies, increasingly dependent on scientific research driven by Mathematics, at the forefront. Mathematics also plays an increasing role in the efficient development of novel products and technologies, which are essential for our ageing societies combined with growing worldwide population and limited resources. Mathematics provides the tools, which enable us to understand and reduce the complexity of the mutual interdependencies in economics, and leads the way in predicting, optimizing and controlling the respective systems.
The study of these mathematical objects and of their relationships and interconnections is a pillar of modern sciences, guiding the design and interpretation of empirical observations and laboratory experiments. In almost all industries Mathematics opens the way to virtual experiments, the analysis and simulation of multiple scenarios for a given phenomenon and its control and optimization. Besides its role in science and engineering, the domains of application of mathematics include social, environmental, and economic phenomena. This is especially true in areas where innovation is contributing to the wellbeing of society, such as health, security, communications, and environmental stewardship. The search for new life-saving drugs, the development of high-performance materials, the continued miniaturization in electronics, and the protection of sensitive ecosystems – all of these application-oriented activities, and many others, are strongly dependent on fundamental research, and that research is inextricably linked to mathematics.
The essential program of the applied mathematician when collaborating with industry follows essentially the following paradigm: first, identify the problem of concern; then, build a quantitative mathematical model, analyse and solve it, apply the results, and potentially create appropriate mathematical software that can be commercialised. The emphasis is in pointing out which are the important and relevant variables controlling the problem, which are the constraints and what is the goal. This is done through the understanding of the underlying mechanisms involved in combination with the analysis of the respective observations and data. The next steps concern the analysis of the created mathematical model, its numerical simulation in different scenarios, and the validation the model in comparison with experimental data.
Google is the apotheosis of how innovation in mathematics and technology can transform a few people into a world-leading services company. Google evolved from a research project by Larry Page, a PhD student in the Computer Science department at Stanford University. Page’s dissertation explored the mathematical properties of the web, treating its link structure as a huge graph and the number and nature of links to a particular page as an indicator of its importance. From this, Page and Sergey Brin (another Stanford PhD student who joined the project later on) evolved a page ranking algorithm and a search engine based on the rankings, forming a company based on the technology in 1998, in a garage in Silicon Valley. From these small beginnings, the company has since grown to over 10,000 employees worldwide.
This example illustrates that mathematics should be recognized as a true innovation enabler for industry. There is a lack of understanding of this fact in both industry and academia, and it is extremely important for society that this gap is closed.
