Mathematics and cities: A long-standing relationship fit for the future?

Abstract

Mathematics helps us to deal with time and space, an important truism for those individuals who work on behalf of society to impose order on nature. Civil engineers in particular have to seek to harmonise their creations with the natural environment while working within temporal and special constraints. For example, engineers have to synthesise natural and man-made rhythms, meaning that timings need to be synchronised, often with a very high degree of precision. Their creations need to be harmonised with the natural landscape, and while some can hug the contours of the landscape, canals, railways, pipelines, tunnels and major roads need to cut through it such that they are linear or curved in plan and uniform in gradient. This is simple geometry made complicated by myriad engineering calculations. As we transition to a world of autonomous vehicles and robotics to mimic human thinking and actions, multiple data feeds and near instantaneous conversions into intelligent movements stretch our capacity to make calculations. Harmonising this with our infrastructure and urban systems to yield a safe, efficient and effective world today, and one that is sustainable and resilient as we look to the far future, is one of the most important mathematical challenges of the modern age. Mathematics pure and simple, or applied and complicated, permeates everything we do, therefore.