Mathematics for designing, building, and traveling

Mathematics also plays a key role in ensuring that space flights run smoothly! Katherine Johnson, an American mathematician and space engineer, was a leading figure in this field. She worked at NASA for many years, calculating and checking trajectories and contingency plans. Her calculations were essential to the success of the missions.

Find out more: The life of Katherine Johnson - Wikipedia

Mathematics plays an essential role in the functioning of GPS systems. These systems use Einstein's theory of relativity in their calculations. Due to the speed of satellites and the effect of gravity, the clocks on board GPS satellites experience a time lag compared to clocks on Earth. This lag must be taken into account to ensure the accuracy of position calculations. Otherwise, measurements would be inaccurate by several meters.

Learn more: Where am I - Accromath - UQAM

Researchers have used mathematical models to control autonomous cars and reduce the accordion effect responsible for traffic jams. The tools deployed should help stabilize traffic by intelligently adjusting vehicle speeds; initial theoretical results are promising in terms of traffic flow and energy consumption.

Find out more: Autonomous cars - CNRS

This is the challenge that the MATritime laboratory has set itself! It uses mathematics to optimize maritime navigation by integrating physical models and statistical approaches. This makes it possible to better anticipate uncertainties related to sea conditions and improve ship design, particularly with a view to reducing their environmental impact. These innovative methods optimize existing fleets and explore other applications, such as the protection of marine wildlife.

Find out more: Maritime transition through mathematics - CNRS

By using optimization software, engineers are able to improve the shapes of the industrial objects they design: the aim is to enhance certain physical properties of the objects (strength, efficiency, durability), while respecting constraints such as weight and cost. This software involves mathematics, sometimes traditional, but more often extremely “advanced” and derived from contemporary research.

Find out more: Design and optimal shapes - CNRS

Airlines face complex organizational and planning challenges. These include issues such as aircraft allocation, revenue optimization through demand forecasting, and downtime minimization. On this subject, for example, mathematical models can reduce runway congestion by taking several factors into account, thereby improving passenger comfort and reducing fuel consumption.

Find out more: Reducing airport congestion with mathematics - Madd Maths