A day in the life with mathematics

By activating facial recognition

Facial recognition works using mathematics. It analyzes an image of your face and compares it with other images of you already stored on your phone. To do this, it checks their consistency using calculations and models that identify the distinctive features of your face to verify that it is indeed you.

Find out more: Facial recognition: how does it work? - AFP Animé

By enabling weather forecasting

To forecast the weather, scientists use “partial differential equations” that describe how pressure, temperature, humidity, and wind speed change over time and space. Today, weather forecasts are the result of complex and powerful calculations made possible by computers. These are known as “weather models,” which are fed by satellite data and use probabilities to define different weather scenarios.

Find out more: Weather forecasting models - Météo France

Contributing to the functioning of GPS

Before setting off on any journey, it is important to know your exact location. To this end, mathematics powers GPS systems, which are based on several concepts, including Einstein's theory of relativity. Once your location is known, other mathematical theories can be used to calculate different routes.

Find out more: GPS, how does it work? - Lesics français

By facilitating network management

Mathematics is used in many areas, including rail traffic, to estimate the intervals between two trains on the same track. Statistical models and probabilities can also be used to anticipate and limit delays by analyzing data and predicting their knock-on effects.

Find out more: When maths gets on track - Athena Magazine

To know whether to run!

A mathematical model of the human body can estimate the amount of water absorbed, based on running speed, wind, raindrop size, puddles, etc. By the time she has thought about it, Adina is soaked and late.

Find out more: In the rain, should you walk or run to stay drier? - Unisciel

By allowing him to calculate the best offer and save money

This everyday situation shows how simple percentage calculations can be particularly useful in our daily lives. Mastering basic calculations allows us to save money and sharpen our critical thinking skills when it comes to advertising. Here, if Clement wants to buy two packets of semolina, the second offer is the most advantageous for him.

By enabling the calculation of surface areas and quantities of materials

Less surprising, but useful: Clément's father needs mathematics to calculate the surface area of his future terrace, then determine the quantity of materials to purchase.

Find out more: The area of any polygon - MathZkool

By facilitating image compression

Image compression relies on mathematical tools that reduce file size while limiting the loss of visual quality. For example, the JPEG algorithm begins by dividing the image into 8x8 pixel blocks, then applies a discrete cosine transform (DCT) to convert the spatial information into different frequencies. High frequencies, which are less noticeable to the human eye, are then reduced or removed.

Learn more: JPEG compression - Salem Wizards

Mathematics is the basis of musical harmony

Musical harmony is based on precise mathematical relationships between sound frequencies (such as octaves or fifths, minor or major chords, etc.). Rhythm is also structured by mathematical principles, as are certain classical compositions that use symmetrical and balanced forms.

Find out more: Maths & Music: a series of articles combining science and art - Insmi CNRS

To create the Sudoku grid and solve it using logical deductions

Maths can be fun too! Solving a Sudoku puzzle requires logic. Creating Sudoku grids is also based on mathematics: combinatorics, algorithms, group theory, and programming.

Find out more: The Sudoku Theorem - Automaths - Jason Lapeyronnie

To create an image from data

MRI uses magnetic fields and radio waves to create detailed images of muscles and organs. A mathematical operation called the “Fourier transform” breaks down a signal into its frequency components, thereby converting raw data into images.

Find out more: From Fourier transforms to medical imaging - Interstices.info

By enabling the creation of digital images

Mathematics makes it possible to create images for animated films by modeling shapes, animating movements, and simulating light. Equations define the curves of a face, calculate trajectories, and ensure smooth, realistic rendering, bringing characters and settings to life.

Find out more: The math behind video games - House of Mathematics and Computer Science

Using Benford's law

Benford's law shows that, in financial data, certain digits appear more often than others in the first position. This rule specifies that in many cases, numbers beginning with 1 appear much more often than those beginning with 9. By comparing this distribution with tax returns, Benford's law makes it possible to identify anomalies and thus potential fraud.

Find out more: Journeys to the Land of Math - Arte TV