# Math is beautiful and also very, very useful

For most people pure maths can seem seem entirely theoretical and far removed from daily life. But there are advanced mathematical technologies at work all around, in the systems and machines, transport, online connectivity, etc. Maria J Esteban has devoted her life’s work to understanding and developing the mathematical technologies behind innovation. Speaking at ICM 2018, she explained how math is changing the world, and urged mathematicians to recognize the value they bring to society, explained how maths impacts the modern world.

Through techniques such as modeling, simulation and optimization, mathematicians make continual breakthroughs, Estaban noted, and directly contributes as much as 15% to the GDPs of countries like Britain, France and The Netherlands. In France, one in ten jobs require a high level of math, she told an assembly of international mathematicians. Citing several examples, from aerodynamics to heart-bypass operations and image processing, Esteban highlighted the importance of pure math, and told ICM attendees that “maths is beautiful as well as very very useful”. She said the discipline will have increasing impact new technologies evolve. “All equations of physics and mechanics are written in mathematical terms,” she said. “Math is the language of science and the language of innovation.”

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Estaban illustrated the pleasure she gets from crossing the imaginary divide between disciplines, and she uses applied math to help people understand the world. Recently, she was able to improve on an imperfect algorithm that quantum chemists had been using for years to understand the properties of materials and how they interact within a system. She is regularly invited to international congresses to explain her work to chemistry experts. “I’m able to say that not only am I working on a problem, but I’m having a real impact on other people’s lives and work. I’m really doing something that is useful and this feels good.”

“How do you think Google became the best and most popular search engine in the world?” she asked the engaged audience, before answering her own question. “Using maths to develop better and better algorithms of course.” Estaban explained how medium to small-sized companies globally are realizing the potential of advanced mathematics to increase profits and squeeze costs and how this represents new opportunities which must be taken advantage of. “Us mathematicians need to be conscious of the value we bring to the economy,” she concluded. “We need to shout about this to push for more investments and more mathematicians to help improve the world and be more valued and appreciated around the globe.”