Amazing Science

Today’s mathematical research, both pure and applied, is paving the way for major scientific, engineering, and technological breakthroughs. Cutting-edge work in the mathematical sciences is responsible for advances in artificial intelligence, manufacturing, precision medicine, cybersecurity, and more. Find out how the mathematical sciences are helping to improve our everyday lives by checking out the stories and infographics below.

This series of illustrations shows how advances in the mathematical sciences anticipate and enable later technologies that profoundly impact our daily lives, including life-saving advances in medical imaging and treatment, predictive traffic-avoiding routing, communications advances enabling GPS and high-speed cellular communications, safer online commerce with cryptographic security protocols, development of novel materials based on advanced simulations, improved forecasting of extreme weather events, and much more.

The leaps forward in technology have often built upon theoretical work whose impact would not have been predicted at the time of their creation. The same is true today: researchers and practitioners in the mathematical sciences continue to innovate, and we can only begin to imagine the future inventions their work will enable. Mathematical and statistical advances are playing a key role in emerging areas such as cyber warfare, quantum computing, artificial intelligence and machine learning for automation, genetic sequencing and related advances in vaccine creation to fight novel and existing viruses, and supply chain management.

The increasing pace of technological and social development will require many more advances in the mathematical sciences because they are a foundation for advances across science, medicine, business, finance, and even entertainment. New discoveries in mathematics happening today will reverberate for decades and centuries to come.

Thomas Baruchel’s website shows images derived from complex analysis. John D. Cook used the ImageQuilts software by Edward Tufte and Adam Schwartz to create a large variety of scientific and artistic images.

In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system.[1] System values that get close enough to the attractor values remain close even if slightly disturbed.

An attractor is called strange if it has a fractal structure.[1] This is often the case when the dynamics on it are chaotic, but strange nonchaotic attractors also exist. If a strange attractor is chaotic, exhibiting sensitive dependence on initial conditions, then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together. Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.[5]

The term strange attractor was coined by David Ruelle and Floris Takens to describe the attractor resulting from a series of bifurcations of a system describing fluid flow.[6] Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable. Strange attractors may also be found in presence of noise, where they may be shown to support invariant random probability measures of Sinai–Ruelle–Bowen type.[7]

Examples of strange attractors include the double-scroll attractor, Hénon attractor, Rössler attractor, Tamari attractor, and the Lorenz attractor.