Very Brief Background:
In 1960, the quantum mechanist Eugene P. Wigner famously wrote about "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." He was referring to the profound ability of abstract concepts to predict real-world phenomena. While this ability has found what seems to be an endless number of successful use cases in science, engineering, and medicine, it remains mathematically unproven. At about the same time, and enabled by quantum technologies such as the transistor, the first high-performance computers (HPCs) were being built. The internet's precursor, ARPANet, was also enabled by such quantum technologies as the transistor and housed four of these early HPCs. HPCs automated the execution of fundamental computations, including the singular value decomposition (SVD) and the pseudo-inverse. Ultimately, the quantum mechanics-enabled computing automation and internet communication brought about advances in data science, from chaos theory to deep learning, which were previously limited to mostly unsolvable equations. Today, these mathematical methods are contributing solutions, not just to science, engineering, and medicine, but to all human and societal urgent challenges.

Goal:
This year, as the world is celebrating the 100th anniversary of quantum mechanics, the AIM Quantum Research Community will start work to define, develop, and deploy novel advances in mathematics and its applications that are inspired and enabled by, as well as inspiring and enabling of, new quantum science and technology. This interplay is expected to advance such active mathematical fields as linear and multi-linear algebra, topology, probability and statistics, calculus of variations, spectral theory, and information theory, and disparate application fields as personalized medicine, drug and biomarker development, materials science, climate modeling, quantitative finance, and cybersecurity.

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