The TRESUR (pronounce "treasure") mathematical synergy project combines key research activities in impactful mathematics that are currently being undertaken in various premier research institutes. The network is interdisciplinary, intersectoral, unconventional and ambitious. It is unconventional because it connects stakeholders from seemingly separately developed fields in research and industry. It is ambitious because the consortium stretches from mathematics to applications in computational science, engineering, biomedical imaging and finance.

When looking at the state-of-the-art on the various keywords Tensor, appRoximation, exponEntial, sparSe, cubatUre, oRthogonality, to explore what connects them rather than what distinguishes them, with a view to align these connections, a treasure trove of new results is there to decipher.

The TRESUR staff exchange network is built around the theme of Sparsity in Approximation and Recovery (SpAR), with an interest in challenges encountered in both theoretical developments and practical applications. SpAR enables the deployment of simpler mathematical models with reduced computational efficiency for a large variety of application domains.

These developments are important for the larger STEM field and its fast-growing industry for which mathematics is absolutely indispensable. To quote Shakuntala Devi: ``Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.``

The general audience may not be aware how much SpAR touches the daily life. We mention some use cases to which members of the TRESUR team have contributed and plan to continue doing so: localisation problems, antenna array synthesis, direction and angle of arrival problems, medical imaging, parallel MRI, radio astronomy, defect detection in industry, liquidity risks in banking.

SpAR is the passion that connects 12 countries and brings 14 universities, 1 research institution and 8 companies together.