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Recent advances in both theoretical mathematics and efficient mathematical software have stimulated the use of algebra and geometry in tackling problems arising from the sciences. Conversely, developments on these topics inspire fundamental questions in algebra and geometry. This involves algebraic geometry, commutative algebra, combinatorics, polyhedral geometry, and more. This talk aims to exhibit showcase examples along the lines. In this framework, the first part of the talk will be a discussion about the Wasserstein distance of data distribution to a model that is defined by polynomials. Computing this quantity means solving a non-convex optimization problem. The second part targets making a rapid excursion into the study of integrable systems through the lens of computational algebraic geometry. Specifically, the emphasis will be on exploiting tools from the areas to investigate solutions of the differential equations. Also, there will be an exhibition of some fundamental questions emerging from this investigation.