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One of the most challenging open questions in mathematical fluid dynamics is whether an inviscid incompressible fluid, described by the 3-dimensional Euler equations, with initially smooth velocity and finite energy can develop singularities in finite time. This long-standing open problem is closely related to one of the seven Millennium Prize Problems which considers the Navier-Stokes equations, the viscous analogue to the Euler equations. In this talk, I will describe why and how the physics-informed neural networks (PINNs) can be a robust and universal tool to find the smooth self-similar blow-up solution for various fluid equations, from the simple 1-D burgers equation to the 3-D Euler equations in the presence of a cylindrical boundary. To the best of our knowledge, the latter represents the first example of a truly 2-D or higher dimensional backwards self-similar solution. This sheds new light to the century-old mystery of capital importance in the field of mathematical fluid dynamics.