the singularity formation problem is a central question in fluid dynamics, and it is still widely open for fundamental models such as the 3d incompressible euler equations and the navier-stokes equations. in this talk, i will first review the singularity formation problem, and i will describe how particle transport poses the main challenge in constructing blow-up solutions — an effect known as “regularization by transport.” i will then outline a new mechanism, arising from the classical taylor-couette instability, allowing us to overcome regularization by transport in the 3d euler equations, thereby constructing the first swirl-driven singularity in r^3. this is joint work with tarek elgindi (duke university).