Explore interval methods for scientific computing in Julia through this JuliaCon 2019 conference talk by David P. Sanders. Discover how interval constraint propagation provides guaranteed descriptions of feasible sets for nonlinear inequalities using contractors. Learn about the IntervalConstraintProgramming.jl package and its applications in root finding and global optimization. Delve into the mathematical foundations, including IntervalArithmetic.jl and the Forward-Backward contractor. Gain insights into implementation details, higher-dimensional intervals, and unbounded optimization. The talk covers an introduction to the speaker, an outline of the presentation, practical applications, mathematical explanations, and concludes with a summary and Q&A session.