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Explore rigorous numerical computation through interval arithmetic in this conference talk from JuliaCon Local Paris 2025, where Benoît Richard presents the 1.0 version of IntervalArithmetic.jl. Learn how interval arithmetic addresses the limitations of floating point numbers by providing strict guarantees and accuracy when working with continuous subsets of the real line. Discover how intervals enable rigorous numerical proofs of mathematical facts, including establishing the existence or absence of solutions to equations. Understand the implementation strategies developed for the package's 1.0 version that allow safe and seamless use of interval computations in Julia code, even when the code is unaware of interval arithmetic operations. See practical applications of this approach to root-finding problems and gain insights into how IntervalArithmetic.jl brings rigorous numerical methods to the Julia ecosystem without sacrificing the language's flexibility.
