The Abel-Ruffini theorem states that there is no general solution in radicals for polynomial equations of degree five or higher. This means that while quadratic, cubic, and quartic equations can be solved using a formula involving their coefficients, no such formula exists for quintic equations or higher. The theorem is named after mathematicians Niels Henrik Abel and Giovanni Ruffini, who contributed to its proof in the early 19th century. Their work laid the foundation for modern algebra and highlighted the limitations of solving polynomial equations, leading to further developments in Galois theory.