In solids, the high density of charged particles makes many-body interactions a pervasive principle governing optics and electronics(1-12). However, Walter Kohn found in 1961 that the cyclotron resonance of Landau-quantized electrons is independent of the seemingly inescapable Coulomb interaction between electrons(2). Although this surprising theorem has been exploited in sophisticated quantum phenomena(13-15), such as ultrastrong light-matter coupling(16), superradiance(17) and coherent control(18), the complete absence of nonlinearities excludes many intriguing possibilities, such as quantum-logic protocols(19). Here, we use intense terahertz pulses to drive the cyclotron response of a two-dimensional electron gas beyond the protective limits of Kohn's theorem. Anharmonic Landau ladder climbing and distinct terahertz four-and six-wave mixing signatures occur, which our theory links to dynamic Coulomb effects between electrons and the positively charged ion background. This new context for Kohn's theorem unveils previously inaccessible internal degrees of freedom of Landau electrons, opening up new realms of ultrafast quantum control for electrons.