This chapter argues that understanding economics requires grappling with complexity, contrasting traditional reductionist approaches with antireductionist perspectives. The argument focuses first on historical examples from physics that clarify a few implications of complexity for empirical research. Newton’s inability to prove the stability of the solar system was due to non-linear interactions not yet mastered by mathematics. Analogously, Boltzmann’s reductionist explanation of the second law of thermodynamics had to rely on arbitrary and implausible initial conditions that sidelined irreversible time. Poincaré’s qualitative geometry of differential equations marked a breakthrough in the analysis of non-linear systems without solving them explicitly, clarifying the characteristics typical of complex systems, like sensitivity to initial conditions, multiple equilibria, and bifurcations. This chapter appraises Poincaré’s qualitative geometry of differential equations that marked a breakthrough in the analysis of non-linear systems. Economic systems are inherently complex and organic, making standard reductionist microfoundations inadequate, as argued by Keynes. The legacy of Keynes in complexity economics, was carried on by unconventional followers such as Goodwin (non-linear cycles) and Minsky (financial instability). Finally, the chapter advocates a more constructive complementarity between mathematical and ordinary language to handle complexity’s different dimensions.