Recent network neuroscience has established that creative cognitive performance depends on dynamic switching between the Default Mode Network (DMN) and the Executive Control Network (ECN), with an inverted-U relationship indicating that optimal creativity requires balanced network dynamics rather than dominance of either network alone. At the same time, neuroimmunology has shown that pro-inflammatory cytokines such as interleukin-6 (IL-6) and tumor necrosis factor-alpha (TNF-α), as well as anti-inflammatory cytokines such as interleukin-10 (IL-10), directly modulate large-scale brain network connectivity and synaptic plasticity in a dose-dependent manner. However, the upstream molecular mechanisms that regulate DMN–ECN switching frequency and quality remain unknown. This paper proposes the Cytokine Equilibrium Hypothesis of Creativity: the ratio of pro-inflammatory to anti-inflammatory cytokines — specifically, the dynamic equilibrium between IL-6, TNF-α and IL-10 — constitutes a primary molecular mechanism regulating Salience Network sensitivity, which in turn determines the frequency and quality of DMN–ECN switching. This switching frequency follows an inverted-U relationship with creative cognitive performance, such that cytokine equilibrium — not cytokine absence — represents a key biological substrate of peak human creativity and elevated cognition. Chronic deviation from equilibrium in either direction is predicted to produce dissociated cognitive profiles characterized by domain-specific enhancement alongside domain-specific deficit. The hypothesis is supported by converging evidence that: (i) IL-6 modulates DMN connectivity in a dose-dependent fashion; (ii) TNF-α is associated with Salience Network connectivity; (iii) IL-10 provides negative feedback regulation and neuroprotection; (iv) both insufficient and excessive inflammatory signaling impair cognition, whereas balanced signaling supports optimal network dynamics. The framework yields concrete, falsifiable predictions and offers a mechanistic explanation for paradoxical clinical and historical observations, including the cognitive profile of Srinivasa Ramanujan.