The differential geometry of spheres has long been a source of central problems in mathematics, and Sasaki–Einstein metrics—odd-dimensional analogues of Kähler–Einstein metrics—offer a particularly rich perspective, with significance both in geometry and in theoretical physics. In joint work with Yuchen Liu and Taro Sano, we construct infinitely many Sasaki–Einstein metrics on odd-dimensional spheres that bound parallelizable manifolds, thereby confirming conjectures of Boyer–Galicki–Kollár and Collins–Székelyhidi. Our approach is based on establishing the K-stability of certain Fano weighted hypersurfaces.