The paper explores the intrinsic correlation between hardness and elasticity in polycrystalline materials and bulk metallic glasses (BMGs). Despite extensive research, hardness remains challenging to formally describe due to its mechanical complexity. The widely used Teter's empirical correlation between hardness and shear modulus is not always valid for various materials. Inspired by Pugh's modulus ratio, the authors develop a theoretical model that robustly correlates hardness with elasticity for a wide range of materials, including BMGs. The model provides strong theoretical evidence for Teter's empirical correlation and also demonstrates that hardness can be correlated with the product of the squared Pugh's modulus ratio and the shear modulus. The model accurately predicts Vickers hardness for both crystalline materials and BMGs, showing that the hardness of intrinsically brittle materials (like BMGs) linearly correlates with the shear modulus. The findings suggest that hardness is fundamentally based on the same principles as elasticity in both crystalline and BMGs, providing valuable insights for designing and developing ultra-hard and superhard materials.The paper explores the intrinsic correlation between hardness and elasticity in polycrystalline materials and bulk metallic glasses (BMGs). Despite extensive research, hardness remains challenging to formally describe due to its mechanical complexity. The widely used Teter's empirical correlation between hardness and shear modulus is not always valid for various materials. Inspired by Pugh's modulus ratio, the authors develop a theoretical model that robustly correlates hardness with elasticity for a wide range of materials, including BMGs. The model provides strong theoretical evidence for Teter's empirical correlation and also demonstrates that hardness can be correlated with the product of the squared Pugh's modulus ratio and the shear modulus. The model accurately predicts Vickers hardness for both crystalline materials and BMGs, showing that the hardness of intrinsically brittle materials (like BMGs) linearly correlates with the shear modulus. The findings suggest that hardness is fundamentally based on the same principles as elasticity in both crystalline and BMGs, providing valuable insights for designing and developing ultra-hard and superhard materials.