Uncontrolled proliferation in cancer is primarily driven by genetic mutations and alterations in the cell cycle. These mutations can occur in various genes, including oncogenes and tumor suppressor genes. Oncogenes promote cell division and survival, while tumor suppressor genes regulate and inhibit cell growth. When mutations activate oncogenes or deactivate tumor suppressor genes, the balance between cell division and cell death is disrupted, leading to uncontrolled proliferation.