The most important lasting impact of Alexander the Great's conquests is often considered to be the spread of Hellenistic culture across the regions he conquered. This cultural diffusion resulted in the blending of Greek culture with those of Persia, Egypt, and the Indian subcontinent, leading to significant developments in art, architecture, science, philosophy, and governance.
The establishment of cities, most notably Alexandria in Egypt, became centers of learning and culture, promoting the exchange of ideas and knowledge. The Hellenistic period that followed Alexander's death saw advancements in various fields, including mathematics, astronomy, and medicine, influenced by both Greek and local traditions.
Moreover, Alexander's conquests facilitated trade and communication across a vast area, contributing to a more interconnected world. The legacy of his empire also paved the way for the later rise of the Roman Empire and the spread of Greek culture throughout Europe and the Mediterranean.
In summary, the most important lasting impact of Alexander's conquests was the establishment of a Hellenistic world, characterized by the fusion of cultures and the dissemination of ideas, which shaped the subsequent course of history in the regions he touched.