Writing, of course!
While one could cite things like medicine, governance, or logic, my vote for the most influential ancient invention impacting modern life is writing. Writing bolstered cultural transmission and what I call Transcendental Intelligence (TI), allowing for the creation of major civilizations and accelerating progress toward the future. This higher level of cultural transmission enabled societies to preserve knowledge, share ideas across generations, and build complex institutions.
Learn more about Transcendental Intelligence (TI) in my Mindscape Framework: Mindscape Framework.
Before writing systems, language allowed for a rich oral tradition facilitating TI across generations for millennia, likely at least back about 700,000 years. However, while much was accomplished during the epics before writing systems, it was writing systems that brought a semi-permanent nature to external knowledge, allowing for greater longevity. Writing systems like cuneiform in Mesopotamia and hieroglyphics in Egypt laid the groundwork for recorded history, law, literature, and science. By documenting knowledge, writing allowed humans to transcend the limitations of oral communication, fostering a collective intelligence that propelled human advancement. This leap in cognitive capability and cultural sophistication was pivotal in shaping the world we live in today.
For more, take the deep dive, explore the timeline: Ancient History Timeline.