Hellenistic philosophy largely shifted away from the concerns of Greek philosophers of the Classical Age. Because philosophers were discouraged from studying politics, as had Socrates, Plato, and Aristotle, they turned instead to investigations of personal ethics, of how to live one's life to be happy, even if a larger kind of social justice remained elusive. All of the major schools of Hellenistic philosophy shared the same pursuit, albeit in different ways: to live in pleasure and tranquility. Three are of particular note: the Epicureans, Stoics, and Cynics.
The Epicureans, named after their founder Epicurus, believed that humans ought to turn their backs on the pointless drama of politics and social competition and retire to a kind of inner contemplation. Epicurus taught that even if gods existed, they clearly had no interest in human affairs and thus did not need to be feared. Death was final and total, representing release and peace, not an afterlife of torment or work, so there was no need to worry about it, either. In short, the Epicureans believed in a virtuous renunciation of earthly cares and an indulgence in pleasure. Pleasure was not about overindulgence, however (which led to suffering - think of indigestion and hangovers), but a refined enjoyment of food, drink, music, and sex, although one interesting aspect of this philosophy was the idea that sexual pleasure was fine, but emotional love was to be avoided since it was too likely to result in suffering. To this day, the word “epicurean” as it is used in English means someone who enjoys the finer things in life, especially in terms of good cooking!
The Cynics believed that social conventions were unfortunate byproducts of history that distracted people from the true source of virtue and happiness: nature. In turn, the only route to happiness was a more aggressive rejection of social life than that espoused by the Epicureans (who, again, were quite sedate). They advocated a combination of asceticism and naturalism, indulging in one’s physical needs without regard to social convention. Practically speaking, this involved deliberately flouting social mores, sometimes in confrontational or even disgusting ways: Diogenes, founder of the Cynics, notoriously masturbated and defecated in public. Most Cynics were slightly more restrained, but most took great pleasure in mocking people in positions of political authority, and they also belittled the members of other philosophical schools for their overly rigid systems of thought. One story had it that Alexander sought out Diogenes and found him lying in the street in a suburb of the polis of Corinth, asking him what he, the king, might do for him, the philosopher. The Cynic replied “stop standing in my sunbeam.”
Originally an offshoot of the Cynics, the Stoics became philosophers of fate and rationality. Unlike the Epicureans, the Stoics believed that humans had an obligation to engage in politics, which formed part of a great divine plan, something linked to both fate and nature. As participants in the natural order, humans ought to learn to accept the trials and tribulations of life rationally, without succumbing to emotion (hence the contemporary meaning of the word “stoic”: someone who is indifferent in the face of pain or discomfort). The Stoics accepted the necessity of being part of a society and of fulfilling social obligations, but they warned against excesses of pride and greed. Instead, a Stoic was to do his duty in his social roles without the distraction of luxury or indulgence. They were one possible version of a philosophy that believes in the existence of fate, of accepting one's place in a larger scheme instead of resisting it, and they also celebrated the idea that the rational mind was always more powerful than emotional reactions.
What these three schools of philosophy had in common, despite their obvious differences, is that they all represented different approaches to accepting the (political) status quo. The Epicureans avoided politics, the Stoics supported existing political structures, and the Cynics mocked everything without offering positive suggestions for change. This was a far cry from the earnest inquiry of a Socrates, a Plato, or an Aristotle in trying to establish a virtuous form of politics. While Greek culture enjoyed a period of unprecedented influence during the Hellenistic period, its experiments in rational (let alone democratic) political analysis were not a major component of that influence.
While political theory did not enjoy a period of growth during the period, there were significant accomplishments in science and mathematics. The most important Hellenistic mathematicians were Euclid and Archimedes. Euclid was the inventor of the mathematical discipline of geometry. He was the first to use obvious starting points called axioms – for instance, the idea that two parallel lines will never intersect – to be able to deduce more complex principles called theorems. Euclid is one of those relatively few ancient thinkers who really “got it right” in the sense that none of his major claims were later proved to be inaccurate. His work on geometry, the Elements, was still used as the standard textbook in many courses on mathematics well into the twentieth century CE, thousands of years after it was composed. Archimedes was also a geometrician, best remembered for his applications of geometry to engineering. He discovered the principle of using the displacement of water to calculate the specific gravity of objects, and he devised a number of complex war machines used against Roman forces when his home city of Syracuse, in Sicily, was under attack (including, according to some accounts, a giant mirror used to focus the sun's rays on Roman ships and set them on fire).
Hellenistic thinkers also made important discoveries in astronomy, most notably the fact that certain astronomers determined that the sun was the center of the solar system. Hellenistic astronomers also refined the calculations associated with the size of the Earth; one astronomer named Eratosthenes calculated the circumference of the Earth that was only off by 200 miles. Another astronomer named Hipparchus created the first star charts that included precise positions for stars over the course of the year, and to help keep track of their positions he created the first system of longitudes and latitudes.
Perhaps the most memorable achievement in scholarship during the period was the institutional form it took at the Library of Alexandria and its associated Museon, often considered to be the first research university in the western world. Funded directly by the Ptolemaic government, the Library collected and translated every scrap of available scholarship from the Hellenistic world and played host to scholars who based their own work on its archives. It housed lecture halls as well, representing the preeminent site of learning in the Hellenistic world as a whole. It was eventually destroyed, although to this day there are competing versions of who was to blame for its destruction (ranging from the forces of Julius Caesar during his involvement in an Egyptian civil war to either Christian or Muslim fanatics centuries later).
Thus, there were certainly important intellectual breakthroughs that occurred during the Hellenistic period. There were not, however, corresponding achievements in technology or engineering. That is not surprising in that the pace of technological change in the ancient world was always glacially slow by modern standards. Instead, what mattered at the time was the spread of ideas and knowledge, much of which had no immediate and practical consequences in the form of applied technology - this was as true of ancient Rome as it was of the Hellenistic kingdoms.