The Ancient Greeks were the first people to systematically examine the world to attempt to discover why it worked the way it appeared to. Their ideas were so influential that, for two millennia, Western science was influenced almost entirely by Greek ideas. The later Romans, Arabs, and medieval Europeans did little more than enlarge on Greek ideas. (source)

The Greek philosopher Thales (624–546 B.C.) is generally considered to be the first philosopher. He was the first man in recorded history to ask questions such as "Of what is the Universe made?", and to answer without introducing gods and demons. In later centuries, when the Greeks constructed lists of "seven wise men", Thales was always placed first. (source)

The Lydians, who were allies of the Greek Spartans, and the Medes, who were dominated by Cyrus of Persia, had been locked in a five-year war in Asia Minor on May 28^th, 586 B.C., when the two armies were again preparing for another battle. At this point a solar eclipse happened, one that is believed to have been pre­dicted by Thales, a Greek mathematician. When the Medes and Lydians observed the eclipse, they stopped fighting and signed a peace treaty. Incidentally, this is the earliest event in human history to which an exact date can be assigned, due to the eclipse. (source)

The first person we know who realized the Earth couldn't be flat was the Greek philosopher Anaximander. Around 560 B.C., he suggested that the shape of the Earth was a cylinder. By 350 B.C., the concept of a spherical Earth was so satisfying and free of paradox that it was generally accepted by scholars even in the absence of direct proof. Eighteen more centuries would pass before there was a direct proof, in the form of Ferdinand Magellan's expedition to circumnavigate the globe. (source)

The true size of the Earth was known seventeen and a half centuries before it was first circumnavigated. In 230 B.C., the Greek philosopher Eratosthenes worked out its circumference of 25,000 miles by studying shadows cast by the sun in both Alexandria and Syene on the day of the summer solstice. (source)

In the sixth century B.C., a half-mile tunnel was dug on the Aegean island of Samos under the supervision of the Greek architect Eupalinus. Though the tunnel was started at both ends and worked toward the middle, the two halves met only a couple of feet off centre—a stunning achievement for those days. (source)

When Greek mathematicians first proved the the square root of two is an irrational number, they celebrated by sacrificing 100 oxen. (source)

In 435 B.C., the Greek philosopher Anaxagoras suggested that the sun was not just a small glowing circle of light. He maintained that it was a glowing rock larger than the Peloponnesus. For maintaining such beliefs (and, to be fair, for political reasons too), he was exiled from Athens. (source)

Euclid is the most successful textbook writer of all time. His Elements, written around 300 B.C., has gone through more than 1,000 editions since the invention of printing. (source)

The longest-lasting contribution of the Phoenicians, a group of seafaring Canaanites who lived on the eastern Mediterranean seacoast, was an alphabet that, with some modifications, was later adapted by the Greeks.

Socrates.

Socrates was said to have always worn an old, worn-out coat, gone shoeless, and to have been ugly. (source)

The nature of sound was one area of physics in which the ancient Greeks made significant progress in understanding. Around 400 B.C., Archytas of Tarentum stated that sound was produced by bodies striking together, with swift motion producing high pitch and slow motion low pitch. Later, Aristotle included air as a body that produces sound when struck, stating that sound was propagated by one part of the air striking the next until it reached the ear, and also correctly noted that, without a medium such as air or water, man could not hear sound. (source)

The Greek physician Hippocrates (ca. 460–ca. 377 B.C.) taught that south winds cause deafness, dimness of vision, heaviness of the head, and torpor. (source)

Socrates, one of the greatest Ancient Greek philosophers, was forced to commit suicide by drinking hemlock after being found guilty of "corrupting the youth of Athens." (source)

The ancient Greeks ground lenses from crystals of quartz; they were used to kindle fires. (source)

A northeastern spotted dolphin.

Aristotle noticed that dolphins give birth to live young who were attached to their mothers by umbilical cords, so he classified dolphins as mammals in Generation of Animals. Not until the nineteenth century did modern science confirm his statement. (source)

Aristotle believed that a body falls at a speed in proportion to its weight (in other words, a ten-pound weight would fall ten times faster than a one-pound weight), and that the speed of a falling body is inversely proportional to the resistance of what it falls through (so that a body falling in a vacuum would fall at an infinite rate). These beliefs were not challenged until Galileo did so in the 17th century, even though it would have been trivial for anyone to drop two objects of different weights and notice that they fell at the same speed. (source)

Aristarchus of Samos.

The first Greek astronomer to suggest the sun was the centre of the solar system was Aristarchus of Samos, around 290 B.C. No one took him seriously, and most of his writings were lost. We know of him today primarily because Archimedes (whose writings do exist) referred to Aristarchus as holding this apparently nonsensical notion. (source)

The Greek scientist Aristarchus believed that the motions of the heavenly bodies could easily be understood if it were assumed that all of the planets, including Earth, revolved around the sun and that the stars must be infinitely far away because they seemed motionless. Copernicus knew of Aristarchus' views and mentioned them in a passage in De Revolutionibus Orbium Coelestium that he later eliminated, as though not wishing to compromise his own originality.

The first Greek to observe ocean tides, in the Atlantic in the early third century B.C., was the navigator and astronomer Pytheas, who also produced the correct explanation for them. He was 2,000 years ahead of his time; Sir Isaac Newton was the first person to correctly attribute them to the influence of the moon. Before Newton's time, most scholars refused to believe that the moon could have any effect on the ocean, especially because one tide each day took place when the moon was not even visible in the sky. (source)

The best-known story about Archimedes is that when he discovered the principle of buoyancy in the bathtub, he ran naked through the streets of Syracuse, shouting "Eureka! Eureka!" ("I have found it! I have found it!"). That was not a very astonishing thing for him to have done. The Greeks habitually exercised in the nude, and the sight of a naked male figure meant little to them. (source)

The Greek engineer Hero invented a primitive steam engine in the first century A.D. The principle behind it is still used today in the rotating lawn sprinkler. (source)

Electrical shocks given by torpedo fish were used for medicinal purposes by the ancient Greeks and Romans. From the fifth century B.C. the Greeks applied torpedo fish on the thorax of sick people in order to stimulate their vital reflexes, and the Roman doctor Scribonius Largus mentioned the efficacy of the fish's shocks in treating chronic diseases. (source)

Hypatia (ca. 355 or ca. 370–415 A.D.) was a soaring figure of beauty, eloquence, and learning, and the last recorded member of the great Library of Alexandria and the only noted woman scholar of antiquity. She taught Neoplatonism (hence, she was a pagan) and helped to demonstrate Euclid's ideas. Although Christian bishops were among her pupils, she was the subject of violent antagonism on the part of zealots. She was murdered in 415 by rioting fanatic monks, under the leadership of bishop Cyril, who brutally sliced her body to pieces with oyster shells gathered from the Alexandrian harbour. (source)

Twenty-three centuries passed between the Greek philosopher Xenophanes' surmise that mountains on which seashells were found must originally have been covered by the sea and the Scottish geologist James Hutton's scientific deduction that made sober sense of what had seemed lunacy. (source)

The first person to propose that everything is made of atoms was the Greek philosopher Democritus, around 440 B.C. He reasoned that, if he were to attempt to cut an object in half over and over again, he would eventually reach a tiny grain of matter that could not be cut in half. Democritus called these hypothetical building blocks of matter "atoms", after the Greek atomos, "uncuttable". (source)

The ancient Greeks constructed pyramids of porous rocks in desert climates, which were used as water catchers. They could capture and condense surprisingly large quantities of water. A group of 13 pyramids at Theodosia in the Crimea that were built around 500 B.C. averaged almost 40 feet high and were placed on hills around the city. As the wind moved through the stones, the changing temperatures throughout the day caused moisture to condense, run down, and feed a network of pipes. (source)

Claudius Ptolemy, a second-century astronomer working in Alexandria, Egypt, wrote thirteen volumes on his observations that were so influential that they came to be known as the Almagest, Arabic for "the greatest". Ptolemy's theories, which held that the Earth stood still in the heavens while the moon, sun, and planets moved around it and that the stars sat in a concave dome that arched over the universe, were completely wrong; however, the influence of these theories held back the science of astronomy for nearly 1,500 years. (source)

Aristotle believed that swallows passed the winter buried in heaps at the bottom of rivers.

Archytas of Tarentum, is reported, around 400 B.C., to have made a mechanical pigeon that could fly. (source)