“The safest general characterization of
the whole Western philosophical tradition is that it consists of a
series of footnotes to Plato.”
-Alfred North Whitehead
The ancient Greeks didn't make a distinction between philosophy and science, nor did they recognize the range of disciplines such as physics, chemistry, mathematics, astronomy, etc. that we do today. There simply wasn't the depth of knowledge and range of information that later made separate disciplines practical. In the Greek era, one individual could be an expert in several fields. Nowadays, with the tendency of specialists to know more and more about less and less (i.e. intensive knowledge about a rather limited field) the ability to keep abreast of detailed research in more than one area becomes almost impossible. But in the days of Thales, Pythagoras and Aristotle that was the norm. People expected an individual knowledgeable in one area to also be proficient in others. And many were.
The Greeks had great success in the areas of mathematics, particularly geometry, borrowing heavily from the Egyptians (who were concerned primarily with practical applications) while raising the theoretical and intellectual bar to new heights. Euclid's classic book on the Elements of Geometry was the world's main textbook for almost two millennia.
They also made their mark in astronomy. An understanding of astronomy was important in understanding and regulating the business of agriculture. It was also essential in developing an accurate calendar and critical for navigation. While the Egyptians and Babylonians had made great advances in astronomy, their work was based heavily on centuries of observation. It was the Greeks who introduced mathematics into astronomy greatly expanding the range of questions that could be asked and answered about the solar system. In the 3rd Century BC, the Greek astronomer Aristarchus advanced the theory that the sun, not the earth, was the center of the solar system. It took the world the better part of two millennia to come to the same conclusion. Eratosthenes, another Greek, accurately calculated the earth's circumference and its diameter.
Physics, the study of the nature of things, began seriously in Greece in the 6th Century BC. With few exceptions (e.g. the work of Aristotle and Pythagoras) the study was an intellectual pursuit unaided by much in the way of controlled experimentation, which is standard practice today.
It was Aristotle, equally at ease as a philosopher and as a scientist, whose several treatises on animals laid the foundations of zoology. Aristotle also did important work on plants, although not nearly to the same extent as his thorough publications on animal life, but he did have a strong influence on other scholars, such as Theophrastus, who laid the groundwork for the science of botany.
Socrates, although we have no evidence he ever wrote anything, was the first of the great thinkers of Athens. We can get some understanding of his ideas from the writings of Plato and Xenophon. Socrates challenged the morals and quest for power of his fellow citizens and paid the ultimate price of his life. He is remembered as the father of the study of ethics.
There were several factors that influenced the development of medicine in ancient Greece. First, there was the potent force of religion with its gods and goddesses who dealt with healing, death and pestilence. Then there was the influence of trading contacts such as Egypt (which had learned much from its mummification practices) and Mesopotamia (which had published comprehensive medical documents on clay tablets well before 1000 BC). From these and other Eastern areas, the Greeks also developed an encyclopedic range of herbal medicines.
To cap it off, there was the sad result of war - a variety of wounds and amputations caused by arrows, swords, spears and accidents- and described so vividly and accurately in Homer's Iliad. Just dealing with these casualties provided lots of experience and practical information applicable elsewhere. Although Greek religion frowned on human dissection in the Archaic and Classical periods, after the founding of the Alexandrian School that changed. Physicians and researchers made advances in some areas that were not surpassed until the 18th Century.
The transition from believing that illnesses originated with the gods and the realm of evil spirits (a belief perhaps universally shared with all early civilizations) to the realization that there were natural causes involved did not happen easily or suddenly. For many generations two belief systems, one rooted in religion and one based on an emerging science, co-existed. Hippocrates, the Greek Father of Medicine, wrote “prayer indeed is good, but while calling on the gods a man should himself lend a hand.” To that end there were healing centers established where the faithful might pray while receiving the benefits of medical treatment. Hippocrates and his followers took a giant step forward in the science of medicine when they asked themselves the question “How did this illness come to be?” instead of “What god or force of evil caused this illness?”
Just as war drove significant improvements in medical practices so, too, did it have an impact on the field of engineering. Scholars such as Archimedes became military engineers, inventing and improving defensive and offensive weapons. There were, in addition, other innovations such as the gear, the screw, the steam engine, the screw press and so on but the prevailing Greek attitude towards manual labor and labor-saving devices did not greatly encourage nor reward innovation (except in the military sphere) so many inventions remained curiosities rather than instruments of change.