Thales of Milieus is known as the father of science. He was a philosopher who tried to find the meaning of the world through scientific and natural reasoning rather than through supernatural causes. He was also a Greek, causing many scientific achievements to be credited to Ancient Greeks. The Ancient Greeks also made many other scientific advances. For example, a Greek student of Aristotle named Theophrastus studied and classified plants, and is known as the father of botany. This was important because all food eaten from humans comes from plants in some way or another. The Greeks also invented earth science, the science of studying the earth. Furthermore, the Greeks also made many advances in public water works, such as the invention of Archimedes' screw, which lift water from a lower elevation to a higher one. Another field of science the Ancient Greeks excelled at was biology. One of our most famous guides in this field is the quote "survival of the fittest" (which came from the Greek Aristotle) showing that nature had no mercy, and only strong animals/plants would survive. One last field of science the Greeks studied was zoology. The Greeks made many advanced classifications of the animals they studied.
Ancient Greece made many contributions to our modern ideas about mathematics. Their main influence on mathematics was from Egypt, a neighbouring kingdom. In fact, a famous Greek named Pythagoras (known for his breakthrough on finding the hypotenuse of right-angled triangles) traveled to Egypt and worked with engineers building the pyramids. Followers of Pythagoras, called the Pythagoreans, learned about square numbers and square roots. When trying to solve the square root of two, they discovered the concept of irrational numbers. The consternation created by this discovery lead to an attempt by the pythagorean brotherhood to keep this discovery secret. Greek mathematics introduced rigour and precision which resulted in a deeper and more precise understanding of concepts such as pi and geometry. Another famous Greek mathematician was Euclid, who organized greek mathematics into a single cohesive set of books, the elements. The elements are the second best selling books of all time with only the bible being more widely distributed. Overall, mathematics was one of the Greek's most intellectually developed achievements.
Originally, the Greek thought that illness was a punishment and reward of the gods. As time went on, however, they discovered this was not the case. They understood how lifestyle factors (such as food diets and the environment of a person) could make people more or less susceptible to certain illness and diseases. They also practiced basic surgical operations such as installing and removing stitches. The Greeks understood the science of a human body from examining wounded soldiers. For instance, in Homer's stories treatment such as washing wounds with warm water were described. Ancient Greek doctors did not only treat patients, but also gave detailed medical advice. The Greeks made many discoveries in the human anatomy as well (however, human dissection was not explored until after Alexander the Great's conquest of Greece).
Ancient Greek astronomy was incredibly advanced for its time. The Greeks discovered that the earth was a sphere, an idea not revisited until the 18th century AD. Aristotle, a great Greek astronomer, discovered that the planets of our solar system are all round and move in a rotational pattern. Hipparchus of Nicea, another greatly respected and skilled Ancient Greek astronomer, was able to calculate the lunar month with an error that was less than a second off, and calculated the entire solar year with an error of no more than six minutes. The Ancient Greeks also invented many advanced astronomical tools that are the base for our astronomical tools today.
Bloodletting was a common practice in Ancient Greece. Doctors thought that when a patient was sick, it could be because they had too much blood, or dirty, unclean blood. They would cut open the patient's skin to let the unhealthy blood out, as you can see in this picture.
This is a photo of a journal belonging to a Greek botanist. As you can see, the Greeks paid very close and careful attention to plants and excelled in this field of science.
This photo shows the unique Greek number system. Other ancient civilizations partially based their number system off of this one, such as Rome.
The Greeks invented many helpful astronomical tools, such as the telescope shown above.