As told before, the Greeks didn't separate natural science from other knowledge.  To them, the pursuit of all knowledge was Philosophy The logical inquiring minds of the  Greeks added a great deal to man's knowledge about the earth and the universe. They explained many principles which once understood gave man the possibility of understanding much more. 

     A. Mathematics:

  - Euclid: the "Father of Geometry" collected and published everything known in this field of study.

  -Archimedes: he produced formulas for working with all shapes, which  included the circle

  - Hipparchus: "Father of Trigonometry" - he invented this branch of math to help with his work in astronomy

   B. Chemistry:

  - they made little or no progress in this field (how can you understand things if you can’t see them (atoms)? You need a microscope.

  C. Physics: (how things work such as electricity)

  - The "Father  of Physics" was undoubtedly Archimedes, a brilliant native of Syracuse.

  - He is most famous for formulating "Archimedes Principle", the law of floating bodies (displacement) which
     led to the idea of specific gravity.

  - he also did much useful work with levers, pulleys, cogged wheels, catapults and cranes.

  - Democratus stated the world’s first atomic theory. He believed that all matter is composed of material that
     is so small that they cannot be divided.

  D. Astronomy:

  - a number of Greek scientists knew the earth was spherical

  - Distarchus of Samos:  he knew that the earth and other planets revolved around the sun. Other scientists
    didn't like to state this belief because it was so dangerous and unpopular at the time.

  - Hipparchus: he calculated the solar year to be 365 1/4 days minus a few minutes. He was six minutes off
    the exact calculation.
  - His calculation of the lunar month was less than one second off.  His estimation of the earth's distance from
    the moon was only off by 5%.

  - Eratopthenes: he calculated the circumference of the earth and also caused most of the known world to be
    mapped.

  - Hipparchus:  Designed a method of finding position on the earth by lines of latitude and longitude.

  E. Medicine:                                                  

  - In general, Greek doctors were not as advanced as those from other areas such as Egypt

  - In early times, medicine was associated with religion and superstition

  - Hippocrates: is known as the "Father of Medicine", he understood that disease had natural causes (not
    supernatural) and should be cured by natural means

  - he recommended good eating habits, and exercise as a means of preventing disease

  - he recommended that doctors should follow a logical and scientific sequence with their patients - examination,
    diagnosis, treatment, prognosis and follow-up.

  - he is best known however for the "Hippocratic Oath" which set standards for doctors, so much that today’s
    doctors still are required to take the oath