It became apparent that civililization was advancing as mathematics was as well. Babylonians began with addition and subtraction to algebra. Greeks came in with advancements in geomtry and astronomy. The discovered irrational numbers but didn't like as they weren't helpful in their areas. The concept of "negative numbers" was something considered controversial at the time. Islamic civilization improved on irrational numbers as they were good with decimal numbers, also trigonementry and advancing on Greek geometry discoveries. This later part was part of the "Golden Age of Islam"
Experimental medicine
Avicenna (Ibn Sina) is considered the father of modern medicine, for his introduction of experimental medicine and clinical trials, the experimental use and testing of drugs, and a precise guide for practical experimentation in the process of discovering and proving the effectiveness of medical substances, in his medical encyclopedia, The Canon of Medicine (11th century), which was the first book dealing with experimental medicine. It laid out the following rules and principles for testing the effectiveness of new drugs or medications, which still form the basis of modern clinical trials:
"The drug must be free from any extraneous accidental quality."
"It must be used on a simple, not a composite, disease."
"The drug must be tested with two contrary types of diseases, because sometimes a drug cures one disease by Its essential qualities and another by its accidental ones."
"The quality of the drug must correspond to the strength of the disease. For example, there are some drugs whose heat is less than the coldness of certain diseases, so that they would have no effect on them."
"The time of action must be observed, so that essence and accident are not confused."
"The effect of the drug must be seen to occur constantly or in many cases, for if this did not happen, it was an accidental effect."
"The experimentation must be done with the human body, for testing a drug on a lion or a horse might not prove anything about its effect on man."
Peer review
The first documented description of a peer review process is found in the Ethics of the Physician written by Ishaq bin Ali al-Rahwi (854–931) of al-Raha, Syria, who describes the first medical peer review process. His work, as well as later Arabic medical manuals, state that a visiting physician must always make duplicate notes of a patient's condition on every visit. When the patient was cured or had died, the notes of the physician were examined by a local medical council of other physicians, who would review the practising physician's notes to decide whether his/her performance have met the required standards of medical care. If their reviews were negative, the practicing physician could face a lawsuit from a maltreated patient.
This is just on the Philosophy front. Greeks get a well deserved focus but what was left out was the civilization advancing right there with them.
On the subject of Socrates I highly recommend his statements to the jury where he was executed for "corrupting young minds if you can believe it".
http://rocket.csusb.edu/~tmoody/Death%20of%20Socrates.html
This is a from Plato who wrote the book on Socrates -- the truth they spoke as incredible "the difficulty is not so much to escape death; the real difficulty is to escape from doing wrong,
On edit -- this is probably better for an overview but it is the mathematics, science, & philosophy stuff I had in mind when I made my statements -- http://en.wikipedia.org/wiki/Islamic_Golden_Age
In addition to clinical trials there is this
Healthcare
Hospitals in this era were the first to require medical diplomas to license doctors. In the medieval Islamic world, hospitals were built in most major cities.
Medical facilities traditionally closed each night, but by the 10th century laws were passed to keep hospitals open 24 hours a day, and hospitals were forbidden to turn away patients who were unable to pay. Eventually, charitable foundations called waqfs were formed to support hospitals, as well as schools. This money supported free medical care for all citizens. In a notable example, a 13th-century governor of Egypt Al Mansur Qalawun ordained a foundation for the Qalawun hospital that would contain a mosque and a chapel, separate wards for different diseases, a library for doctors and a pharmacy. The Qalawun hospital was based in a former Fatimid palace which had accommodation for 8,000 people - "it served 4,000 patients daily." The waqf stated,
"...The hospital shall keep all patients, men and women, until they are completely recovered. All costs are to be borne by the hospital whether the people come from afar or near, whether they are residents or foreigners, strong or weak, low or high, rich or poor, employed or unemployed, blind or sighted, physically or mentally ill, learned or illiterate. There are no conditions of consideration and payment, none is objected to or even indirectly hinted at for non-payment."
The first institutions for the care of mentally ill people were also established.q
The History of Mathematics in a way that wasn't deliberate, the parallels were clear. Famous philosophers such as Socrates were mathematician. Leonardo Da Vinci -- mathematician which his Treatise On Painting is filled entirely with math. Philosphy was the most fascinating. The concepts used in math were behind on a lot of philosophy Socrates "The key to understanding mathematics is necessary for a sound grasp of ethics"
Philosophy of education
In the medieval Islamic world, an elementary school was known as a maktab, which dates back to at least the 10th century. Like madrasahs (which referred to higher education), a maktab was often attached to a mosque. In the 11th century, Ibn Sina (known as Avicenna in the West), in one of his books, wrote a chapter dealing with the maktab entitled "The Role of the Teacher in the Training and Upbringing of Children", as a guide to teachers working at maktab schools. He wrote that children can learn better if taught in classes instead of individual tuition from private tutors, and he gave a number of reasons for why this is the case, citing the value of competition and emulation among pupils as well as the usefulness of group discussions and debates. Ibn Sina described the curriculum of a maktab school in some detail, describing the curricula for two stages of education in a maktab school.[57]
Primary education
Ibn Sina wrote that children should be sent to a maktab school from the age of 6 and be taught primary education until they reach the age of 14. During which time, he wrote that they should be taught the Qur'an, Islamic metaphysics, language, literature, Islamic ethics, and manual skills (which could refer to a variety of practical skills).[57]
Secondary education
Ibn Sina refers to the secondary education stage of maktab schooling as the period of specialization, when pupils should begin to acquire manual skills, regardless of their social status. He writes that children after the age of 14 should be given a choice to choose and specialize in subjects they have an interest in, whether it was reading, manual skills, literature, preaching, medicine, geometry, trade and commerce, craftsmanship, or any other subject or profession they would be interested in pursuing for a future career. He wrote that this was a transitional stage and that there needs to be flexibility regarding the age in which pupils graduate, as the student's emotional development and chosen subjects need to be taken into account.[58]
Philosophy of science
See also: Islamic science
Scientific method
The pioneering development of the scientific method by the Arab Ash'ari polymath Ibn al-Haytham (Alhacen) was an important contribution to the philosophy of science. In the Book of Optics (c. 1025 AD), his scientific method was very similar to the modern scientific method and consisted of the following procedures:[35]
Observation
Statement of problem
Formulation of hypothesis
Testing of hypothesis using experimentation
Analysis of experimental results
Interpretation of data and formulation of conclusion
Publication of findings
In The Model of the Motions, Ibn al-Haytham also describes an early version of Occam's razor, where he employs only minimal hypotheses regarding the properties that characterize astronomical motions, as he attempts to eliminate from his planetary model the cosmological hypotheses that cannot be observed from Earth.[59]
In Aporias against Ptolemy, Ibn al-Haytham commented on the difficulty of attaining scientific knowledge:
"Truth is sought for itself [but] the truths, [he warns] are immersed in uncertainties [and the scientific authorities (such as Ptolemy, whom he greatly respected) are] not immune from error..."[36]
He held that the criticism of existing theories — which dominated this book — holds a special place in the growth of scientific knowledge:
"Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency."[36]
http://en.wikipedia.org/wiki/Islamic_philosophy#Aristotelian_logic
I have strong appreciation for Greek & Islamic pioneers. Don't know much about the Roman Empire & not familiar with the Egyptians in all this -- the History of Mathematics touched on a wide variety of notable figures and movements. He began with the number counting system from Babylonians.
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