Aristotle was not primarily a mathematician but made important contributions by systematising deductive logic. He wrote on physical subjects: some parts of his Analytica posteriora show an unusual grasp of the mathematical method. Primarily, however, he is important in the development of all knowledge for, as the authors of write:-
Aristotle, more than any other thinker, determined the orientation and the content of Western intellectual history. He was the author of a philosophical and scientific system that through the centuries became the support and vehicle for both medieval Christian and Islamic scholastic thought: until the end of the 17th century, Western culture was Aristotelian. And, even after the intellectual revolutions of centuries to follow, Aristotelian concepts and ideas remained embedded in Western thinking.
Aristotle was born in Stagirus, or Stagira, or Stageirus, on the Chalcidic peninsula of northern Greece. His father was Nicomachus, a medical doctor, while his mother was named Phaestis. Nicomachus was certainly living in Chalcidice when Aristotle was born and he had probably been born in that region. Aristotle's mother, Phaestis, came from Chalcis in Euboea and her family owned property there.
There is little doubt that Nicomachus would have intended Aristotle to become a doctor, for the tradition was that medical skills were kept secret and handed down from father to son. It was not a society where people visited a doctor but rather it was the doctors who travelled round the country tending to the sick. Although we know nothing of Aristotle's early years it is highly likely that he would have accompanied his father in his travels. We do know that Nicomachus found the conditions in Chalcidice less satisfactory than in the neighbouring state of Macedonia and he began to work there with so much success that he was soon appointed as the personal physician to Amyntas III, king of Macedonia.
There is no record to indicate whether Aristotle lived with his father in Pella, the capital of Macedonia, while Nicomachus attended to king Amyntas at the court there. However, Aristotle was certainly friendly with Philip, king Amyntas's son, some years later and it seems reasonable to assume that the two, who were almost exactly the same age, had become friendly in Pella as young children.
When Aristotle was about ten years old his father died. This certainly meant that Aristotle could not now follow in his father's profession of doctor and, since his mother seems also to have died young, Aristotle was brought up by a guardian, Proxenus of Atarneus, who was his uncle (or possibly a family friend as is suggested by some authors). Proxenus taught Aristotle Greek, rhetoric, and poetry which complemented the biological teachings that Nicomachus had given Aristotle as part of training his son in medicine. Since in latter life Aristotle wrote fine Greek prose, this too must have been part of his early education.
In 367 BC Aristotle, at the age of seventeen, became a student at Plato's Academy in Athens. At the time that Aristotle joined the Academy it had been operating for twenty years. Plato was not in Athens, but rather he was on his first visit to Syracuse. We should not think of Plato's Academy as a non-political organisation only interested in abstract ideas. The Academy was highly involved in the politics of the time, in fact Plato's visit to Sicily was for political reasons, and the politics of the Academy and of the whole region would play a major role in influencing the course of Aristotle's life.
When Aristotle arrived in Athens, the Academy was being run by Eudoxus of Cnidos in Plato's absence. Speusippus, Plato's nephew, was also teaching at the Academy as was Xenocrates of Chalcedon. After being a student, Aristotle soon became a teacher at the Academy and he was to remain there for twenty years. We know little regarding what Aristotle taught at the Academy. In  Diogenes Laertius, writing in the second century AD, says that Aristotle taught rhetoric and dialectic. Certainly Aristotle wrote on rhetoric at this time, issuing Gryllus which attacked the views on rhetoric of Isocrates, who ran another major educational establishment in Athens. All Aristotle's writings of this time strongly support Plato's views and those of the Academy.