What is Galileo's contribution to science and mathematics?
Galileo was the first scientist to introduce experiments into mechanics. He determined some important mechanical laws through the combination of experiment and mathematics. 1582, after long-term experimental observation and mathematical calculation, he got the isochronous law of pendulum. Later, he dropped out of school on 1585 due to family financial difficulties. When he left the University of Pisa, he deeply studied the works of ancient Greek scholars Euclid and Archimedes. He wrote his first paper entitled "Balance" based on the principle of lever and buoyancy. Soon after, he wrote a paper on gravity, which revealed the essence of gravity and center of gravity for the first time and gave an accurate mathematical expression, so he became famous at one fell swoop. At the same time, he questioned many viewpoints of Aristotle. During the period of 1589 ~ 159 1, Galileo made a detailed observation on the motion of falling objects. Theoretically and experimentally, it is denied that Aristotle, who has ruled for thousands of years, established the correct "law of free fall" on the "law of falling body motion", that is, under the condition of ignoring air resistance, balls with different weights fall to the ground at the same time, and the falling speed has nothing to do with the weight. According to V. viviani, a student in Galileo's later years, the falling experiment was conducted in public on the leaning tower of Pisa: 1589, one day, Galileo dropped an iron ball weighing 10 pounds and landed almost at the same time, and all the competitors present were dumbfounded and shrugged their shoulders in laughter. However, Galileo's works did not clearly indicate that the experiment was carried out on the leaning tower of Pisa. So it has been controversial for several years. Galileo made a detailed study on the basic concepts of motion, including center of gravity, speed and acceleration, and gave a strict mathematical expression. Especially the concept of acceleration is a milestone in the history of mechanics. With the concept of acceleration, the dynamic part of mechanics can have scientific basis, while before Galileo, only the static part was described quantitatively.