Ancient Babylon and ancient Egypt, as two ancient civilizations, made the land of barbarians shine with mathematics. From their history, we can see that mathematics was just a tool at first, or used to calculate calendars, so as to master more accurate time to worship the gods; Or to calculate the tax in order to collect the land tax more accurately. Mathematics in ancient Babylon and ancient Egypt always emphasized arithmetic over reasoning. Maybe they don't consider strict reasoning at all, but only pay attention to calculation skills and practicality. Both ancient Babylon and ancient Egypt made some attempts to express numbers. Although they are not modern and concise, the number system of ancient Babylon, like the one used today, is a mixed number system formed by many historical conditions and regional habits, but they prefer the 60-digit number system in mathematics and astronomy, and cuneiform characters record these; The ancient Egyptian count was based on 10. Everyone has some knowledge of logarithmic addition and subtraction and some calculation skills of multiplication, but they are not systematic. They have no concept of division. For example, 1/2 is a number in their understanding, and they use clever but tedious continued fractions to make up for the vacancy without division. Algebra in ancient Babylon and ancient Egypt also made some progress. They can solve some quadratic equations. The ancient Babylonians even gave some very accurate approximate solutions to the quintic equation, but their solutions were very skillful. They never discussed the existence of the solutions of the equation. These are similar to the mechanical solutions of today's algebraic equations, but only the algorithm does not talk about the calculation principle. Ancient Babylon and ancient Egypt also made some explorations in geometry, because their government officials had to levy taxes on land and accurately calculate the area of land of various shapes. They can also calculate the area of some triangles, quadrangles and even circles, in which approximate solutions are used, but the approximate degree is already very high. Similarly, they are very skilled in these processes, but there is no strict reasoning. It can be seen that the initial development of mathematics is not as abstract as modern mathematics, but produced under the demand of very specific practical problems. At first, mathematics was just a tool to solve problems. It is not a subject in itself, but a very effective calculation tool at most. During this period, the so-called mathematicians were only skilled calculators, and they never explored strict reasoning until the emergence of the Greek school of mathematics. Ancient Babylonians and ancient Egyptians opened the door for human beings to explore mathematics from ingenious algorithms, and their symbol counting brought great changes and convenience to mathematics and even the whole life of later generations.