It is recorded by the history of statistics that "political arithmetic" and " staatenkunde" date back to the 17th century:primary social statistics, originated in Britain and Germany. Almost at the same time, "gambling mathematics':primary probability theory, appeared in Italy. Primary mathematical statistics did not come into being until the 19th century when law of large numbers and error theory were discovered and added to probability theory. So we can draw the conclusion thatsocial statistics came into use two centuries earlier than mathematical statistics.Because social statistics is widely used in economy and politics,the governments of all nations have been attaching great 'importance to it and made it develop systematically.After 1940s, mathematical statistics developed rapidly owing to the development of probability theory. After 400 years' development, two branches of learning have been formed:social statistics and mathematical statistics,both of which are in constant competition and neither of them can win easily.