This is a particularly pernicious myth among the Chinese. The idea here is that Taiwan has been a part of China for over a thousand years. This is one of the most absurd things that I have ever heard in my life, and of course, there is no basis for this absurd claim.
There are no concrete Chinese records of an island called Taiwan, just vague references to islands in the seas collectively known as Liuqiu. This is largely because China historically has not concerned itself much with the seas as its most immediate threats were from the land. It is possible that during the Tang Dynasty that there was limited contact, but this is disputed. In AD 607, Emperor Yangdi sent Zhu Guan to explore the eastern sea. Liuqiu was reached (believed to be Taiwan but it is not certain). However, no conversation was possible because the inhabitants of the land were no Chinese but were in fact Malayo-Polynesians who had settled on the island hundreds of years earlier from the Indonesian-Philippine archipelago. Four years later, General Chen Ling did return with an interpreter. Conflict occurred, and although Chen was victorious, he returned to China. There is no evidence that constant contact was made with the island because the Tang had problems, both at home and from the Northwest, to deal with.
It wasn't until the 13th century when migrants from China made their way to Taiwan. From 1250-1279, when China was under the threat of the Mongols, one-third of all Hakka (�Ȯa�H) in Guangdong Province made their way to Taiwan. However, as no governmental link was made to China, there is no way China can make any argument that Hakka settlement on the island can imply that it has sovereignty over the island, expecially considering that there were already non-Chinese inhabitants of the island.
The Mongol Yuan Dynasty was more concerned with its adventures in Indonesia and Japan to concern itself much with Taiwan. An administrative post was established in the Pescadores (Penghu), but it was considered a part of Fujian Province. No such post was established on the much larger island of Taiwan.
The Ming Dynasty was initially indifferent to the seas, but under Emperor Chenzi, Zheng He led massive fleets throughout the South China Sea and the Indian Ocean. It is clear that he did make a stop in Taiwan, but the Chinese had no official presence on the island. Following the 1430s, the Ming virtually ignored the seas until the 17th century dawned.
It was the Japanese who next turned an eye toward Taiwan. At that time, Taiwan had loosely organized local governments with no overarching authority. Japan demanded that tribute be paid in 1593, but the demand was ignored. Military expeditions were sent against the island in 1601 and 1615, but both were unsuccessful.
In 1604, the Dutch occupied the islands of Penghu. Chinese economic blockades forced the Dutch to vacate the islands. However, after 15 years of China's rebuffing Dutch requests to establish a trading post, Admiral Kornelius Rayerszoon led a fleet to conquer the islands. Two years later, after the Chinese blockaded the island, the Ming authorities and Dutch came to an agreement. The Dutch could set up shop on Taiwan. Obviously the Ming had no problem with this because they had no claims of sovereignty on the island.
It is clear that during the 15th century that there was immigration from the Minnan People (�ԫn�H) of Fujian Province. However, the numbers were not high and the island was still rather sparsely populated. These Minnan were not treated well by the Dutch and were eager for someone to lift their chains of bondage. That help was soon to come.
Their deliverance would come at the hands of a half-Japanese Ming loyalist by the name of Zheng Chenggong (�G���\). After the Ming Dynasty fell, those who wished to continue their resistance against the invading Manchus from the north were looking for places of refuge. Taiwan, as a resource-rich island, was targeted. Zheng led a fleet to liberate the Minnan People on the island from the Dutch.
Zheng did not represent Chinese authority because the dynasty he was loyal to had already collapsed. China was once again run by foreigners, the Manchu. The Zheng family ran the island, creating a prosperous trading society. However, after Zheng's son died, court intrigues gave the Qing the opening that they were looking for and they took the western part of the island. This is the first time in history that an actual Chinese government set up shop in Taiwan, and this was a government run by the foreign Manchu people.
Well, needless to say, the people of Taiwan were not happy with their new overlords. During the eighteenth century, Taiwan had several rebellions. The people of Taiwan were not so pleased to see the Qing Dynasty come to rule.
In 1871, Japanese sailors were driven ashore on the eastern side of Taiwan. At this time, the Chinese Zongli Yamen, the ministry created to deal with foreigners, claimed that it lay outside their domains. So, as late as the 1870s, China was making the argument that the eastern shore of Taiwan was not within its jurisdiction.
To the north in Korea, China and Japan fought a war over influence in the peninsula. China lost badly and surrendered soveriegnty of Taiwan forver in the Treaty of Shimonoseki.
It is clear that from history, Taiwan is not historically a part of China. No Han Chinese administration was ever extended to the island prior to the twentieth century. The only "Chinese" administration on the island was that of the Manchu Qing Dynasty, a foreign people who conquered China in 1644.