Shintaro Ishihara, the governor of Tokyo, may not be a household name in the United States. But in East Asia, he is often at the center of international controversy because of nationalistic-themed statements that regularly infuriate China and South Korea.

The octogenarian head of the world's largest city for the past 13 years raised eyebrows again on Monday during a visit to the United States when he mentioned a group of islands at the heart of a major territorial dispute between China and Japan.

Speaking in Washington at the Heritage Foundation, a conservative think tank, Ishihara said that Tokyo would buy the Senkaku, or Diaoyu, islands. Ishihara did not disclose what price the Tokyo government would offer.

A statement from Beijing's foreign ministry on Tuesday said that the Diaoyu islands have been an immovable part of China's territory since ancient times; any unilateral measures taken by Japan are illegal and invalid.

But whose islands are they in the first place? That depends on who you ask.

Japan, which refers to the islands as the Senkakus, held them from 1895 to 1945, after which the United States administered them until 1972. Japan states that when the U.S. returned territories that the U.S. military administered after World War II to Japanese administrative control, the Senkakus were included. Japan further argues that before 1895, there were no signs of Chinese control at all.

Neither the government of the People's Republic of China, nor the government of the Republic of China on Taiwan, has ever supported the transfer of the islands' control from the U.S. to Japan.

China refers to them as the Diaoyu islands and believes that ownership was transferred back to it at the end of WWII. China consistently states that it has inviolable sovereignty over the territory; both the People's Republic and Republic of China argue that their claims to the islands date back to the fourteenth century.

The Senkaku / Diaoyu are located approximately 120 nautical miles, or 220 kilometers, east of Taiwan, and 200 nautical miles, or 370 kilometers west, from Okinawa.

A diplomatic headache and a major stumbling block in Sino-Japanese relations, the Senkaku / Diaoyu dispute has become more than a simple disagreement over a few islands. It has come to represent a whole slew of geopolitical disagreements between China and Japan. 

These issues include development rights for hydrocarbons in the East China Sea, fishing rights, shipping transit rights and overlapping control of the two countries' Exclusive Economic Zones. More generally, they have come to highlight an ongoing struggle for control over use, ownership and exploitation of East Asia's maritime regions.

In 2010, a collision between a Chinese fishing vessel and a Japanese coast guard vessel near the islands led to large scale boycotts of Japanese products and protests across China.

Analysts believe that after these events, the governments decided to soften diplomatic tones and restrain themselves from highlighting overly sensitive political and historical issues. Relations between the two nations have warmed over the past two years, especially after Japan's earthquake and nuclear disaster.

But the thaw hasn't stopped municipal leaders in Japan like Ishihara from rocking the boat. 

Ishihara is especially controversial in both China and Korea. In the past he has denied that the Nanjing Massacre occurred, describing it as Chinese propaganda.  He has also claimed that Japan's annexation of Korea in 1910 was a legitimate historical development. Even in Japan, he drew resentment by describing the 2011 tsunami and earthquake as divine punishment for his own country's material greed.

The Nanjing Massacre, or Rape of Nanking, occurred after Japan's capture of the city, at the time the capital of China, in 1937. According to most historians, 200,000 to 300,000 deaths were caused by the Imperial Japanese Army during the first two months of the city's occupation.

Tokyo's governor is not the only politician in Japan embroiled in controversy with China. In February, the mayor of Japan's third-largest city, Nagoya, told a visiting delegation from Nanjing that he thought the massacre probably never happened. 

The Nanjing municipal government broke off all relations with Nagoya in response.

Historical tensions with Japan are a source of anger for Chinese youth and students, who use the Internet to voice their displeasure not only at Japan, but also at what they see as inadequate responses from their own government to Japanese provocations.

While Japan's politicians are attracting criticism internationally, such blunt comments are seen by some as a refreshing change from the usual platitudes of anodyne politicians, as well as a way to stand up to a rising China.