When the American merchant ship Empress of China arrived in the Middle Kingdom in 1784, the crew probably could have known they were making history, but they could never have predicted where the current of history would take the ship of China-U.S. relations.

More than two centuries after the vessel's arrival, the earliest contact between the two nations as believed by American historian Jonathan D. Spence, President Barack Obama's maiden visit to China, which came within a year after his inauguration, invited attentions and expectations on how the two countries would advance their relations and cooperate to tackle global challenges.

As American geostrategist Zbigniew Brzezinski said at a January seminar marking the 30th anniversary of the two countries' diplomatic ties, China and the United States have become important forces in global political and economic stability.

Since the ice-breaking visit by late U.S. President Richard Nixon to China in 1972 against the backdrop of the Cold War, bilateral cooperation has expanded to the areas of politics, economy, military and culture.

Both countries are aware of the importance of their relations.

Though Obama won the presidential election under the banner of "Change," he decided to keep the U.S.' China policy of communications and cooperation unchanged, according to Harry Harding, a leading China specialist in the United States who has advised several presidents.

President Hu Jintao also stressed more than once that healthy development of Sino-U.S. relations is not only in the fundamental interests of both countries, but is also conducive to peace, stability and prosperity in the Asia-Pacific region and the world at large.

Given the interwoven relations that China and the United States share in a global village, both nations see huge potential in seeking their common interests through expanded cooperation.

And major challenges, such as the global economic downturn, terrorism, nuclear proliferation, and climate change, cannot be tackled by a single country on its own. Instead, they need the joint efforts of the international community, where the United States and China, as two influential countries, should play exemplary roles.

Obama's visit to China offered an opportunity for China and the United States to reach understandings and agreements and seek solutions to a variety of global issues.

China served as an important engine to drive forward global economic recovery while the United States saw its economy reverse the trend of recession in the third quarter of this year.

To reinforce the positive economic momentum and promote global development in a steady, orderly manner, the United States and China need to join hands in the spirit of mutual support.

Among all of the issues, global warming is a problem of immediate consequence. Earlier this month in Barcelona, representatives from more than 40 small-island countries warned during a five-day convention on climate change that any delay in a solution to the problem would increase the possibility of their homes being flooded.

As the world's two major greenhouse gas emitters, how the United States and China will cooperate and assume responsibility is a concern with global ramifications.

Undoubtedly, China and the United States still, and will always, have disagreements, especially in the fields of trade, currencies, greenhouse gas emissions, and political and military trust.

But disagreements provide room for talks, improved communications and enhanced cooperation.

Both the United States and China have showed their seriousness in resolving those disagreements. The two sides in July upgraded the China-U.S. economic dialogue to a strategic level.

In addition, during their meetings at the G20 Summit in London in April and at the United Nations General Assembly in New York, Hu and Obama signaled willingness to promote a "positive, cooperative and comprehensive relationship in the 21st century."

When addressing the first round of the China-U.S. Strategic Economic Dialogue in July, Obama quoted ancient Chinese philosopher Mencius: "A trail through the mountains, if used, becomes a path in a short time, but, if unused, becomes blocked by grass in an equally short time."

The American president said that he hoped China and the U.S. "forge a path to the future" to "prevent mistrust or the inevitable differences" from blocking that path.

A possible solution for keeping the path clear may rest in the words of Confucius -- "Wishing to be established himself, he seeks also to establish others; wishing to be enlarged himself, he seeks also to enlarge others."

The world has every reason to closely watch Obama's China visit, as whether the two countries will travel the path of understanding and cooperation or choose to collide and confront will affect the world as a whole.