Mishra immediately saw the opening Mao was creating for ties to resume, and was relieved it meshed with his own brief. Before he left for Beijing, then prime minister Indira Gandhi had laid it out for him in one sentence: "I am in a box so far as relations with China are concerned, and I want us to get out of that box."

Despite this common yearning for détente, China and India would soon drift further apart - this time over the Bangladesh liberation war in 1971. While India backed the Bengali freedom fighters, Beijing threw its lot behind its "all-weather friend" Islamabad - a relationship that would dog Sino-Indian relations for decades.

It wasn't until the 1990s that China and India would finally start a structured process of normalising ties. Economic relations have since gone from strength to strength, with China now India's largest trading partner. But as the recent three-week Himalayan stand-off brought home, the undercurrent of animosity still runs deep, and the possibility of unfriending each other all over again is never far away.

Arcing a curious trajectory, India and China's modern history would easily qualify for an "it's complicated" relationship status: active courting, followed by demonstrative friendship, violent break-up and now cautious reconciliation. It is this pull of a volatile past and the prospect of profitable cohabitation that Premier Li Keqiang will negotiate as he starts his India visit on Sunday.

Li has already had a foretaste of the job at hand. His goodwill gesture of picking India as his first foreign destination on assuming power almost came undone with last month's border crisis. Even though both sides agreed to stand down, the episode will continue to hang heavy when Li lands in New Delhi.

According to Neville Maxwell, author of the seminal , such run-ins are natural as history shows an undefined border acts as a running sore between even the least bellicose of neighbours and can quickly turn malignant.

"However much the neighbours may try to develop cordial relations in other aspects, the territorial dispute lurks in the background, making full trust unattainable," he says.

Not that the "other aspects", notably economic engagement, are insignificant. Chinese goods have flooded Indian markets and Indian companies routinely raise yuan debt from Chinese banks. As the two sides have set a goal of US$100 billion trade by 2015, Li's visit is likely to see a raft of billion-dollar deals, with the attendant fanfare and boilerplate diplomatese on "strategic partnership".

But Professor Ma Jiali, executive deputy director of the Strategy Study Centre at the Beijing think tank China Reform Forum, points out: "The border dispute is the biggest obstacle to building strategic trust between China and India. It is directly related to the territorial sovereignty, core interests and national sentiment of the people of both countries."

The dispute is over two separate territories, one in the western sector of the border and the other in the east. In the west, both China and India lay claim to 38,000 square kilometres of snowy wastelands known as Aksai Chin.

There is no demarcated border there, only a Line of Actual Control that fuzzily separates the territories controlled by them. And, each side has its own perception of where that line lies. It was in these icy heights that the recent stand-off took place.

In the eastern sector, China claims some 90,000 square kilometres to the south of the McMahon Line, which was agreed to by Britain and Tibet in a secret deal in 1914 and not recognised by China. While China calls the region South Tibet, for India it is its Arunachal Pradesh state. The McMahon Line is the de facto border in this sector.

Although China never accepted the McMahon Line, it was open to a land swap, under which India could keep what it claims on the eastern border while China would keep Aksai Chin in the west. Providing the best route into Tibet from the rest of China, Aksai Chin was non-negotiable for Beijing. For Delhi, both territories were off the table as inviolable flanks of national identity.

India and China have held 15 rounds of border talks at the special representative level since the mid-1990s but the gains have been limited. The border is remarkably well managed, with not a shot fired across it in over 20 years, but it's far from being settled, meaning the pre-1962 claims still hold for both sides.

Half a century later, the border war today is seen largely as a dispute over land in the high mountains. But for a long time, India's first prime minister, Jawaharlal Nehru, who invested, and lost, substantial political capital in a policy of friendship with China (embodied in the early 1950s Indian slogan of , or India and China are brothers), would describe Aksai Chin as a place "where not a blade of grass grows".

And, in the course of the 1962 war, Chinese troops swept towards the plains as Indian forces retreated. Rather than holding on to their gains, China called a ceasefire and the troops returned to their old positions. Land was not the only thing the war was about.

Far deeper factors were at play. The war coincided with the Sino-Soviet split. Declassified documents show Soviet leader Nikita Krushchev's irritation with China's handling of the border tension, and the Chinese leadership's anger at the Soviet backing of Nehru. For China, showing India its place was also a loaded message for the Soviet Union.

In India, Nehru was being squeezed between a rising left movement and the ascent of the right. In China, Mao was trying to reassert power within the party as the voices against the Great Leap Forward grew louder.

And then there was Tibet. Nehru, while accepting China's sovereignty over Tibet, sought greater autonomy for it to act as a buffer between the two Asian giants. For him, Sino-Indian friendship was the cornerstone of Asia's rise, and for the relationship to work, China and India needed some space. Tibet would give them that space and guarantee the two armies would never come face to face.

But for China, as Ma puts it, Tibet is a "core national interest". It is just as central to China's national pride as the border lands are for India's, with or without grass.

Dibyesh Anand, an associate professor at London's Westminster University, says: "There is a nationalist-security dissonance at the heart of how China and India approach Tibet and the border dispute. For China, Tibet is a nationalist issue and the border is a strategic issue, while for India, Tibet is a strategic issue and the border is a nationalist issue. The difference is, you can bargain over a strategic issue but not over a nationalist one."

In , sinologist John Garver notes the "brief period of Sino-India friendship from 1954 to 1958 coincided with a limited but genuine degree of Tibetan autonomy". India interpreted a 1954 pact signed with China on Tibetan border trade as an implicit guarantee of Tibet's relative autonomy while China read it as India's promise to keep its hands off Tibet. The honeymoon ended when they started blaming each other for breaking the deal.

Things came to a head when the Dalai Lama fled to India following the Lhasa revolt of March 1959. China was furious that India provided him refuge and allowed him to set up a government-in-exile. Nehru was peeved that China wasn't cutting him any slack on Tibet, weakening his position at home.

Mao was convinced India was colluding with the Americans to incite Tibetan refugees and India started patrolling the far-flung borders more aggressively under a "forward policy". From there on, war was but a matter of time.

Many of the anxieties of 1962 linger. China still feels encircled by hostile powers and is as insecure over Tibet. "India uses the special status of Dalai to allow Tibetan refugees to launch separatist activities for creating trouble to resolve the border problem in the future. Indian politicians also interact with officials of the government-in-exile and Dalai," complains Ma.

But Professor Susan Shirk, author of , believes that for the Chinese, it should be possible to shelve the territorial dispute. "This is because the media and the nationalist public don't pay much attention to it," says Shirk.

China sees India as one of the possible sources of trouble. For India, China the trouble. India's sense of betrayal, at what it sees as a sudden and unwarranted land grab by a trusted friend, has festered with time, with China's rise and its proximity to Pakistan only fuelling its own fears of encirclement.

"Tibet and the border dispute can take them back to a 1962-like situation. Economic interdependence should not be seen as replacing political negotiation," warns Anand.

Unless, of course, they find a way to live with their differences and yet profit from each other.

Mishra, the chargé d'affaires in Beijing who went on to become India's national security adviser, would later recall in that during his stint in China, he would attend the regulation diplomatic banquets but never actually got to eat anything. This was because the speeches would start during the second course and since the Chinese hosts would invariably lay into India and praise Pakistan, Mishra and his wife would have to walk out in protest.

This went on for a while until Mishra noticed the speeches weren't starting until after the cakes and ice cream came out. A Pakistani diplomat told him the Chinese had noticed the Mishras were missing out on the food and decided to hold the speeches until after dessert.

Maybe Li's trip will help the dragon and the elephant find a way to have their fights and eat their cakes too.