What was going on when I was born?

Some of Mexico's most treasured pre-Columbian artifacts were stolen from the National Museum of Anthropology on Christmas Eve, authorities said today. In all, 140 objects made of gold, jade, obsidian and turquoise, crafted by the Mayas, Aztecs, Mixtecs and Zapotecs before the Spanish conquest of Mexico, were discovered missing Christmas morning. They had been in seven glass cases in three of the museum's galleries on the first floor and in a basement exhibition area. Symbol of Cultural Heritage The museum, in Chapultepec Park in the heart of Mexico City, is one of the city's most famous tourist attractions. The museum and its contents are regarded by Mexicans, who are fiercely proud of their Indian heritage, as one of their national treasures, a symbol of the cultural richness of the advanced civilizations that existed in Central America before the arrival of the Europeans in the 16th century.

After a week of intelligence analysis of the slayings of Paul Castellano and Thomas Bilotti, law-enforcement officials now say that Mr. Bilotti was a primary target and possibly the main one, because he had emerged as the underboss of the Gambino crime family. As underboss, he would have been the family's No. 2 leader and thereby the heir apparent to Mr. Castellano, the officials said. They added that a faction of the group led by John Gotti had feared that if Mr. Castellano were slain or sentenced to prison, Mr. Bilotti would be powerful enough to take over as acting boss. A Rising Figure Based on confidential intelligence reports and analysis, the officials from the New York City Police Department and the Federal Justice Department said Mr. Bilotti had been gunned down along with Mr. Castellano on a Manhattan sidewalk as part of a struggle to replace Mr. Castellano as the head of the Gambino organization. Mr. Castellano, who was 70 years old, and Mr. Bilotti, 45, were killed in a fusillade Dec. 16 on East 46th Street near Third Avenue as they emerged from a limousine driven by Mr. Bilotti. Organized-crime experts in the Justice Department and the Police Department identified Mr. Castellano as the leader of the Gambino organization since 1976 and Mr. Bilotti as a rising and important figure in the group.

International Syria has moved missiles back into eastern Lebanon, Prime Minister Shimon Peres told Israeli newspaper editors. The Syrian action raised concern that the redeployment of the Soviet-built antiaircraft missiles might pose a new challenge to Israeli planes flying over Lebanon. The missiles were withdrawn two weeks ago after the United States had told Syria, on Israel's behalf, that the weapons unnecessarily raised tension in the area. [Page A1, Column 6.] Lebanon's warring militias have agreed on a pact to end 10 years of civil war, a Shiite militia leader said. The leader, Nabih Berri, said the groups had reached agreement on the Syrian-mediated pact after three months of talks in Damascus. [A1:5.]

FREDERIC REMINGTON spent his life making art and scouring the world looking for action. He played football, built a tennis court near his studio on Ingleneuk Island in the St. Lawrence River and ate and drank excessively. He traveled to Cuba, Mexico and Europe and was about to embark on a canoe trip down the Volga when Russian authorities smashed his canoes, escorted him to the border and told him to get lost. To the public, he is probably the best known of the many artists to be lured by the romance of the American West, and he remains something of a cult figure for the way he mythologized its conflicts, individualism and pioneer spirit. While Remington is best known for his calvalrymen, cowboys and Indians, almost all of his Wild West paintings were, in fact, painted back East, in another wilderness, one he knew far better. He had grown up in northern New York and as an adolescent roamed up and down the North Country - which stretches across New York, Pennsylvania and Canada, from the Adirondacks to the St. Lawrence River to the forests of Quebec. Remington often returned to the North Country to hunt and canoe and paint. He stayed there regularly in the decade before his death in 1909, at the age of 48.

FROM carols, creches and the rustle of Christmas wrappings to clinking glasses and the rustle of evening dresses. The grown-ups have taken over the holidays with a weekend warmup before the New Year's Eve exhilaration. The countdown is on! As usual, the New Year's half of the holiday season offers an abundance of quality entertainment for every taste. The interlocking worlds of cabaret and jazz traditionally reach a peak of activity on New Year's Eve, and this year is no exception. Extended engagements by the singer Barbara Cook at Michael's Pub and the trumpeter Wynton Marsalis at the Joyce Theater are among the high points of a week that is rich array of pop and jazz talent. Classical music lovers can savor everything from Bach (the Y Chamber Symphony playing the complete ''Brandenburg'' Concertos at the 92d Street Y) to Wagner (the New York Philharmonic performing an all-Wagner program at Avery Fisher Hall). At Tramps, Staten Island's gift to rock, David Johansen, will perform as his raucously funny alter ego, Buster Poindexter. The rock comedians Flo and Eddie will appear for their fifth straight New Year's engagement at the Bottom Line. The salsa star Ruben Blades and Seis del Solar will ring in the New Year at Sounds of Brazil, and the popular young comedian Richard Seinfeld is back at Caroline's. Following are selections ranging from the cabarets and comic acts, to jazz, pop, rock and the opera.

The Union Carbide Corporation's investment bankers held meetings yesterday to decide on a countermove to the GAF Corporation's increased $5.1 billion takeover bid for the chemical manufacturer, according to sources familiar with the situation. On Wall Street, meanwhile, there was a sense that Carbide would continue to strongly resist GAF's advances, although no decision is expected for a few days. Some analysts and traders, however, felt that the improvement of $6 a share that GAF made in its offer for Carbide, to $74, has shifted momentum in GAF's favor, at least for now. That feeling sent Carbide's stock up 1 3/8 points yesterday, to 72 3/8, on the day's heaviest volume of 2.7 million shares on the New York Stock Exchange.

After 30 years of decline, there is a perception that this city's slide has stopped and that those who hold power are filled with a vision. ''Folks were saying the city is dead,'' the Mayor said, remembering when he took office four years ago. ''There was no hope for Camden.'' In some ways, this is still a desperate city. Camden officials estimate that between 50 and 60 percent of the 82,500 people who live here survive on some form of public assistance. Unemployment in some neighborhoods is 50 percent, according to the Mayor, Melvin R. Primas Jr. And with 22 murders in 1984, the city's homicide rate is almost four times the national average.

The Federal Reserve Board said today that it would postpone the effective date of its proposed restriction on the use of low-quality bonds to finance corporate takeovers. The proposal had been scheduled to go into effect Jan. 1, but late this afternoon the board announced it would hold a public meeting Jan. 8 to discuss the large number of comments received about the plan. The board's spokesman, Joseph R. Coyne, said a new effective date would be considered at the meeting, which will be open to the public. Asked if the regulation might be made retroactive, Mr. Coyne replied, ''Typically, the board doesn't act retroactively.''

An article in Science Times on Tuesday about the Exodus from Egypt misidentified Dr. Hans Goedicke. He is a professor in the Near Eastern studies department at Johns Hopkins University.

President Reagan's draft budget for the fiscal year 1987 would cut spending on veterans' health care benefits by reducing the number of people treated and, for the first time, by requiring insurance companies to help pay the costs. Harry N. Walters, the Administrator of Veterans Affairs, warned that cutbacks in spending and staff could ''ultimately result in a reduced quality of medical care'' for veterans. He made the comment in a letter to the Office of Management and Budget, which wrote the proposals. The draft 1987 budget, to be submitted to Congress in early February, would require many veterans to show financial need to receive care. It would also provide no money for new nursing homes for veterans even as the number of older veterans is rising rapidly because of the large number of men who served in World War II.

Here in Harerge Province, the Ethiopian famine of 1986 is about to begin. In this place, on the western edge of the Ogaden region, which the sun has turned into a desert of dull brown, wind-blown dust, it is difficult to find the skeletal children like those who died by the thousands in feeding camps in the last year. Nor does a visitor see the old people who hobbled for miles searching for food and water, or the young whose youth was stolen by starvation. At the moment, thousands of tons of bulgur wheat, powdered milk and cooking oil are being delivered all over the country and distributed to millions of Ethiopians. Nonetheless, Ethiopian officials, United Nations representatives and private relief officials say this country will require as much food as it received in 1985 if widespread starvation is to be averted. What worries them now is that only one-third of the estimated 1.2 million tons of needed food has been committed so far, that by the United States.

The Koch administration has begun foreclosure proceedings against 11 of the 55 welfare hotels, which collect millions of dollars from the city to house homeless families, because of nonpayment of property taxes, city officials said yesterday. The city has also begun legal action against five other welfare hotels that owe water and sewer bills ranging from about $9,000 to more than $56,000, according to Mayor Koch. One Borough at a Time The 11 hotels threatened with foreclosure are in Brooklyn and Queens and on Staten Island. The five others are in Manhattan. Technically, these five hotels could also be subject to foreclosure, according to Carol Kellerman, deputy finance commissioner. But such proceedings are filed borough by borough, and actions will not be filed in Manhattan until the spring, she said. No action is planned against hotels in the Bronx, officials said. City officials said the city was seeking only the tax money, not control of the hotels. Their hope, they said, is that the owners of the hotels, facing the possibility of losing their properties, will agree to pay what they owe.