What was going on when I was born?

Governor Carey leaves office today, his record a mix of impressive success and puzzling lapses and his place in New York State's history still uncertain. As he has through most of his eight years in office, Hugh L. Carey still stirs strong passion. Admirers talk in heroic terms about the ''crisis manager'' who saved New York City from bankruptcy and led the state in a difficult new era of austerity and retrenchment. Detractors remember the brooding and inaccessible loner who had trouble maintaining ties with friends, subordinates or legislators. Assesments of his administration, gathered from a spectrum of experts both within and outside of the state government, are mixed, and not particulalry along partisan lines.

Two years ago in the sprawling black township of Soweto in South Africa, Representative Stephen J. Solarz, Democrat of Brooklyn, met an African employee of the United States Consulate in Johannesburg named Thabo Moeti. Mr. Moeti asked Mr. Solarz, who was chairman of the House Foreign Affairs Subcommittee on Africa, whether there was some way the American Government could help black South Africans receive university educations in the United States. There was. Mr. Solarz sponsored legislation that provided $8 million over two years for the black students to attend American universities. The first students to benefit from the legislation arrived in the United States for the current academic year.

In a year that produced the strongest sustained stock market rally in a half century and a new high for the Dow Jones industrial average, the biggest percentage gainers were typically small, obscure issues. To be sure, such household names as International Business Machines, General Electric, Procter & Gamble and American Express forged ahead. But none of these or the other 26 stocks in the Dow Jones industrials rank among the Big Board issues showing the largest percentage gains for this year, as calculated through Dec. 27. Some former Cinderella stocks performed beautifully, while others -notably energy issues - went into a tailspin.

President Reagan announced today that the United States would not pay a United Nations assessment of as much as $1 million a year. This is the first time, American legal experts said, that Washington has claimed the right to withhold funds. The disputed funds are Washington's share of the costs of a commission set up under the Law of the Sea Treaty that will design rules to govern the mining of minerals from the deep seas. Mr. Reagan refused to sign the treaty codifying law for the sea because of the mining provisions. In a statement issued from Palm Springs, Calif., Mr. Reagan said the funds ''are destined to finance the very aspects of the Law of the Sea Treaty that are unacceptable to the U.S.'' Moreover, he said, the assessment is ''improper'' and ''not legally binding'' because the rule-making commission is ''distinct from the U.N.'' Challenge to U.N. Seen The United States is now required to pay 25 percent of the United Nations' costs. Western diplomats here said Mr. Reagan's decision poses a fundamental challenge to the United Nations existence and compared it to the refusal by the Soviet Union and France to pay their share for peacekeepers in the Congo in 1960, the year the Belgian colony became independent.

The Government's index of leading economic indicators rose eight-tenths of 1 percent in November, the Commerce Department reported today. The index, which is intended to predict the future direction of the economy, has risen in seven of the last eight months, which ordinarily would signal that an economic recovery was under way. But at the present time, there are no sure signs that the recession has ended. In fact, a companion index of coincident indicators, which measures the current condition of the economy, declined six-tenths of 1 percent in November, the 14th consecutive drop and a sign the recession is continuing.

In an important policy decision, a Federal official today ordered a pipeline company that supplies natural gas to much of the Northeast to refund $100 million or more to customers that he said had been substantially overcharged. Michel Levant, an administrative law judge of the Federal Energy Regulatory Commission, said the Columbia Gas Transmission Corporation had been guilty of ''abuse'' because it had bought excessive quantities of high-priced gas while reducing purchases of the cheaper gas available to it. Lawyers representing utilities and consumer groups welcomed the action as a significant victory, declaring that the ruling was likely to become policy throughout the nation, provided that it was upheld by the commission. ''It is a very important decision that will mean a great deal to the ultimate consumers of gas'' in the United States, commented Jennifer N. Waters, a lawyer representing the Baltimore Gas and Electric Company in the proceedings.

''THERE may be some perfectly nice people who use the word 'brunch,' '' the late Heywood Broun is reported to have said, ''but I prefer not to know about them.'' However you may feel about the word, brunch probably conjures up generally expensive meals for which reservations must be made and special clothes (at least, casually elegant) must be worn. As pleasant as such a meal can be, after a week of holiday celebrations topped by New Year's Eve, a more relaxed and less self-conscious version of brunch might be just the thing for New Year's Day. Relaxed and generally inexpensive breakfast-lunches can be had in a number of the city's ethnic restaurants, few of which require reservations, nor do they inspire serious attention to dress. The varied and savory Chinese dumplings that comprise a dim sum breakfast make a diverting and soul-satisfying first meal for the New Year. There are several dependable Chinatown meccas for dim sum that will be open tomorrow. Among the best are Hong Gung, 30 Pell Street (571-0545), serving dim sum from 9 A.M. to 3:30 P.M.; Hee Seung Fung (H.S.F.), 46 Bowery (374-1319), with dim sum from 8:30 A.M. to 5 P.M., and the Imperial Inn, 23 Pell Street (233-1014), where dim sum can be ordered from the menu between noon and 3 P.M. Menus at kosher dairy-vegetarian restaurants offer wide choices that are suitable for a brunch. Thick and steaming vegetable soups, omelets or scrambled eggs with smoked salmon and onions, bagels, lox and cream cheese, assorted herrings and blintzes are foremost among such choices.

''Keep New York wet. Save water.'' - Mayor Koch, in TV commercial.

Governor-elect Mario M. Cuomo yesterday announced the appointment of Cesar A. Perales, president and general counsel of the Puerto Rican Legal Defense and Education Fund, as Director of Social Services for New York State. At the same time, Mr. Cuomo announced that he had chosen William J. Donohue Jr., head of the Erie County Industrial Development Agency, to become the state's next Commissioner of Commerce, and he confirmed the appointment of Vincent Tese, a general partner in a Wall Street brokerage house, as Superintendent of Banks. The Governor-elect said he had reappointed Karen S. Burstein as chairman and executive director of the New York State Consumer Protection Board, a position she has held for nearly two years. He also announced that Ronnie Eldridge, a former aide to Mayor John V. Lindsay and the assistant director of public affairs for the Port Authority of New York and New Jersey, would become head of the Women's Division of the Governor's office.

The National Consumer Cooperative Bank announced today that it would not rehire its president, Carol S. Greenwald, when her contract expires on Jan. 31. The bank's action has been expected since last November, when Mrs. Greenwald took a ''sabbatical'' that coincided precisely with the last three months of her contract. Mitchell Rofsky, executive vice president, will continue as acting president until a new president is appointed for the cooperative bank, a quasi-governmental institution chartered in 1979 to lend money to innovative cooperatives in such areas as housing, food, health and cable television. The announcement came on the heels of an audit by the Federal Farm Credit Administration reporting that the bank's portfolio of loans was very weak and that management was ''deficient.'' Another Government report - this one from the General Accounting Office - recently disclosed that a bank director had a conflict of interest in promoting a $5.2 million loan to a housing cooperative in New York.

From now until spring, the search by President Reagan, Congress and a Presidential commission for a way to base the MX missile will drive them well beyond that issue to delve into the fundamental shape of the nuclear deterrent. As the smoke has cleared from the most recent Congressional battle over the proposed MX, senior Administration officials and other advocates of the new multi-warhead missile have acknowledged that no static, undefended land base would be totally secure from Soviet nuclear destruction. Thus the quest will prompt scrutiny of small mobile missiles, air and sea basing schemes and the present components of the strategic nuclear deterrent. The hunt could cause an inquiry into the Administration's doctrine for fighting a protracted nuclear war. Vulnerability of Land Bases The initial charter of the President's commission of former high Government officials, technical experts and prominent citizens clearly points in that direction. But the breadth and depth of the commission's work will be determined as it goes along.

Interior Secretary James G. Watt, apparently ending one of his bitterest disputes with environmentalists, said today that he would issue no more leases for oil and gas drilling in Federal wilderness areas. At a news conference, Mr. Watt also said he would not consider lease applications for millions of acres of Federal land now being considered for possible inclusion in the wilderness system until Congress made the final decision about how these lands should be used. On another issue, Mr. Watt said in a telephone interview that he had decided Kuwaiti oil interests should be allowed to buy energy and mineral rights on Federal lands other than wilderness or other protected areas. First for an Arab Country The Secretary said he decided that Kuwait should be granted reciprocal rights because the Kuwaiti Government permitted United States companies to take oil from Kuwait. While such rights have been given to other nations, including Sweden and Canada, it is the first time such a ruling has been made in favor of an Arab country.