What was going on when I was born?

Red Smith, a Pulitzer Prize-winning sports columnist for The New York Times and one of the nation's most admired sports commentators, died at Stamford (Conn.) Hospital yesterday of heart failure after a brief illness. He was 76 years old and lived in New Canaan. The last column in Mr. Smith's 55-year career, ''Writing Less - and Better?'' appeared Monday and told of his plans to cut back his writing from four to three columns a week. In the column, he recalled years past when he had written seven columns a week and added: ''Between those jousts with the mother tongue, there was al ways a figh t or football match or ball game or horse race that had to be covered after the column was done. I loved it.'' Pulitzer Prize in 1976 In the college textbook ''A Quarto of Modern Literature,'' between an essay by Winston Churchill and a short story by Dylan Thomas, there is an example of spot-news reporting by Red Smith.It is a column on a heavyweight fight between Joe Louis and Rocky Marciano, written on deadline. It is the only piece of journalism in the anthology, and the only sports story.

Mayor Koch, outlining his spending plans for the next fiscal year, said yesterday that New Yorkers could expect fewer improvements in services than he had promised in the election-year budget he put forth eight months ago. Mr. Koch's program for fiscal 1983 included $171 million in new taxes that he called ''inescapable'' and $213 million in spending reductions that he said were needed to help close an impending large budget deficit. He said, however, that despite these cuts the effect on services would be ''minimized'' through an ambitious productivity program. In contrast to last year, when he asserted that ''the worst pain isbehind us,'' the Mayor acknowledged that his goal now was simply to ''hold the li ne.'' As a result, after a burst of hiring before fiscal 1982 ends on June 30, the city expects that the work force will have shrunk - with 1,244 fewer police officers, 225 fewer street sweepers and 4,019 fewer schoolteachers and paraprofessionals - when fiscal 1983 ends 18 months from now.

Negotiators for the International Brotherhood of Teamsters and trucking concerns reached a tentative agreement today on a contract reported to include major concessions made by theunion in the hope of protecting the 300,000 j obs in the troubled industry. The agreement was announced in Washington and Kansas City by Roy L. Williams, president of the union, and Arthur H. Bunte Jr., president of Trucking Management Inc., the industry's principal bargaining arm. The details of the pact were not disclosed, but both sides hailed its terms, saying they were confident that it would preserve the jobs of those still employed and would help return to work some of the 120,000 drivers and warehousemen laid off in the last year. Ford Asks Union Sacrifices In another labor development, the Ford Motor Company said that it was asking the United Automobile Workers to make substantial sacrifices in fringe benefits in return for job protection and profit sharing for its members. (Page 10.)

The highest-ranking Solidarity leader who is still at large has declared in an interview that the union is continuing its activities underground and is prepared for a long struggle to fight for democrac y and to overcome what he called military ''di ctatorship.'' The union official, Zbigniew Bujak, insisted that the struggle must be conducted through peaceful resistance. ''I see that the current situation lends itself very much toward the organization of terrorism, and I fear that very much,'' he said. ''Our country has never known terrorism, and it would be better if it didn't come to that.'' Mr. Bujak, the 27-year-old head of the Warsaw chapter of Solidarity and a man whose popular appeal has made many unionists think of him as a successor to Lech Walesa as the union's leader, is in hiding somewhere in Poland. The interview, the first he has given since the military crackdown began, was conducted by submitting questions through a complicated chain of intermediaries so his whereabouts was not revealed.

The Federal Trade Commission, in a 3-to-1 vote, decided today to dismiss the 1 0-year-old antitrust case againstthe nation's three biggest breakfast cereal makers, Kellogg, General Mills and Gen eral Foods. The commission thus accepted the recommendation of an F.T.C. administrative law judge that the agency's staff had failed to prove the original charges. These had accused the three companies, whose products are consumed by tens of millions of Americans every day, of having operated a ''shared monopoly'' that limited competition among themselves and prevented new competition from entering the market. The judge, Alvin L. Berman, called for dismissal in a recommendation issued last September.

Governor Carey's decision against seeking re-election set the stage yesterday for an unusually crowded gubernatorial primary in a party noted for its primary battles. Even as the Governor was making his announcement in the Red Room of the State Capitol in Albany, prospective Democratic candidates and their aides began maneuvering. A series of declarations of candidacy is likely in the next two months, and a scramble for support is expected at the designating meeting of the Democratic State Committee in June before the primary in September. Lieut. Gov. Mario M. Cuomo of Queens came closest yesterday to making a formal declaration.

Governor Carey announced today that he would not seek re-election to a third term and would devote himself instead to a yearlong battle to make New York ''at once compassionate and competitive.'' Surrounded by his family, his Cabinet and his closest aides, New York's 51st Governor declared himself ''more of a fighter than a politician.'' He explained his decision by recalling his service dur- Transcript of statement, page 28. ing World War II, an experience that Mr. Carey has drawn upon frequently during his 22-year political career. ''As a young officer in the infantry on the battlefields of Europe, responsible for the lives of those who served under me,'' Mr. Carey said, ''I learned the hard and bitter lessons of choosing my battlegrounds - deciding where to fight and for what. In 1982, I have chosen.''

The Producer Price Index for finished goods, a rough measure of the inflation consumers will face in the future, rose three-tenths of 1 percent in December and for all of 1981 was up only 7 percent, the lowest annual increase since 1977, the Labor Department reported today. At the end of the year, producer prices were rising at an even slower annual rate. The December increase of three-tenths of 1 percent, if it continued for 12 months, would translate into a compound annual rate of only 3.1 percent. For the last three months of 1981, the Producer Price Index for finished goods rose at an annual rate of 5.4 percent. The 7 percent increase in producer prices in 1981 was just slightly higher than the 6.9 percent of 1977. The index rose 3.7 percent in 1976 and 9.2 percent in 1978, 12.8 percent in 1979 and 11.8 percent in 1980.

The horse and buggy, its brass fittings gleaming in the sunlight, sits with a forlorn driver for hours near the Happi Hotel waiting for a passenger. The other night a belly dancer, Miss Ahly, undulated in a nightclub with only a handful of customers to view her twitching hips. Out on the glittering waters of the Nile, near the first cataract of the great river, only a few graceful feluccas - small, narrow vessels with lateen sails - moved silently through the water with a scattering of tourists aboard. Many more were moored to piers waiting for customers. Normally at this time of year, Aswan is full of tourists taking advantage of the warm weather, the flawless blue skies and the joys of an easygoing oasis filled with water and greenery and with the desert visible in the distance.

Secretary of State Alexander M. Haig Jr. faced a tricky question on the Bible and politics at a news conference today as he was leaving Israel. He dodged it artfully.

After four days of talks in Cairo and Jerusalem, Se cretary of State Alexander M. Haig Jr. left for Washington to day expressing guarded optimism about the prospects for an accord on Palestinian self-administration. He said he planned to return to Egy pt and Israel at the end of January for further discussions. After those talks, he said at a news conference at Ben-Gurion International Airport, the United States might put forward some suggestions for breaking the impasse that has prevailed for two and a half years in the three-way negotiations. ''I think at this juncture I'm optimistic and hopeful,'' the Secretary said, ''but not unmindful of the great obstacles that have to be overcome in the period ahead in the autonomy category. And I think the optimism comes essentially from the attitude of the leadership in both capitals, which has dedicated itself to an extraordinary effort in the days ahead to achieve an agreement.''

After deliberately avoiding the problem for the last year, Secretary of State Alexander M. Haig Jr. has thrust himself into the intricate negotiations on Palestinian autonomy in the hope of achieving a diplomatic breakthrough between Egypt and Israel in the next three months. The question being raised here, in Cairo and among Mr. Haig's staff is whether he is embarking on an impossible mission or whether his timing is right, however long the odds against him. The negotiations for Palesti nian self-rule in the West Bank and Gaza Strip ha ve dragged on inconclusively for more than two and a half years, a nd have so bogged down Israeli and Egyptian negotiators that hardly a nyone in Cairo or Jerusalem is willing to predict success befor e April 26. On that day, Israel is scheduled to complete its withdrawal from Sinai, completing the formalities of the Egyptian-Israeli peace treaty. Then begins the test of whether the two countries will really live as good neighbors.