What was going on when I was born?

In the more than four years Mayor Koch has been making judicial appointments, he has kept his pledge to erase politics from the system, both critics and admirers say. Despite Mr. Koch's sometimes harsh criticism of the judiciary as too lenient, he has not appointed judges who, as a group, reflect his hard line. Instead, most criminal-justice experts contend, he has named men and women of generally high quality who have proved to be balanced in their approach to criminal justice and independent of the Mayor's philosophy. The Mayor's appointments have been based on standards set by an independent review panel. In a shared judgment usually meant as praise - but not necessarily taken that way by Mr. Koch - a broad range of judges, lawyers and public officials said in interviews that the Mayor's actions bore little resemblance to his often strong public statements.

Secretary of State Alexander M.Haig Jr., in remarks here apparently aimed at exerting pressure on Argentina in the Falkland Islands crisis, reaffirmed Sunday that the United States had longstanding obligations to Britain. At the same time, amid signs that his talks with Argentine leaders were becoming increasingly strained, Mr. Haig suggested that both sides put off for now the problem of dealing with the crucial issue of sovereignty for the disputed islands in the South Atlantic. Mr. Haig's latest round of talks ended at almost 2 A.M. this morning, after some 11 1/2 hours of in the presidential palace. A State Department spokesman, Dean Fischer, said the talks would continue at 9:30 A.M. this morning. In a clear attempt to put further pressure on the Argentines to begin to compromise more, Mr. Fischer said that Mr. Haig would decide today whether to go to London to continue his shuttle diplomacy or return to Washington, an apparent threat to break off his efforts to avert a war.

It will not be easy to watch the New York City Fire Department's new public service message - a message delivered by a woman whose family perished and who was disfigured in a fire that started when her husband fell asleep while smoking a cigarette. The television spot is supposed to be as striking as the statistic cited by its sponsors: Nearly one-third of the deaths and injuries in residential fires occur in blazes started by smoldering cigarettes, far more than any other single cause. Legislators in four state houses and on Capitol Hill have been considering one solution, the self-extinguishing cigarette. The debate over its merits will be coming soon to Albany.

''There is something positive, which is the fact that negotiations continue.

The Israeli Army began evicting Jewish protesters from one of the northern Sinai settlements this morning as Israel's two chief rabbis pleaded with other militants not to carry out their threats to commit suicide. The Defense Ministry ordered all journalists out of the area as the army moved into a small encampment called Talmei Yosef. There were no immediate reports of injuries on either side, although the more militant protesters, located in the township of Yamit, have threatened violence against Israeli troops.

Every summer, first-year business students abandon classrooms for junior managerial posts at major companies. This year, however, many may be lifeguards. Record numbers of business school students have run straight into a bleak economy. This year many companies, including General Motors, Ford, Exxon, Mobil, Bank of America, Champion International and Scott Paper, are either trimming summer intern programs or scrapping them.

International Longstanding obligations to Britain on the part of the United States were reaffirmed in Buenos Aires by Secretary of State Alexander M. Haig Jr. in remarks apparently aimed at exerting pressure on Argentina in the Falkland Islands crisis. There were signs that his talks with Argentine leaders were becoming increasingly strained, and he suggested that both sides put off for now the problem of dealing with the crucial issue of sovereignty over the islands. (Page A1, Column 6.) Phone calls from 10 Downing Street to colleagues were made by Prime Minister Margaret Thatcher as anxiety increased over the continuing deadlock in the peace negotiations in Buenos Aires. The Prime Minister's urgent calls were the second time in 24 hours that she had asked for opinions of Cabinet members on the Falkland Islands crisis. (A1:3-5.)

Some of the most fiscally aggressive states in the country are scheduled to do battle before the Supreme Court today against some of the largest corporations in the world over a method of taxation that has already caused some foreign governments to threaten retaliation against American businesses. It is called worldwide unitary taxation, and it is an increasingly popular way of computing the state tax bills owed by multinational corporations. What makes this tax method unusual is that, if the corporation is deemed to be one unit, the tax computations take into account not only the business it does within the taxing state, but all its operations anywhere in the world. The parties due to come before the court today are the Chicago Bridge and Iron Company, the State of Illinois, and the Caterpillar Tractor Company. Some Companies Benefit The case is procedurally peculiar because Caterpillar, unlike most other multinationals, actually benefits financially from a worldwide unitary tax system, and therefore has allied itself with Illinois.

The semiconductor industry is showing signs of emerging from its protracted slump. Industry executives and analysts say that new orders are at the highest level in nearly two years, excess prouction capacity is diminishing and soft prices have firmed a bit. No one, however, seems willing to proclaim that a recovery is at hand. They fear that the recent upturn might be only temporary, especially if the overall economy does not improve.

As Secretary of State Alexander M. Haig Jr. continued his mediation effort over the Falkland Islands, it was becoming clear how little leverage the United States has to move Argentina toward a compromise with Britain. Argentina's right-wing military junta is one of the most conspicuously anti-Communist regimes on the continent, and, in a switch from the Carter Administration's cold-shoulder approach, President Reagan has been assiduously wooing Buenos Aires as a strategic ally in the struggle against leftist movements in Central America. Lieut. Gen. Leopoldo Galtieri, the bluff general who heads the junta, had until the last few days the reputation of being one of the most pro-American leaders Argentina has had. But the crisis touched off by Argentina's seizure of the Falkland Islands has demonstrated that Argentina's concerns and strategic interests are not necessarily those of the United States, no matter how much Washington and Buenos Aires might agree on what should be done in a place such as El Salvador. Soviet Is Trading Partner ''There is a lot of anti-Communist rhetoric here,'' commented a Western ambassador, ''but underneath it lies a pragmatic understanding with the Soviet Union I think that, no matter what happens, the United States is going to lose here.''

The Rangers played their best game of the Stanley Cup playoffs at Madison Square Garden last night, but the Islanders played their usual excellent game and won, 4-3, after exactly three minutes of overtime. The victory gave the Islanders a 2-1 lead in the four-of-seven quarterfinal series, which continues tonight at the Garden. The Islanders won on a backhand shot from the right side of the Ranger net by Bryan Trottier, who had recovered the rebound of a shot from near the blue line by Ken Morrow. Trottier's shot was not a hard one, but it hit the top of Ed Mio's left leg pad and bounced behind the Ranger goalie to win the game as most of the 17,392 spectators groaned.

Charles Darwin died on April 19, 1882, and 40 free-thinking philosophers and scientists who held a symposium here this weekend agreed that 100 years later a lot of unfinished business remained. The scholars, including some of the leading lights in what the Moral Majority labels secular humanism, talked of the ''raging debate'' and ''Neanderthal undercurrents'' that persist around Darwin's findings about evolution. The scientists among them were unanimous that there was no longer any question about the validity of the evidence supporting Darwin but that much work was left to allow evolution to be freely taught in the United States. ''In my experience, those who are the most vehement in attacking evolution know the least about it,'' said Charles Cazeau, an associate professor of geology at the State University of New York at Buffalo, where the conference was held.