July 19, 1983

Hunger is emerging again as a national issue even as Government stocks of surplus dairy products rise to record levels. The United States Conference of Mayors recently declared that hunger had become ''the most prevalent and the most insidious'' problem facing the nation's cities. The General Accounting Office, an investigative arm of Congress, reported that while ''no one knows precisely how many Americans are going hungry,'' visits to food distribution centers across the country found that hunger had increased in the last two years, partly as a result of high unemployment. An Appeal to Government The National Association of Counties, pleading for Federal help in dealing with a heavy human services caseload, called Sunday for expanded Federal food distribution programs and restoration of food stamp cutbacks.

A German has solved a problem that has baffled mathematicians for more than 60 years and has taken a major step toward solving another that has stumped the profession for three centuries. The German mathematician is Dr. Gerd Faltings, 29 years old, of Wuppertal University, in Wuppertal, West Germany. The problems he has solved lie in the esoteric realms of number theory and algebraic geometry; they relate to the number of solutions that exist for certain kinds of mathematical equations. A 40-page manuscript by Dr. Faltings is now circulating among American mathematicians and is sparking ripples of excitement. Serge Lang, professor of mathematics at Yale University, said Dr. Faltings has solved ''one of the outstanding problems of the century.''

The American educational system has ''deeply entrenched and virtually chronic'' problems and should undergo ''far-reaching restructuring,'' according to a comprehensive study that involved eight years and more than 27,000 interviews. The report, ''A Study of Schooling,'' portrays public school classrooms on all grade levels as a world of talky teachers and uninterested students, who work in a context of unclear goals and serious social and educational inequities. ''American schools are in trouble,'' said the study's director, John I. Goodlad, former dean of the Graduate School of Education at the University of California at Los Angeles. ''Large numbers of students are leaving school ill-prepared for jobs and effective citizenship, and even many of those who appear to be 'making it' are short-changed.'' 43 Researchers Aided Him Mr. Goodlad's study consisted of systematic classroom observation by 43 researchers in 13 communities, as well as questionnaires and interviews. It was sponsored by the Institute for the Development of Educational Activities, an independent reserch organization.

Tax shelters -investment devices designed to shelter income from taxation, usually for a period of years - appear to be on the rise, despite widespread predictions that lower tax rates would reduce their use. Furthermore, experts say the shelters are increasingly spreading from the investment portfolios of the rich to those of the middle class, some with no more than $5,000 to invest. And although certain kinds of tax shelters, such as those dealing with oil and gas, appear to have lost some of their allure during the recent recession, others, such as those in real estate, seem to hold more attraction than ever. ''There's been tremendous activity in the past few months,'' said Douglas W. Banks, a real estate specialist in the Washington office of Touche, Ross & Company, a major accounting firm. Limited Partnerships Measuring tax shelter activity is difficult. In fact, there is no formal definition of just which of a vast array of tax-favored activities should be regarded as shelters. But at least one measure, the public sale of investments registered as limited partnerships, which is how most tax shelters are sold, shows enormous growth.

Private banks virtually suspended new lending to developing countries and to smaller industrial nations during the first quarter, a major international financial instituion reported today. If such cutbacks continued, they could abort the emerging economic recovery, it added. In its latest quarterly report on bank lending, the Bank for International Settlements in Basel, Switzerland, said the lending to the third world and smaller industrial nations, after deductions of repayments of loans outstanding, came to only $500 million in the January-March period. By comparison, lending totaled $9 billion in the last three months of 1982 and averaged $9.8 billion in each quarter last year. During 1981, banks made new loans totaling $65.5 billion to the third world and the smaller industrial nations, an average of almost $16.4 billion a quarter.