athematics is one academic subject that would seem to reside in a world of universality, protected from competing opinions by the objectivity of its laws. But the real universal law is that everything is relative, even in math. The release last month of a new math curriculum for New York City schools by Mayor Michael R. Bloomberg has elicited something just short of vituperation. Back-to-basics advocates denounce as ''fuzzy math'' its inclusion of so-called constructivist teaching techniques. Critics complain that those approaches encourage self-discovery and collaborative problem-solving at the expense of proved practices like memorization, repetition and mastery of algorithm.

It's all the latest in a century of American math wars. The previous generation can remember the struggle over ''new math'' during the 1950's and 60's. (''Hooray for new math,/New-hoo-hoo math!'' Tom Lehrer sang. ''It won't do you a bit of good to review math./It's so simple,/So very simple./That only a child can do it!'') Battles flared even earlier in the century over ''progressive'' agendas for math education of the type pushed by John Dewey.

How tame those struggles seem, however, when compared to the rising vanguard of self-described ethnomathematicians. For some, the new discipline just means studying the anthropology of various measurement methods; they merely want to supplement the accepted canon -- from Pythagoras to Euclid to Newton -- with mind-expanding explorations of mathematical ideas from other cultures. For others, however, ethnomathematics is an effort to supplant the tyranny of Western mathematical standards.

The Postulates

Ethnomathematics has a few parents, but most observers trace its formal birth to a speech given by the Brazilian mathematician Ubiratan D'Ambrosio in the mid-1980's. Now an emeritus professor of math at the State University of Campinas outside S-o Paulo, he explained his thinking a couple of years ago to The Chronicle of Higher Education: ''Mathematics is absolutely integrated with Western civilization, which conquered and dominated the entire world. The only possibility of building up a planetary civilization depends on restoring the dignity of the losers.'' Robert N. Proctor, who teaches the history of science at Pennsylvania State University, says he wants to counter the notion ''that the West is the be all and end all'' when it comes to mathematical studies. ''After all,'' he adds, ''all math is ethnomath -- not just African kinship numerics or Peruvian bead counting, but also the C.I.A.'s number-crunching cryptology and Reaganomics.''

To redress their pedagogical grievances, these ethnomathematicians want math curriculums that place greater emphasis on the systems of previous civilizations and certain traditional cultures. Studies of state civilizations might focus on Chinese or Arabic math concepts. One study, for example, has shown how the Chinese Chu Shih-chieh triangle anticipated by more than three centuries the highly similar arrangement of numerals by Pascal that holds sway in many Western teachings of probability theory.

In her seminal books ''Ethnomathematics'' and ''Mathematics Elsewhere,'' Marcia Ascher, emerita professor of mathematics at Ithaca College, chronicles the astonishingly complex data-storage systems embedded in quipu, bundles of cotton cord knotted by Incans according to a sophisticated base-10 numeration system. At a more quotidian level, Ron Eglash of Rensselaer Polytechnic Institute has written and taught extensively about the nuances of fractals, or repeating patterns, that can be found in certain African craft work. (Eglash stresses a distinction between simple-minded multicultural math -- ''which merely replaces Dick and Jane counting marbles with Tatuk and Esteban counting coconuts'' -- and what he calls the ''deep design themes'' that represent mature, developed mathematical systems too often ignored in the study of many societies.)

What Its Critics Fear

Some of this is just fine, says David Klein, a professor of mathematics with California State University at Northridge. Klein (a self-described liberal who insists on separating his academic critique from any connection to a conservative political agenda) says the danger lies in allowing such precepts to crowd out fundaments on which modernity is based. He argues that the statistically lower achievements of some female and minority math students have resulted in an overreaction that doesn't serve their interests. ''The practical effect,'' Klein says, ''has been watered-down math books that overemphasize inductive reasoning (like continuing visual patterns), because this is supposed to be good for women and minorities, and de-emphasizing deductive reasoning and mathematical proofs, which is the heart of mathematics, because that supposedly favors white males.

''But mathematics is a worldwide monoculture. Look at the chalkboards in math departments at universities all around the world -- in Africa, Asia, Europe, Latin America. You will see the same symbols everywhere you go on this planet, except perhaps in colleges of education where fads reign supreme.'' Klein says he does spend some class time discussing the math of Mayans, Egyptians and other early civilizations. ''But ancient techniques and early discoveries in math will not take students very far who want to do something in the modern world with mathematics,'' he says.

Will It Pass?

Some proponents argue that whatever the freestanding authenticity of the cross-discipline, it is useful as a carrot to attract indifferent students. Philip Straffin, who has been teaching the popular ''Cultural Approaches to Mathematics'' at Beloit College for about 10 years, says that the lectures lure a mix of teachers in training and art students: ''Every time we give this course, there are twice as many students who want to take it as we have room for.'' As long as such developments complement and enhance rather than take time from and substitute for other mathematics learning, Judith Grabiner, who teaches at Pitzer College, says they are a plus. ''I don't want people teaching students that Mohammed ibn Musa al-Khwarizmi gave a systematic treatment of quadratic equations in the 10th century instead of learning how to solve quadratic equations,'' she says. ''But that's a false choice. Putting the math in its cultural context helps teach the mathematics and makes it more meaningful to students, since it has a human context.''

Indeed, those who think this threatens to spawn a brave new world of mathematical correctness might search their memories to recall if they didn't have a fourth- or fifth-grade teacher who brought an abacus to class.