# Scholar Finds Ancient Way To Think Mathematically

PARIS — A ROTUND, fish-eyed legal-scholar-turned-mathema-tician, poring over ancient tablets in a quest for long-forgotten wisdom, uncovers mathematical equations that challenge one of the foundations of Western knowledge.

If Hollywood were writing the script, no doubt the story would unfold in the sand and rocks of some exotic archaeological ruin, with shadowy lighting and cymbal-heavy music all around.

As it turns out, the settings are much more prosaic: a university museum and a cramped walk-up apartment in Paris's quiet, residential 16th arrondissement, where Lucio Gaidorou-Astori, independent researcher and disciple of pre-Hellenistic mathematics, presses his search for ``a more complete wisdom'' than Western-based knowledge sometimes offers.

After careful study of 4,000-year-old stone tablets of the Mesopotamic period, one of which he viewed at New York City's Columbia University, in his Paris home Mr. Gaidorou-Astori came up with a theorem that he says allows for resolving equations relative to right triangles without using squared numbers.

The famous Pythagorean theorem, a2 + b2 = c2, where c is the hypotenuse and a and b the smaller sides of a right triangle, existed well before Pythagoras in an equation without squared numbers, Gaidorou-Astori says. And it proceeded from a different way of thinking from that of ancient Greece, he adds.

Since the news was carried across European wire services over the summer, the scholarly Italian's work has garnered growing attention. Journalists harboring unpleasant memories of the labors Pythagoras and his theorem put them through in high school seemed especially eager to take a jab at the ancient Greek.

``He who uprooted Pythag-oras,'' punned the Quotidien de Paris, a Paris daily, in a full-page article on Gaidorou-Astori. ``Good-bye, Pythagorean theorem, as a mathematical diktat,'' Milan's Corriere della Sera crowed.

More recently, the Italian researcher, born between the two world wars, used his ``ancient'' methods to present a new demonstration of 17th-century mathematician Pierre Fermat's enigmatic theory concerning the nth power of numbers.

``It's a different solution from what the Briton Andrew Wiles revealed earlier this year,'' he says, referring to the British mathematician's widely publicized solution to Fermat's theory last spring. ``But the two solutions, including one using different methods developed by the ancients, can enrich our understanding of science.''

For Gaidorou-Astori, the interest of his work is not in toppling a towering ancient like Pythag-oras, whose work he respects deeply, or in rivaling a contemporary mathematician. What motivates him, he says, is the investigation of another, earlier way of thinking, which he believes can benefit today's world but which has been lost in the limited scope of Western thought.

``We refer to the Greeks as our philosophical fathers, as if they came out of a spontaneous generation,'' Gaidorou-Astori says. ``If I have dedicated so much time to studying the work of the Egyptians and Mesopotamians, it's because I think we can find there certain paths, certain illuminations revealing not just a different way of thinking, but perhaps some different solutions to some of our problems.''

When Corriere della Sera wrote recently about the Italian researcher's work, the newspaper titled its piece with the quote, ``With their equations, the Sumerians could have gone to the moon.''

``Obviously they weren't technologically advanced enough to make that trip,'' says a chuckling Gaidorou-Astori of his quote about the ancient Mesopotamian people. ``But with their equations they could have controlled the trajectory of a rocket with the moon as its destination.''

Gaidorou-Astori does not work in a university setting and says that the independent nature of his research has allowed him to go farther in uncovering the ancient scholars' procedures.

``I think the originality of my research is due to the fact that it has been done outside the university and the accepted families of thinking,'' he says.

Although he has presented his methods at a number of Egyptologist conferences and has had his theorems approved by noted mathematicians, he continues to favor the method of the lone researcher.

If the quick-smiling, slightly quixotic researcher hopes to accomplish any one thing with his work, it is to render modern mathematics ``less abstract.''

``What this new-old theorem of right triangles demonstrates is that the existence of `whole' right triangles is a pure convention,'' says Gaidorou-Astori. ``What my work does is to honestly reintroduce the human factor, which always has its part in mathematical work, even today's,'' he adds.

He would like to encourage a ``marriage'' of what he considers two different procedures - ultimately two different ways of approaching a problem - which he believes could unite the advantages of the two.

Acknowledging that the work of the pre-Hellenistic ancients was often less simply formulated - the length of his own ``right triangle theorem'' is an example - Gaidorou-Astori says that, ``What we would lose in rapidity, we might gain in wisdom.''