Contemporary society likes to think that it has advanced far beyond the science of its forebears, but in one important area — mathematics — the greatest geniuses lived and died hundreds of years ago. Today’s mathematicians are still trying to grasp and build upon everything those intellectual giants formulated, says Ronald Calinger, a CUA history professor whose specialty is the history of mathematics.
The four greatest mathematicians of all time, according to Calinger and many contemporary mathematicians, are the ancient Greek Archimedes (circa 287–212 B.C.), the Englishman Isaac Newton (1642–1727), the Swissborn Leonhard Euler (1707–1783), and the German Carl Friedrich Gauss (1777–1855). No living mathematician seems to approach their depth of genius, Calinger says.
The one of these four with the broadest range of seminal discoveries — Euler — has never had a fulllength biography written about him, though he was one of the greatest and most prolific mathematicians and scientists the world has ever known. Professor Calinger plans to rectify that situation soon: His biography of Euler (pronounced like “oiler”) is scheduled to be published by Princeton University Press in 2009.
Also the editor of an ongoing series of books on the history of mathematics published by the Johns Hopkins University Press, Calinger came to his specialty as a result of his longtime desire to combine the interests of his parents — his mother liked to study history and his father, math. The combination seems inspired: Many consider Calinger to be one of the nation’s most influential historians of mathematics.
The 20thcentury historian and philosopher Michel Foucault likened mankind’s current scientific knowledge to a fabric that separates humanity from an ocean of yet undiscovered knowledge. Only the work of a genius can create a rip in the fabric, he wrote, allowing a flood of knowledge to rise through it and transform the world’s understanding of different sciences. Euler was just such a knowledgereshaping genius, says Calinger.
In particular, Euler systematized differential and integral calculus and was the principal inventor of four of its core branches: the calculus of variations, differential geometry, differential equations and infinite series. He applied those discoveries to every science of his day, improving telescopes and shipbuilding and revolutionizing physics and astronomy as well as mathematics. “Through the phenomenal success of Euler’s application of calculus to the sciences, he was the one primarily responsible for making astronomy and optics into modern exact sciences,” says Calinger. “Without his discoveries, we couldn’t do space flight and modern engineering.”
The Swiss mathematician still has a lot of fans among the cognoscenti. In 1988, the journal Mathematical Intelligencer asked its readers to list what they considered to be the most beautiful equations in mathematics. Three of their top five equations were discovered by Euler.
Though he isn’t currently well known outside of the worlds of math and physics (and outside of Switzerland where his face appeared on the country’s 10franc bill from 1975 to 1995), Euler didn’t toil in obscurity during his lifetime. During the latter half of his life, he was considered to be Europe’s second most famous thinker, after Voltaire, Calinger reports.
The CUA professor wants his Euler biography to be understandable and interesting to everyone from math and physics professors to historians of the Enlightenment to high school students with a strong interest in math. The book will probe Euler’s mathematical and mechanical discoveries, but without including lots of equations and complex mathematical explanations. “As a matter of fact,” Calinger quips, “there’s a rule: Put one equation in a book and you lose half your audience.” He does admit he’ll need to have some equations in the text, but most will be relegated to endnotes and mathintensive appendices.
Like fellow math geniuses Newton and Gauss, Euler was a devout Protestant — in his case, a Calvinist of a variety that emphasized the love of God. “Euler was atypical because he was deeply religious during a time when most of the leading Enlightenment thinkers had doubts about the beliefs and institutions of Christianity,” says Calinger.
“I’m grateful to be writing about someone I like,” adds the professor. “Euler was an admirable person. He enjoyed telling stories and jokes, made friends easily, and gave others the credit for discoveries that he actually helped make.” — R.W.
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