Forty years ago, Paul A. Samuelson was a household name. The first American Nobel laureate in economics, he wrote a regular column for Newsweek (alternating with Milton Friedman) and was widely remembered as President Kennedy’s personal economics tutor. Hundreds of thousands of college students each year were introduced to the principles of economics through his best-selling textbook—the most successful economics textbook ever written.

Today Samuelson, who died in 2009 at age 94, is no longer so familiar to the general public, nor does “Economics” (1948) still stand atop the textbook heap (although its current, 19th edition—edited by William Nordhaus—sells well). But Samuelson left a deep and abiding impression on his field. He, Kenneth Arrow and John Maynard Keynes are arguably the most important creative economists of the 20th century. (Friedman was also immensely influential, but—except in his magisterial volume with Anna Schwartz on U.S. monetary history—more as a public intellectual than an economic researcher.) If Samuelson’s papers no longer appear frequently on graduate-course reading lists, it’s only because their lessons have been so thoroughly absorbed into the subject. Physics students no longer read Newton’s “Principia,” either.

The first volume of Roger E. Backhouse’s two-volume biography, “Founder of Modern Economics,” makes the case for Samuelson’s importance, and largely succeeds. Mr. Backhouse—who here gives us the story through 1948, when Samuelson was 33—notes that the life was neither dramatic nor especially colorful, and so concentrates mainly on Samuelson’s work and the people who influenced him.

Unlike Arrow (the father of social choice theory) or Keynes (who revolutionized macroeconomics), Samuelson created no new branch of economics. Instead, as the 1970 citation from the Royal Swedish Academy observes, his distinctive contribution was “raising the level of analysis in economic science.” He modernized the discipline.

Economics was hardly devoid of mathematics before Samuelson; such 19th-century economists as Léon Walras, A.A. Cournot and F.Y. Edgeworth invoked it freely. But even by 1950 many prominent economic scholars—including Jacob Viner, who taught Samuelson at the University of Chicago—had little mathematical skill and were skeptical that math was useful in economics. Alfred Marshall, the foremost economist at the turn of the 20th century, was no mathematical slouch but wrote that mathematics should be used as a “shorthand language, rather than as an engine of inquiry.” And once the inquiry was done, the mathematics should be “translated into English”—and then “burned.”