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Published by EH.NET and H-Business (August 2002) 
 
E. Roy Weintraub, _How Economics Became a Mathematical Science_. Durham, 
NC: Duke University Press, 2002. xiii+ 313pp. ISBN 0-8223-2871-2. 
 
Reviewed for EH.Net by Robert D. Tollison, Department of Economics, 
University of Mississippi. <[log in to unmask]> 
 
Professor Weintraub has given us two books in one. First, he traces from 
Marshall forward how high-level mathematics came into and changed the 
presentation of modern economics. What he means by mathematics is set 
theory and the type of axiomatic proof offered by Arrow and Debreu in their 
famous "existence" paper. Second, he tells the story of his father, Sydney 
Weintraub, who was a pioneer in mathematical economics, his father's 
influence over his son's work in economics, and the shaping of his son's 
intellectual agenda as a renowned historian of economics. Math happily runs 
in the Weintraub family. 
 
His methodology is biographical. He relates many interesting stories of 
mathematicians and economists and their interactions and intersections, at 
times (as with Debreu) reporting discussions that he had with them. Stigler 
to the contrary not withstanding, Professor Weintraub amply demonstrates 
the value of a biographical approach to the history of science. Along the 
way, we meet names that are familiar (Patinkin) and some new names 
(Volterra) from the little known world between economics and mathematics. 
Particularly fascinating is the tale of the editorial review of the 
Arrow-Debreu paper by Econometrica, in which the mathematician referee 
(Phipps) argued strenuously against publication while the economist referee 
(Baumol) easily acquiesced. 
 
To me the central message of the book is that axiomatic economic theory was 
a by-product of the intellectual curiosity of cerain economists and 
mathematicians working on the boundaries of their disciplines. But for 
these personalities, there may not have been an axiomatic economics. In 
this respect the biographical method is the core contribution of the book. 
And, of course, Weintraub is correct. Great economists are highly 
specialized resources, and the history of economics is undoubtedly greatly 
influenced by their preferences and constraints. In this way we are the 
product of our own science. Axiomatic proofs became a part of modern 
economics because scientific entrepreneurs discovered their usefulness and 
import. The only oddity in this case is that we know who the economists 
were but not for the most part the mathematicians. Weintraub brings these 
scholars to light. 
 
I have nothing critical to say about the book. It is an important 
contribution to the history of economics, it is interesting in all 
respects, and I recommend it to economists and historians of science. Ah, 
but I do have a few quibbles. 
 
The first concerns the focus on the axiomatic mathematics that has enabled 
general equilibrium theory to play such a prominent role in modern 
economics. While quite important in its own right, this focus deflects us 
from such issues as the role of R.G.D. Allen's textbook, as well as 
Samuelson's Foundations. These works did not lead to existence theorems, 
but they were very important in changing the presentation of modern 
economics. Perhaps some distinction between higher and lower mathematics 
would be helpful here. It could be argued, for example, that calculus has 
had more useful effects in economics than set theory. 
 
The second quibble is empirical in nature. The latter part of the last 
century saw the rise and fall of mathematical economics. If one examines 
the leading journals of economics, for example, the American Economic 
Review, from 1950-2000, the number of equations per page has been in 
decline since the early 1980s. For whatever reason, mathematical 
presenttion is on the wane. What are the causes of this development? Is 
there a turn away from math? Is the level of math the same, with the result 
being driven by a more concise presentation? There is work to be done here. 
 
A related and final quibble is that the data may be suggesting that math 
has diminishing returns in economics. Indeed, economics has diminishing 
returns in that any science is finite; there is only so much that we can 
learn. And the data indicate that citations to economic research have 
fallen dramatically over recent years. Are we at the end of economics? Have 
all the crucial relationships been discovered? Is mathematical economics 
the capstone to the history of our discipline? Does mathematical economics 
mean that once we are able to express ourselves in so precise and general a 
way, there is little of value left to say? 
 
These, of course, are all subjects for another time. For now, let us salute 
Professor Weintraub for his excellent and stimulating book. One can only be 
heartened at Duke's continuing preeminence in and emphasis on the history 
of economics. 
 
Robert D. Tollison is the author of numerous books and papers. He is a 
Senior Editor of Public Choice, and a past President of the Southern 
Economic Association and the Public Choice Society. 
 
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