Eugen von Böhm-Bawerk · 1894
Böhm-Bawerk’s review of Knut Wicksell’s 1893 book combines an appreciative assessment of its theoretical contribution with a sustained argument about mathematical method in economics. Its governing distinction is between mathematics as an aid to research and mathematics as a medium of exposition: valuable for checking economic reasoning, formal calculation can nevertheless obscure faulty premises and impede persuasion.
The opening places Wicksell within the international renewal of economic theory associated with Jevons, Walras, and Austrian economists. Böhm-Bawerk welcomes Scandinavian participation because it involves independent criticism, not merely the transmission of established doctrines. Wicksell seeks both substantive improvements and more exact formulations. His principal contributions concern capital and rent, fields Böhm-Bawerk regards as less developed than value theory. Working substantially within the reviewer’s own theory of capital and interest, Wicksell challenges details and proposes extensions, notably the incorporation of land services and land rent into the relationship between interest and wages. Böhm-Bawerk praises these contributions while reserving their detailed evaluation for another occasion.
The review then turns from theoretical substance to method. Wicksell’s successful and restrained use of mathematics prompts Böhm-Bawerk to reconsider his reservations, but does not substantially alter his judgment:
Wir trennen uns, wenn ich nicht irre, erst bei der Frage des verhältnismässigen Gewichts, das wir jedem dieser Momente zuerkennen wollen, eine Frage, deren Beantwortung dann aber freilich für den Ausfall der Gesammtbilanz entscheidend ist.
English translation: We part company, if I am not mistaken, only on the question of the relative weight which we wish to concede to each of these factors, a question whose answer, however, is then of course decisive for the outcome of the overall balance.
The disagreement thus concerns the weighting of shared considerations rather than mutually exclusive standards of inquiry. Böhm-Bawerk grants that formulas can express complicated relationships more economically, precisely, and generally than verbal reasoning supplemented by numerical examples. They can also check conclusions reached through ordinary logic. Yet formal correctness does not guarantee economic validity:
Für die Forscher besteht die grosse Gefahr, dass der Mathematiker in ihnen dem Nationalökonomen durchgeht und vermeintliche Problemlösungen aus Ansätzen herausrechnet, die mathematisch untadelig scheinen, nationalökonomisch aber es durchaus nicht sind.
English translation: For investigators there exists the great danger that the mathematician in them runs away with the economist, and that they compute supposed solutions of problems out of formulations which appear mathematically irreproachable, but which economically are by no means so.
Wicksell’s own warnings against sacrificing economic truth to mathematical elegance support this objection. Böhm-Bawerk treats failures of mathematical economics as evidence of an additional methodological danger, not as grounds for rejecting mathematics outright. The substantive economic judgment embodied in the premises remains decisive.
His strongest reservation concerns readers. Few economists, he argues, can or wish to follow advanced formal exposition. He candidly admits that he cannot follow every part of Walras or Auspitz and Lieben; even partial comprehension may leave him unable to detect substantive errors confidently. This matters because scholarly conviction requires more than a correct result: an argument must remain accessible to critical scrutiny. Difficult notation can provide an entrenched opponent with another reason to resist a new theory. For the wider readership, the influence of Smith and Mill illustrates the intellectual importance of lucid, engaging exposition.
Böhm-Bawerk’s practical conclusion separates the researcher’s tools from the author’s presentation. Were he fully proficient in mathematics, he would use calculation extensively to support and check reasoning that remained economic in its foundations. Publication calls for greater restraint:
Im Texte würde ich nur solchen Formeln und Constructionen Aufnahme gewähren, die von geradezu packender Klarheit und Uebersichtlichkeit sind.
English translation: In the text I would grant admission only to such formulas and constructions as are of downright compelling clarity and perspicuity.
More demanding material should appear selectively in notes or appendices, preserving access for readers without mathematical training. The closing commendation credits Wicksell with unusual moderation and affirms Böhm-Bawerk’s willingness to read him even when he writes mathematically. The review’s significance lies in this qualified welcome: it recognizes mathematical economics as an international movement attracting exceptional thinkers while insisting that precision, economic soundness, and communicability remain distinct achievements.
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