Marshall was unable to render an appropriate portrayal of the market. For the correct three-dimensional depiction of a market see Wikimedia AXEC001 and for the underlying rationale see (2014a).
Marshall could not tell the difference between profit and income which is not exactly a recommendation for an economist. For the correct Profit Law see (2014b).
Marshall's application of mathematics bordered on utter dilettantism: “In patriotic duty bound, the Cambridge of Newton adhered to Newton’s fluxions, to Newton’s geometry, to the very text of Newton’s Principia … Thus English mathematics was isolated: Cambridge became a school that was self-supporting, self-content, almost marooned in its limitations.” (Forsyth, quoted in Mirowski, 2004, p. 355)
“Marshall … was a product of this system, which valued … down-to-earth geometry over continental analysis, and regimented conformity in puzzle solving and humble prostration before timeless truths over originality.” (Mirowski, 2004, p. 355)
Quite unsurprisingly, Marshall applied mathematics incorrectly. “As was standard with Marshall, the narrative told one story, the mathematics another.” (Mirowski, 1995, p. 299)
Compare Marshall's approach to the creative use of mathematics in physics: “Experience can of course guide us in our choice of serviceable mathematical concepts; it cannot possibly be the source from which they are derived; experience of course remains the sole criterion of the serviceability of a mathematical construction for physics, but the truly creative principle resides in mathematics.” (Einstein, 1934, p. 167)
The botched application of mathematics by Marshall and the Orthodoxy is no reason to dismiss it. “When very sound and proper mathematics is misused and misapplied to fairyland problems without any basis in the real world, that fact that the mathematics itself is impeccable makes the whole obnoxious game just that more offensive.” (Blatt, 1983, p. 173)
Rule number one of the good hand and brain craftsman: never blame the tool. Not much of Marshall will be part of truly scientific economics. Certainly not his burn-phrase. This is the way forward: “... perhaps the most legitimate research program in economics should generate its own mathematical tools simultaneously with its development of the economic theory, ...” (Mirowski, 1986, p. 221), see also (Velupillai, 2005, pp. 866-870), (Morishima, 1984, p. 67)
To cite Marshall on mathematics is self-defeating.
Blatt, J. (1983). How Economists Misuse Mathematics. In A. S. Eichner (Ed.), Why Economics is Not Yet a Science, 166–186. Armonk: M.E. Sharpe.
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science, 1(2): 163–169. URL
Kakarot-Handtke, E. (2014a). Economics for Economists. SSRN Working Paper Series, 2517242: 1–29. URL
Kakarot-Handtke, E. (2014b). The Three Fatal Mistakes of Yesterday Economics: Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
Mirowski, P. (1986). Mathematical Formalism and Economic Explanation. In P. Mirowski (Ed.), The Reconstruction of Economic Theory,179–240. Boston, Dordrecht, Lancaster: Kluwer-Nijhoff.
Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University Press.
Mirowski, P. (2004). The Effortless Economy of Science?, chapter Smooth Operator: How Marshall’s Demand and Supply Curves Made Neoclassicism Safe for Public Consumption but Unfit for Science. Durham, London: Duke University Press.
Morishima, M. (1984). The Good and Bad Use of Mathematics. In P. Wiles, and G. Routh (Eds.), Economics in Disarray, 51–73. Oxford: Blackwell.
Velupillai, K. (2005). The Unreasonable Ineffectiveness of Mathematics in Economics. Cambridge Journal of Economics, 29: 849–872.