Above, Norman L. Roth gave a fine characterization of Marshall. I have nothing to add, except that nobody doubts Marshall's personal qualities. However, they are not relevant to the question of why Marshall openly downgraded mathematics.
Marshall was well acquainted with the Cambridge version of mathematics which focused on geometry. Now, you cannot study geometry and Newton without coming across Euclid. In my mind, nobody who understands only a little of Euclid's role in the history of science can ever say ‘Burn the mathematics.’
Newton's Principia starts with the famous 'Axioms, or the Laws of motion' and the role of Euclidean geometry in Newtonian physics cannot be overestimated. “During five years, Humphrey saw Newton laugh only once. He had loaned an acquaintance a copy of Euclid. The acquaintance asked what use its study would be to him. ‘Upon which Sir Isaac was very merry.’ (Westfall, 2008, p. 192)
There is a direct line of highest praise from Newton to Einstein: “We honour ancient Greece as the cradle of western science. She for the first time created the intellectual miracle of a logical system, the assertions of which followed one from another with such rigor that not one of the demonstrated propositions admitted of the slightest doubt -- Euclid's geometry. This marvellous accomplishment of reason gave to the human spirit the confidence it needed for its future achievements. The man who was not enthralled in youth by this work was not born to be a scientific theorist.” (Einstein, 1934, p. 164)
And this last sentence contains my argument against Marshall's mathematical competence.
Curiously, there is one among the Top 20 heterodox economists, who understood better than Marshall what mathematics was all about: “We are therefore justified in saying that with Euclid's Elements the causa materialis of geometry underwent a radical transformation; from a more or less amorphous aggregate of propositions it acquired an anatomic structure. Geometry itself emerged as a living organism with its own physiology and teleology,... And this true mutation represents not only the most valuable contribution of the Greek civilization to human thought but also a momentous landmark in the evolution of mankind comparable only to the discovery of speech or writing.” (Georgescu-Roegen, 1966, p. 9)
There is no better way to run Heterodoxy into the ground than to forget what Georgescu-Roegen has said about mathematics and to praise what Marshall has said.
Paul Schächterle correctly observes: “In economics, the hard part is to get reasonable axioms. So any modeling in economics should be based on very thorough reasoning what assumptions were made, why they were made, what was possibly omitted etc.”
The claim of Heterodoxy to replace Orthodoxy with something better implies the replacement of the accustomed behavioral axioms with something better. This is called a Paradigm Shift. There is no way around this.
Burn the neoclassical axioms! And then take these on Wikimedia AXEC121i.
Einstein, A. (1934). On the Method of Theoretical Physics. Philosophy of Science, 1(2): 163–169. URL
Georgescu-Roegen, N. (1966). Analytical Economics, chapter General Conclusions for the Economist, 92–129. Cambridge: Harvard University Press.
Westfall, R. S. (2008). Never at Rest. A Biography of Isaac Newton. Cambridge: Cambridge University Press, 17th edition.