resist the approach and conclusions of Lakoff and Núñez. Reviews of WMCF by mathematicians in professional journals, while often respectful of its focus on conceptual strategies and metaphors as paths for understanding mathematics, have taken exception to some of the WMCFs philosophical arguments on the grounds that mathematical statements have lasting 'objective' meanings. For example, Fermat's Last Theorem means exactly what it meant when Fermat initially proposed it 1664. Other reviewers have pointed out that multiple conceptual strategies can be employed in connection with the same mathematically defined term, often by the same person (a point that is compatible with the view that we routinely understand the 'same' concept with different metaphors). The metaphor and the conceptual strategy are not the same as the formal definition which mathematicians employ. However, WMCF points out that formal definitions are built using words and symbols that have meaning only in terms of human experience. Critiques of WMCF include the humorous: and the physically informed: Lakoff made his reputation by linking linguistics to cognitive science and the analysis of metaphor. Núñez, educated in Switzerland, is a product of Jean Piaget's school of cognitive psychology as a basis for logic and mathematics. Núñez has thought much about the foundations of real analysis, the real and complex numbers, and the Basic Metaphor of Infinity. These topics, however, worthy though they be, form part of the superstructure of mathematics. Cognitive science should take more interest in the foundations of mathematics. And indeed, the authors do pay a fair bit of attention early on to logic, Boolean algebra and the Zermelo–Fraenkel axioms, even lingering a bit over group theory. But neither author is well-trained in logic, the philosophy of set theory, the axiomatic method, metamathematics, and model theory. Nor does WMCF say enough about the derivation of number systems (the Peano axioms go unmentioned), abstract algebra, equivalence and order relations, mereology, topology, and geometry. Lakoff and Núñez tend to dismiss the negative opinions mathematicians have expressed about WMCF, because their critics do not appreciate the insights of cognitive science. Lakoff and Núñez maintain that their argument can only be understood using the discoveries of recent decades about the way human brains process language and meaning. They argue that any arguments or criticisms that are not grounded in this understanding cannot address the content of the book. It has been pointed out that it is not at all clear