This would be like saying written language is reducible to words. Stories reducible to their constituent sentences. Mathematics does more than that. The entities of mathematics may be abstract objects - conceived in a Platonic or formalistic sense -, but what they are concerned with are not necessarily abstract objects.
It's often forgotten that people do mathematics, they make it through a series of creative leaps in a space of rational connections. The space itself is conditioned by its history through its internalisation of previous creations as rules and topics of study. Further, these rules and topics are always avenues of further expression and coalescing forms of expanding (phenomenally demarcated, formalised, symbolically mediated) sense. Mathematics is an interplay of its history with the creative, interpretive and synergistic acts of its current practitioners, especially researchers. In this regard, it resembles any form of rational inquiry.
There is a relevant question whether the function of mathematical objects is reducible to the instantiation/conditioning of its objects of concern within some stratum of being. Be the concerns of mathematics real (modelling, interface with the actual and its potentials, the domain of applied mathematics) or ideal (imaginative, interface with its own objects and their potentials, the domain of pure mathematics); mathematical objects function in mathematised forms of inquiry. They don't sit around doing nothing in a pre-individuated realm distinct from mathematical history or the patterns in things. This suggests that mathematical objects function to the concerns of their imaginative background (constrained by the historicality of mathematics manifesting as given rational structures), and insofar as that imaginative background reflects the unfolding of material components, mathematical objects are as real as the mathematised reality they partake in.
This is to say: mathematical objects aren't purely ideal abstractions, in the same way that ideation in general can produce patterns (behavioural, material=actual/potential) acting as the embodiment of ideas. Like "I'm going for lunch now', and I'm off to lunch.
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It's often forgotten that people do mathematics, they make it through a series of creative leaps in a space of rational connections. The space itself is conditioned by its history through its internalisation of previous creations as rules and topics of study. Further, these rules and topics are always avenues of further expression and coalescing forms of expanding (phenomenally demarcated, formalised, symbolically mediated) sense. Mathematics is an interplay of its history with the creative, interpretive and synergistic acts of its current practitioners, especially researchers. In this regard, it resembles any form of rational inquiry.
There is a relevant question whether the function of mathematical objects is reducible to the instantiation/conditioning of its objects of concern within some stratum of being. Be the concerns of mathematics real (modelling, interface with the actual and its potentials, the domain of applied mathematics) or ideal (imaginative, interface with its own objects and their potentials, the domain of pure mathematics); mathematical objects function in mathematised forms of inquiry. They don't sit around doing nothing in a pre-individuated realm distinct from mathematical history or the patterns in things. This suggests that mathematical objects function to the concerns of their imaginative background (constrained by the historicality of mathematics manifesting as given rational structures), and insofar as that imaginative background reflects the unfolding of material components, mathematical objects are as real as the mathematised reality they partake in.
This is to say: mathematical objects aren't purely ideal abstractions, in the same way that ideation in general can produce patterns (behavioural, material=actual/potential) acting as the embodiment of ideas. Like "I'm going for lunch now', and I'm off to lunch.