We analyse the fluctuations of the ground-state/funnel solutions proposed to describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter ABJM theory of multiple membranes. We show that in the large N limit the fluctuations approach the space of functions on the 2-sphere rather than the naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in the context of Matrix Theories, which uses bifundamental instead of adjoint scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory on R 2,1 × S 2 is recovered at large N , which is consistent with a single D4-brane interpretation in Type IIA string theory. This is as expected at large k, where the semiclassical analysis is valid. Several aspects of the fluctuation analysis, the ground-state/funnel solutions and the mass-deformed/pure ABJM equations can be understood in terms of a discrete noncommutative realisation of the Hopf fibration. We discuss the implications for the possibility of finding an M2-brane worldvolume derivation of the classical S 3 geometry of the M2-M5 system. Using a rewriting of the equations of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show them to be different.with N units of magnetic flux. From the point of view of the U(N ) theory the D1⊥D3 system is described in terms of a solution involving fuzzy 2-spheres [19][20][21] through the Myers effect [22]. These are related to families of matrices obeying(1.1)The X i enter the physics as ansätze for solving the equations of motion and their commutator action on the space of all N × N matrices organises these matrices into representations of SU(2) ≃ SO (3). An important aspect of the geometry of the fuzzy 2-sphere involves the construction of fuzzy (matrix) spherical harmonics in SU (2) representations, which approach the space of all classical S 2 spherical harmonics in the limit of large matrices [20]. This construction of fuzzy spherical harmonics allows the analysis of fluctuations in a nonabelian theory of Dp-branes to be expressed at large N in terms of an abelian higher dimensional theory of a D(p+2) brane. At finite N the higher dimensional worldvolume theory becomes a noncommutative U(1) with a UV cutoff [23][24][25][26].The relation (1.1) also appears as an F-flatness condition for a particular mass deformation of N = 4 SYM, called N = 1 * , where all three adjoint chiral multiplets have acquired equal mass. This theory has a discrete set of vacua that satisfy the above condition, which from the string theory point of view can be interpreted as N D3 branes blowing up into concentric D5 branes with flux that adds up to N [27]. The matrix structure of these solutions is the same as for the D1⊥D3 spikes, with the relative transverse directions between the D3 and the D5 forming a fuzzy S 2 at finite N , which can again be seen by analysing small fluctuations around the vacua [28][29][30]. The lift of this system to M-theory has been disc...