In 1979, \textit{J. H. Conway} and \textit{S. P. Norton} [Bull. Lond. Math. Soc. 11, 308--339 (1979; Zbl 0424.20010)] conjectured that the existence of the Fischer-Griess ''monster'' or ''friendly giant'' finite simple group \(M\) might be explained by some infinite-dimensional Lie algebra \(L\). The paper under review, which contains no results, discusses some possible approaches to constructing candidates for \(L\). The discussion is given in terms of a certain Lie algebra \(L_{\infty}\) of infinite rank generated by elements \(e(r)\), \(f(r)\), and \(h(r)\) corresponding to the Leech roots \(r\) in the even unimodular lattice \(\Pi_{25,1}\) of elements \(x=(x_0,x_1,\ldots,x_{24}| x_{70})\) such that either \(x_i\in \mathbb Z\) for all \(i\) or \(x_ i\in \mathbb Z_+\) for all \(i\) and the inner product of \(x\) and \(h=(,,\ldots,| {})\) is in \(\mathbb Z\). A Leech root satisfies \(r\cdot r=2\) and \(r\cdot w=-1\), where \(w=(0,1,2,\ldots,24| 70).\) The authors conjecture that \(M\) might arise as a subquotient of the automorphism group of some subquotient algebra \(S\) of \(L_{\infty}\). Some possibilities for obtaining \(S\) are offered, including replacing \(L_{\infty}\) by some kind of completion, to allow infinite linear combinations of generators. They discuss subalgebras of \(L_{\infty}\) corresponding to ''deep holes'' and ''small holes'' of the Leech lattice as described by \textit{J. H. Conway}, \textit{R. A. Parker} and \textit{N. J. A. Sloane} [Proc. R. Soc. Lond., Ser. A 380, 261--290 (1982; Zbl 0496.10020)]. Deep holes correspond to Niemeier lattices \(N\), which have a Witt component \(W\) that is a direct sum of root lattices of classical Lie algebras of one root length. \(L_{\infty}\) has a subalgebra \(L[N]\) that is a direct sum of Euclidean Lie algebras \(E(W)\) and that can be extended to a large finite rank hyperbolic subalgebra \(L^*(N)\) having one additional fundamental root corresponding to a ''glue vector'' of the appropriate hole. \textit{J. H. Conway} and \textit{N. J. A. Sloane} [Proc. R. Soc. Lond., Ser. A 381, 275--283 (1982; Zbl 0496.10021)] have shown that there are 23 different constructions of the Leech lattice from Niemeier lattices \(N\), which prompts the conjecture that there might be multiple constructions of \(M\) from algebras \(L[N]\). Small holes correspond to maximal subalgebras of \(L_{\infty}\) of finite rank, which might afford a handle for constructing \(M\). The authors conclude by describing calculations in progress for \(L_{\infty}\) based on the result of \textit{P. Diaconis}, \textit{R. L. Graham}, and \textit{W. M. Kantor} [Adv. Appl. Math. 4, 175--196 (1983; Zbl 0521.05005)] that the Mathieu group \(M_{12}\) is generated by two permutations of \(\{n\in N\mid 0\leq n\leq 11\}\) related to standard playing card shuffles.