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A new starting-point and a new method are requisite, to insure a
complete [classi?cation of the Steiner triple systems of order 15].
This method was furnished, and its tedious and di?cult execution
und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S.
White (1917) [129] The history of classifying combinatorial objects
is as old as the history of the objects themselves. In the mid-19th
century, Kirkman, Steiner, and others became the fathers of modern
combinatorics, and their work - on various objects, including (what
became later known as) Steiner triple systems - led to several
classi?cation results. Almost a century earlier, in 1782, Euler
[180] published some results on classifying small Latin squares,
but for the ?rst few steps in this direction one should actually go
at least as far back as ancient Greece and the proof that there are
exactly ?ve Platonic solids. One of the most remarkable
achievements in the early, pre-computer era is the classi?cation of
the Steiner triple systems of order 15, quoted above. An onerous
task that, today, no sensible person would attempt by hand calcu-
tion. Because, with the exception of occasional parameters for
which com- natorial arguments are e?ective (often to prove
nonexistence or uniqueness), classi?cation in general is about
algorithms and computation.
A new starting-point and a new method are requisite, to insure a
complete [classi?cation of the Steiner triple systems of order 15].
This method was furnished, and its tedious and di?cult execution
und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S.
White (1917) [129] The history of classifying combinatorial objects
is as old as the history of the objects themselves. In the mid-19th
century, Kirkman, Steiner, and others became the fathers of modern
combinatorics, and their work - on various objects, including (what
became later known as) Steiner triple systems - led to several
classi?cation results. Almost a century earlier, in 1782, Euler
[180] published some results on classifying small Latin squares,
but for the ?rst few steps in this direction one should actually go
at least as far back as ancient Greece and the proof that there are
exactly ?ve Platonic solids. One of the most remarkable
achievements in the early, pre-computer era is the classi?cation of
the Steiner triple systems of order 15, quoted above. An onerous
task that, today, no sensible person would attempt by hand calcu-
tion. Because, with the exception of occasional parameters for
which com- natorial arguments are e?ective (often to prove
nonexistence or uniqueness), classi?cation in general is about
algorithms and computation.
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