Professor
George Andrews assessed:
The
most interesting item in this box was a manuscript of more than
one hundred pages in Ramanujan's distinctive handwriting which
contains over six hundred mathematical formulae listed one after
the other without proof. It is my contention that this manuscript,
or notebook, was written during the last year of Ramanujan's life
after his return to India from England. My evidence for this assertion
is all indirect; in the words of Stephen Leacock, 'It is what
we call circumstantial evidence - the same that people are hanged
for'.
While
it is impossible to categorize the various formulas completely,
a rough approximation of its contents is the following:
q-series
and related topics including mock
θ-functions:
60%
Modular equations and relation, singular moduli: 30%
Integrals, Dirichlet series, congruences, asymptotics, misc.:
10%
I give only this rough break down because of the chaotic nature
of this manuscript. On many pages, there are fragments of numerical
computations and infinite series running off in all directions.
It may be possible eventually to make sense out of some of these
pages; if so, the above percentage breakdown may change.
In
any event, it is clear that q-series investigations make up the
bulk of the work in the Lost Notebook. Indeed I count about 380
formulae that I consider to belong more to q-series than to modular
relations or other topics.