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In statistical mechanics one packages the possible energies of a system intoa partition function. In number theory, and elsewhere in mathematics, onepackages the spectrum of a phenomenon, say the prime numbers, into a$\zeta$-function or more generally into an L-function. These packagingfunctions have symmetries and properties not at all apparent from the energiesor the primes themselves, often exhibiting scaling symmetries for example. Onemight be able to understand those symmetries and compute the packaging functionindependently of the actual packaging. And so one finds a way of puttingtogether objects into a package, and ways of discerning symmetries of thatpackage independent of the actual mode of packaging. This is a recurrent themeof the Langlands Program as well. Packaging is also found in Weyl's asymptoticsand "hearing the shape of a drum" (Kac), the Schwinger Greens function inquantum electrodynamics packaging the Feynman sum of histories, and moregenerally in the Selberg trace formula.

Packaging Spectra (as in Partition Functions and L/$\zeta$-functions) to Reveal Symmetries (Reciprocity) in Nature and in Numbers