Tychonov's Solution: An Overlooked Opportunity to Blend Pure Mathematics into Mechanical Engineering Education

Tychonov's 1935 solution of the heat equation, exhibiting nontrivial heat fluxes spontaneously appearing along an isolated conducting rod initially held at zero degrees, has intrigued some specialists for almost a century. No doubt those practicing heat engineers who took mathematics seriously were initially relieved to learn that the construction was valid only for infinitely long rods; the integrity of their published exchanger designs could be defended by citing this weakness, together with the known discrepancies between the heat equation and physical reality. Some mathematicians contrived additional hypotheses to disqualify the Tychonov solution. Recently a computer simulation was executed, revealing just how astonishingly unbridled the solution is. But there remain incongruities in this singular example that invite metaphysical speculation. We fuel the latter with a recap of the history from a lighthearted perspective, providing heat transfer engineering students with a rare insight into the practical value of the mathematicians' exacting obsession with generality. [For the complete proceedings, see ED655360.]