Heaviside on the "clumsy" standardization of vector notation for print: "It is by differences that mathematicians read mathematics easily"
English autodidactic electrical engineer, mathematician, and physicist (1850-1925) who brought complex numbers to circuit analysis, invented a new technique for solving differential equations, independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today. Reclusive and often at odds with the scientific establishment, Heaviside nevertheless changed the face of telecommunications, mathematics, and science. ALS, one page both sides, 6.5 x 8, June 3, 1915. Handwritten letter to Dr. Ludwik Silberstein, offering—in long and explicit detail—guidance for the representation of vector mathematical notation in print, and lamenting the poor choices made by both German physicists, and typesetters in general. Heaviside is perhaps most well-known for his introduction of 'vector calculus' into physics—particularly in electromagnetic theory. Maxwell’s original formulation of the equations of electrodynamics are completely unrecognizable today—twenty equations for twenty variables. Heaviside’s use of the tools of vector calculus—gradient, divergence, curl—and his combining of some of those variables into three simple vector functions, enabled him to cast twelve of those equations into the four 'Maxwell’s Equations' we know today.
In part: "Instead of saying 'multiply scalarly by a' or 'multiply vectorially by a,' it is sufficient to say 'multiply by a' or multiply by Va'; if not so explicit, as the long way, it is quite distinct enough, (& perhaps more), & more convenient. The ∇ should be the same size as the bodies of the small letters instead of the large…it is neater, and more easily read…I am really surprised at the Germans settling upon [ab] which makes very clumsily [c[ab]]. [d[c[ab]]], etc.!! Couldn't they see what [….] would lead to? And the use of ( ) in matrices, many of which may come together…makes very clumsy work. Impossible sometimes. When half educated men meet together to settle rules, what can you expect? I refer to what I heard of a Conference in Germany to settle the many notation in Vec. Alg."
He goes on to discuss terminology of linear and vector operators, before continuing to complain about the printing process: "This lowering of the indices has been going on a long time. I usually make the printers lift them up. They follow certain rules. I once asked a Master-printer why they kept on doing it (and other things I correct) over & over again. He said they did it because they wanted to make everything look exactly alike. But it is by differences that mathematicians read mathematics easily…But there are so many improvements wanted in math'l printing that it is little use talking about them now. It means educating the designers." Silberstein notes the dates of receipt and reply at the top. In fine condition. Heaviside's autograph is exceedingly rare—we find no records of any having been publicly offered for sale in the past.
From the collection of physicist Ludwik Siberstein.