---Oliver Heaviside

```
On operators in physical mathematics, part II,
```*Proceedings of the Royal Society of London*,
Vol. 54, 1893, p. 121.

There is nothing by Heaviside in "Bartlett's Familiar Quotations," but
the first phrase of Heaviside's aphorism, "Mathematics is an
experimental science," is widely quoted. A web search can find it
in dozens of places, but only
one
of the ones found by Google, for example,
continues the quotation to the end of the sentence!*

Here is a larger piece of the section in which the saying appears:
"In the preceding, I have purposely avoided giving any definition
of 'equivalence.' Believing in example rather than precept, I have
preferred to let the formulae, and the method of obtaining them,
speak for themselves. Besides that, I could not give a satisfactory
definition which I could feel sure would not require subsequent
revision. Mathematics is an experimental science, and definitions
do not come first, but later on. They make themselves, when the
nature of the subject has developed itself. It would be absurd to
lay down the law beforehand. Perhaps, therefore, the best thing I
can do is to describe briefly several successive stages of knowledge
related to equivalent and divergent series, being approximately
representative of personal experience. (a). Complete ignorance. (b)...."

The epigraph in *Operator Commutation Relations*
by Palle E. T. Jorgensen and Robert T. Moore, D. Reidel, Dordrecht / Boston / Lancaster, 1984,
p. 56,
incorporates the single sentence at the top of the page as a quotation.
That epigraph is taken from a discussion of Heaviside's approach in
*The Historical Development of Quantum Theory, Vol. 3:
The Formulation of Matrix Mechanics and Its Modifications, 1925-1926*
by Jagdish Mehra and Helmut Rechenberg,
Springer-Verlag, New York, 1982:

"Those who insisted on mathematical rigour, on clear definitions of the operators
and well-defined equations obeyed by them could not take Heaviside's solution seriously.
Against these objections Heaviside held that
'mathematics is an experimental science,
and definitions do not come first, but later on.'"

It is on page 227 in vol. 3, and it is a statement by the authors Mehra and
Rechenberg as they describe "the operator method" in connection with Max
Born's work. This part of vol. 3 of Mehra-Rechenberg vol. 3 is primarily about Max Born,
but Born is different from the other architects as he wrote lots of joint
papers, he was the senior of them, and served as math teacher to Heisenberg,
Jordan and other of the "younger" pioneers. And he was mentor to Heisenberg:
At the time, Heisenberg asked Born if his pre-publication 1925 paper
(Über die quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen,
*Zeitschrift für Physik*, vol. 33 (1925), no. 12, pp. 879-893)
was worth publishing.** Heisenberg didn't even know what a
matrix was before 1925. Born told him, and as it turned out, Heisenberg's
paper won him the Nobel Prize.

This part of vol. 3 in the book set is really wonderful, i.e., V. 3 in vol. 3.
Now vol. 3 is primarily about Born. There is a separate volume about
Heisenberg. Born was the more mathematical of the architects of Quantum Mechanics, and he
was mentor for and worked with Heisenberg. But Born was also greatly
influenced by Dirac. Dirac had his own independent version of Heisenberg's
paper, and realized more than perhaps some of the others the significance of
non-commutativity. The operator method is thought to have started with
Heaviside, but to have been revived by Dirac. And then others followed in
Dirac's footsteps. Anyway 7 pages in V. 3 (vol. 3) are about the collaboration
between Norbert Wiener and Max Born. Wiener was visiting Göttingen at the
time. Mehra and
Rehchenberg describe how, motivated by Dirac, Wiener had extended
Heaviside's operator calculus, and how that was the start of the Wiener-Born
collaboration, and how the operators slowly became to be accepted from then
on, approved by the Demigod, David Hilbert, and then how, via John von
Neumann, operators in Hilbert space became the current language of quantum
mechanics. But Wiener's influence on Born, and on the operator formulation
of Quantum Mechanics is generally underestimated, I think.
Similarly, had it not been for Dirac, Wiener, Born and others,
I think it is likely that the original work
of Heaviside would have been completely forgotten.

*

**