Today, a miller takes up mathematics. The
University of Houston's College of Engineering
presents this series about the machines that make
our civilization run, and the people whose
ingenuity created them.

A lifetime of teaching
thermal engineering has left my mind littered with
names that have no faces. Take the mathematical
construction we call a *Green's function.*
First let's meet the function. Then, let's look for
the face -- for the person.

Suppose a large, thin copper plate is at some
uniform temperature. Now we imagine a very tiny
device that pours out heat: We embed the device at
a point in the plate. The resulting plate
temperature will spike upward toward infinity at
the heat source, and drop off sharply in all
directions.

That same spike turns up in many other situations.
Push a pointed stick into a rubber membrane and the
spike looks just like the temperature spike. George
Green was the person who wrote its mathematical
form. And, adding many such spikes together, we
could now determine effects of complicated heat
sources, pressures on membranes, electric fields --
you name it.

George Green was born near Nottingham in 1793, the
son of a successful baker. He had to leave primary
school, after only two years, to help out in the
family business. But, he seems to have been
influenced by a fine local math teacher. He was
excited by math, and he went on to learn the
subject *by himself.*

When he was fourteen, his father built a fifty-foot
grain-grinding windmill in the nearby town of
Sneinton. Green moved there to work in it. But he
set up a study on the top floor of the mill. He
also took up with the mill manager's daughter. For
some reason they never married, yet they raised
seven children.

The year before his father died, Green published
his paper on what came to be known as Green's
functions. He was 34, and people like Charles
Babbage and John Herschel sat up to take notice.

So Green sold the mill and went to college. First,
he filled in gaps in his education at the
University of Nottingham. Then he was admitted to
Cambridge University. He received a low-grade
degree at the age of *forty-four* --
obviously distracted from his studies by an ongoing
production of high-powered mathematical work.

Four years later, now a Fellow at one of the
Cambridge Colleges, and pouring forth mathematical
works, Green fell ill and returned to Sneinton. He
must've known he was dying because he wrote a will
leaving everything to his lifelong companion Jane,
and their children. He didn't quite make it to the
age of forty-eight.

By then he'd written on wave theory, fluid motion,
light, electricity. He'd provided a vast
understanding of a huge family of problems. His
ideas, which are still shaping math, science, and
engineering today, did not come out of the
limestone halls of Cambridge.

They came instead from a small room in a brick
windmill. Colleges are superb places. But Green
reminds us they can only support (they can neither
create nor replace) the passion for learning and
white-hot spikes of understanding, upon which our
world turns.

I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.

(Theme music)

P. J. Wallis, Green, George. *Dictionary of
Scientific Biography* (C.C. Gilespie, ed.) New
York: Charles Scribner's Sons, 1970-1980.
See also, the entry on George Green in the
*Dictionary of National Biography.* (Leslie
Stephen and Sydney Lee, eds.). London: Smith,
Elder, and Co., 1908-9.

This website provides
a very useful history of Green.

Any reasonably advanced book on calculus or
advanced analysis will treat Green's functions, but
I especially like H. S. Carslaw and J. C. Jaeger,
*Conduction of Heat in Solids,* Oxford:
Oxford University Press, Ch. 14, "The Use of
Green's Functions in the Solution of the Equation
of Conduction." See also, the excellent website:
http://www.engr.unl.edu/~glibrary/home/index.html

My thanks to Lionel E. Davis from the University of
Manchester Institute of Science and Technology
(UMIST) for suggesting the topic and providing the
web material in support of it.

The Engines of Our Ingenuity is
Copyright © 1988-2004 by John H.
Lienhard.