The change of attitude towards what used to be called self-improvement
was brought home to me recently when I finally read a book that has been
on my reading pile for nearly 50 years. Mathematics for the Million was
first published on 29 September 1936, but the copy my father gave me as
a present, and which I still have, is labelled as the 13th impression published
in 1941.

Written by Lancelot Hogben and published by George Allen and Unwin,
the book was a great success from the word go. H. G. Wells declared that
‘It should be read by every intelligent youth from 15 to 90.’ The first
and second impressions were sold out almost immediately; the third impression
lasted just three weeks. In all, half a million copies were sold.

A bulky book of some 650 pages, Mathematics for the Million was intended
to demystify mathematics, to take the frighteners off those who had been
badly taught at school. The text is scholarly, long-winded in places, quirky,
with sideswipes at various pet hates such as eugenicists. It is enlivened
with more than 200 clear diagrams drawn by J. F. Horrabin; some of the illustrations,
such as that showing how Eratosthenes measured the Earth, have always fascinated
me.

The treatment of the history of mathematics and the slow development
of new ideas and notations is particularly strong. The author tries to encourage
readers who find difficulty with mathematical methods by saying, in effect:
‘Don’t worry if it takes you a few minutes to come to terms with this; some
very clever Greeks struggled with it for more than 500 years.’ In summary,
the book is a delight for either a browser or a solid reader and is still
well worth ploughing through if you can get hold of a second-hand copy.
To read it from cover to cover is a hard but enjoyable exercise in – dare
I say it – self-improvement.

Hogben was not a professional mathematician. Born in 1895, he was a
physio logist who held a variety of academic appointments in zoology, leading
up to a professorship of zoology at the University of Birmingham (1941-47)
and then the professorship of medical statistics at the same university
(1947-61). He died in 1975.

From published obituaries and biographical notes I get the impression
that he was a somewhat difficult colleague to his fellow academics, with
no respect for pomp or position or power. As a young man he was a Quaker
and was imprisoned briefly for refusing military service in the First World
War, but later became a humanist. He held an academic appointment in South
Africa for only a short period, being unable to stomach the racialist attitudes
of the time. An energetic, restless and probably touchy man, he suffered
from an overactive thyroid gland that was not operated on until late in
his life. He invented Interglossa, an international language with a dictionary
of 8000 words, but never published the dictionary; only his fame and status
aroused a slight glimmer of interest in the language.

Hogben’s great interest in language and grammar comes through in Mathematics
for the Million in frequent analogies between mathemical symbols and nouns,
adjectives, verbs and adverbs. I found this the least satisfactory aspect
of the treatment; if a reader is baffled by the meaning and use of the square
root of minus one, does it help to talk about gerunds, the nouns that behave
like verbs? But no matter: there are plenty of other explanations and illustrative
examples for this topic.

Mathematics for the Million was written in 1933, as an amusement when
the author was convalescing from an illness. Friends pleaded with him to
send the manuscript to a publisher: he agreed only on condition that his
friends undertook the correcting of proofs, a chore that would otherwise
interfere with his academic duties. Hogben described the book as a popular
self-educator and as the first of the Primers for the Age of Plenty.

Here one gets a whiff of the middle 1930s, the sense of optimism and
vigour as the effects of the Great Depression receded. In addition to the
serious business of improving one’s qualifications there were opportunities
for lively debates in adult school and Fabian discussion groups. It was
the heyday of cycling and camping, of amateur foot ball teams and orchestras
and dance bands, of private tennis clubs and public tennis courts, of open-air
swimming pools with desperately cold water, of well-attended evening meetings
where people could hear of the latest discoveries in science, particularly
astronomy.

The second of the Primers for the Age of Plenty was Science for the
Citizen, also by Hogben, which was published in 1938 and sold nearly as
well. I possess a copy of that book too, and intend to read it as soon as
possible. The problem is it runs to 1100 pages. Perhaps though, now that
my badminton classes have finished for the summer, I can make the time for
some more self-improvement.

Phillip Gething is based in Fleet, Hampshire.

I use a masculine form of the possessive pronoun because, in my experience,
cranks appear to be mainly elderly gentlemen. In the days when I was on
the editorial board of a magazine for professional astronomers, a small
but steady stream of the manuscripts submitted for our consideration came
from such contributors.

The signs were unmistakable. First, the manner of presentation bore
no relation to the rules and house style of the magazine, which the author
appeared not to have studied at all. The paper or letter offered to us really
was a manuscript. It was usually written in green or violet ink, in a crabbed
but very neat handwriting, on many small sheets of lightweight notepaper.

It was invariably sent from a private address. In remembering Teddington
as a favourite haunt of the crank I imply no disrespect to that fair district
of London, but I must bring the facts fearlessly to my readers. Any private
address, no matter how attractive, rather lacks the cachet of Jodrell Bank
or the Cavendish Laboratory.

So much for the outer wrappings, so to speak. Any deficiencies here
might have been excused and accepted if the content had been of high quality.
However, the overwhelming impression left by a careful reading of the text
was that the argument rambled. Occasional dogmatic statements, such as ‘The
Earth has two moons, but one is always in darkness,’ were not, alas, supported
by any evidence. At least they provided a frisson of excitement sufficient
to make me splutter over my morning cornflakes. I speak of those far-off
days when the first post came before breakfast.

Other characteristic features, not necessarily all present in any one
offering, were a supposed link with the theory of relativity (special, general,
both or unspecified), a complete lack of any references to the scientific
literature, a smattering of genuine technical terms and a suggestion that
the author’s original ideas were being suppressed by those in high places.
Einstein, I have been assured, was on the right track but didn’t really
understand relativity; the author added, more in sorrow than in anger, that
the prime minister of the day was trying to prevent this news leaking out.

The only way for an editor to deal with such manuscripts is to reject
them politely. To publish them as a joke would be cruel, and unfair to more
worthy authors crowded out by lack of space. No responsible editor has the
slightest desire to stifle original ideas, but thought and reason are not
to be confused with guesses and assertions.

What drives a man to spend his time in preparing cranky manuscripts?
Perhaps it is an agreeable retirement occupation, a way of filling in the
gaps when the weather makes gardening impossible. Presumably a desire for
fame is a strong motivation. And fame, in the crank’s version of science,
comes from making an inspired guess which later turns out to be true. I
hope that’s not right, but it is a myth rather encouraged by the popular
media.

Are you a crank? If so, here’s how to uncrank yourself and increase
your chances of publication. Throw away that bottle of green ink and buy
yourself a typewriter, or better still a word processor. Forget about relativity
and Einstein. Don’t speculate about black holes unless you really know your
subject. Don’t write about perpetual motion, unseen moons, or limitless
communications bandwidths with zero error rates whatever the noise level.
Find instead a topic in one of the quieter backwaters of science, write
something obscure and throw in a few genuine references to related papers,
whether you have read them or not.

I’m afraid you’ll have to move from Teddington. Why not try Oxford,
and call your house The Clarendon? I promise not to reveal your new hideout
to those in high places.

Phillip Gething writes from a private address in Hampshire.