I first
tried to read it in my teens, and have recently been delighted to
rediscover it in a 1993 American reprint. Lancelot Hogben's Mathematics
for the Million: How to Master the Magic of Numbers, first published
in England in 1937, with later revised editions up till 1967. My copy (a
reissue of the fourth edition) has an ISBN of 0 393 31071 X.
As its title
implies, its main purpose is to explain mathematics in a simple way for
those adults hitherto offput by the subject. Nothing but the most basic
of knowledge is assumed, yet Hogben manages to cover everything from
elementary arithmetic to the maths of navigation and logarithms.
Hogben
(18951975) was born and educated in England. He held several academic
appointments, including professorships in zoology and medical statistics.
He was the author of at least seven books, the best known and most
popular, apart from Mathematics for the Million, being Science
for the Citizen.
Another book
with which his name is now always associated was Frederick Bodmer's The
Loom of Language, which Hogben edited. Though trained as a scientist,
Hogben was passionately interested in matters linguistic, and was one of
those language addicts who proposed his own international language. In
Hogben's case it was "Interglossa", an artificial concoction
which he based on Greek and Latin roots together with a syntax resembling
that of Chinese, and the principles of which he set out in The Loom of
Language.
(By
the way, Harlish Goop, how about something for Bikwil on
Interglossa, Esperanto, Volapük and their other synthetic cousins?)
There was a
slight political edge to Hogben’s writings, principally relating to his
strong belief in the power of education, such as his book of essays
entitled Dangerous Thoughts. A couple of quotes of his I found on
the Internet follow.
To
be proud of intellectual isolation from the common life of mankind and to
be disdainful of the great social task of education, is as stupid as it is
wicked.
People
who have to rely on experts, will be subjugated.
So what do I
like about Mathematics for the Million?
Primarily,
its social perspective. From the very start of his Prologue, Hogben
has us appreciating the historical evolution of whatever aspect of maths
he is explaining. He begins, appropriately enough I suppose, with Zeno's
Paradox of Archilles and the Tortoise, which he uses as a engaging and
easytounderstand launch pad to
.
. . narrate how the grammar of measurement and counting has evolved under
the pressure of man's changing social achievements, how in successive
stages it has been held in check by the barriers of custom, how it has
been used in charting a universe which can be commanded when its laws are
obeyed, but can be never propitiated by ceremonial and sacrifice.
Later in the
Prologue he speaks of his approach in these terms:
The
customary way of writing a book about mathematics is show how each step
follows logically from the one before without telling you what use there
will be in taking it. This book is written to show you how each step
follows historically from the step before and what use it will be to you
or someone else if it is taken. The first method repels many people who
are intelligent and socially alive, because intelligent people are
suspicious of mere logic, and people who are socially alive regard the
human brain as an instrument for social activity.
From then
on, we are treated to the following chapter topics:
Mathematics in
Remote Antiquity
The Grammar of Size, Order, and Shape
Euclid as a Springboard
Number Lore in Antiquity
The Rise and Decline of the Alexandrian Culture
The Dawn of Nothing
Mathematics for the Mariner
The Geometry of Motion
Logarithms and the Search for Series
The Calculus of Newton and Leibnitz
The Algebra of the Chessboard
The Algebra of Choice and Chance. 
One chapter
definitely worth reading is The Dawn of Nothing, which, as you may
have guessed, is partly about the invention of Arabic (strictly, Hindu)
numerals, in particular the concept of a symbol for zero. Incidentally,
did you know that the word "algebra" is derived from the name of
an ancient Arab mathematician? He was Abu Al Khwarizmi, who worked in
Baghdad in the 8th century, (not the 13th, as Hogben claimed, which was
when his writings became known in Europe in Latin).
Another
passage of fascinating interest is Hogben's discussion of the sectarian
uses arithmetic was put to during the period of the Reformation:
Peter
Bungus, a Catholic theologian, wrote a book of 700 pages to show that the
number 666 of the Beast was a cryptogram for the name of Martin Luther . .
. Luther replied by interpreting it as a prophecy of the duration of the
papal regime, which was happily approaching its predestined end . . .
Perhaps the
most "useful" section of the book is Hogben's very serviceable
method for translating problems "in the language of everyday life
into the language of algebra". It could well be used in high schools,
where many a young person has difficulty knowing even where to start when
confronted with something like the following:
A
train leaves London for Edinburgh at one o'clock, going at 50 miles per
hour. Another train leaves Edinburgh for London, going at 25 miles per
hour. If Edinburgh is 400 miles from London, when do they meet?
Or, worse:
When
I am as old as my father is now, I shall be five times as old as my son is
now. By then my son will be eight years older than I am now. The combined
ages of my father and myself are 100 years. How old is my son?
But it
doesn't stop there. Want to know about the mathematics of Stonhenge?
Diophantus? James Bernoulli? Fermat? The Binomial Theorem? De Moivre’s
Theorem? Maclaurin’s Theorem? Pascal’s triangle? Spherical triangles?
Be of good
cheer: all such things are possible with Hogben’s help.
Assuming
you've mastered all that, you are now invited by Hogben to seat yourselves
at High Table and to partake of some really cryptic mathematical cuisine.
Namely, a repast of heady treats like imaginary numbers, differential
calculus, permutations and combinations, probability theory . . . As the
Gershwins were more than once heard to remark, "Who could ask for
anything more?"
Seriously,
though, folks . . .
For such a
book to get reprinted so often (I fancy it’s never been out of print),
many others must have liked it as much as I have. As a convenient exit,
two obvious ones had better be quoted — Albert Einstein ("It makes
alive the contents of the elements of mathematics") and H.G. Wells
("A great book, a book of first class importance").
(The
above article's title is from a 16th century history of Scotland by
Raphael Holinshed. His Chronicles enjoyed great popularity in
Elizabethan times, and indeed formed the basis for many of Shakespeare’s
historical plays.)
Did you spot the
error in the above article?
We make amends
here. 

