% LaTeX source for Macfarlane's lecture on De Morgan

\documentclass{article}

\renewcommand{\thefootnote}{\fnsymbol{footnote}}

\usepackage{times}

\begin{document}

\begin{center}
\Large{AUGUSTUS DE MORGAN}\footnote{This Lecture was delivered April 13,
1901.---\textsc{Editors}} \\
\Large{(1806--1871)}
\end{center}

\textsc{Augustus De Morgan} was born in the month of June at Madura in
the presidency of Madras, India; and the year of his birth may be found
by solving a conundrum proposed by himself, I was $x$ years of age in
the year $x^2$.'' The problem is indeterminate, but it is made strictly
determinate by the century of its utterance and the limit to a man's
life. His father was Col.\ De Morgan, who held various appointments in
the service of the East India Company. His mother was descended from
James Dodson, who computed a table of anti-logarithms, that is, the
numbers corresponding to exact logarithms. It was the time of the Sepoy
rebellion in India, and Col.\ De Morgan removed his family to England
when Augustus was seven months old. As his father and grandfather had
both been born in India, De Morgan used to say that he was neither
English, nor Scottish, nor Irish, but a Briton unattached,'' using the
technical term applied to an undergraduate of Oxford or Cambridge who is
not a member of any one of the Colleges.

When De Morgan was ten years old, his father died. Mrs.\ De Morgan
resided at various places in the southwest of England, and her son
received his elementary education at various schools of no great
account. His mathematical talents were unnoticed till he had reached the
age of fourteen. A friend of the family accidentally discovered him
making an elaborate drawing of a figure in Euclid with ruler and
compasses, and explained to him the aim of Euclid, and gave him an
initiation into demonstration.

De Morgan suffered from a physical defect---one of his eyes was
rudimentary and useless. As a consequence, he did not join in the sports
of the other boys, and he was even made the victim of cruel practical
jokes by some schoolfellows. Some psychologists have held that the
perception of distance and of solidity depends on the action of two
eyes, but De Morgan testified that so far as he could make out he
perceived with his one eye distance and solidity just like other people.

He received his secondary education from Mr.\ Parsons, a Fellow of
Oriel College, Oxford, who could appreciate classics much better than
mathematics. His mother was an active and ardent member of the Church of
England, and desired that her son should become a clergyman; but by this
time De Morgan had begun to show his non-grooving disposition, due no
doubt to some extent to his physical infirmity. At the age of sixteen
he was entered at Trinity College Cambridge, where he immediately
came under the tutorial influence of Peacock and Whewell. They became
his life-long friends; from the former he derived an interest in the
renovation of algebra, and from the latter an interest in the renovation
of logic---the two subjects of his future life work.

At college the flute, on which he played exquisitely, was his
recreation. He took no part in athletics but was prominent in the
musical clubs. His love of knowledge for its own sake interfered with
training for the great mathematical race; as a consequence he came out
fourth wrangler. This entitled him to the degree of Bachelor of Arts;
but to take the higher degree of Master of Arts and thereby become
eligible for a fellowship it was then necessary to pass a theological
test. To the signing of any such test De Morgan felt a strong objection,
although he had been brought up in the Church of England. About 1875
theological tests for academic degrees were abolished in the
Universities of Oxford and Cambridge.

As no career was open to him at his own university, he decided to go to
the Bar, and took up residence in London; but he much preferred teaching
the London University took shape. The two ancient universities were so
guarded by theological tests that no Jew or Dissenter from the Church of
England could enter as a student; still less be appointed to any office.
A body of liberal-minded men resolved  meet the difficult by
establishing in London a University on the principle of religious
neutrality. De Morgan, then 22 years of ace, was appointed Professor of
Mathematics. His introductory lecture  On the study of mathematics''
is a discourse upon mental education of permanent value---which has been
recently reprinted in the United States.'

The London University was a new institution, and the relations of the
Council of management, the Senate of professors and the body of students
were not well defined. A dispute arose between the professor of anatomy
and his students, and in consequence of the action taken by the Council,
several of the professors resigned, headed by De Morgan. Another
professor of mathematics was appointed, who was accidentally drowned a
few years later. De Morgan had shown himself a prince of teachers: he
continuous center of his labors for thirty years.

The same body of reformers---headed by Lord Brougham, a Scotsman eminent
both in science and politics---who had instituted the London University,
founded about the same time a Society for the Diffusion of Useful
Knowledge. Its object was to spread scientific and other knowledge by
means of cheap and clearly written treatises by the best writers of the
time. One of its most voluminous and effective writers was De Morgan. He
wrote a great work on \textit{The Differential and Integral Calculus}
which was published by the Society; and he wrote one-sixth of the
issued in penny numbers. When De Morgan came to reside in London he
found a congenial friend in William Frend, notwithstanding his
mathematical heresy about negative quantities. Both were arithmeticians
and actuaries, and their religious views were somewhat similar.  Frend
lived in what was then a suburb of London, in   a country-house formerly
occupied by Daniel Defoe and Isaac Watts. De Morgan with his flute was a
welcome visitor; and in 1837 he married Sophia Elizabeth, one of Frend's
daughters.

The London University of which De Morgan was a professor was a
different institution from the University of London. The University of
London was founded about ten years later by the Government for the
purpose of granting degrees after examination, without any qualification
as to residence. The London University was affiliated as a teaching
college with the University of London, and its name was changed to
University College. The University of London was not a success as an
examining body; a teaching University was demanded. De Morgan was a
highly successful teacher of mathematics. It was his plan to lecture for
an hour, and at the close of each lecture to give out a number of
problems and examples illustrative of the subject lectured on;
his students were required to sit down to them and bring him the
results, which he looked over and returned revised before. the next
lecture. In De Morgan's opinion, a thorough comprehension and mental
assimilation of great principles far outweighed in importance any merely
analytical dexterity in the application of half-understood principles
to particular cases.

De Morgan had a son George, who acquired great distinction in
mathematics both at University College and the University of London. He
and another like-minded alumnus conceived the idea of founding a
Mathematical Society in London, Where mathematical papers would be not
only received (as by the Royal Society) but actually read and discussed.
The first meeting was held in University College; De Morgan was the
first president, his son the first secretary. It was the beginning of
the London Mathematical Society. In the year 1866 the chair of mental
philosophy in University College fell vacant. Dr.\ Martineau, a
Unitarian clergyman and professor of mental philosophy, was recommended
formally by the Senate to the Council; but in the Council there were
some who objected to a Unitarian clergyman, and others who objected to
theistic philosophy. A layman of the school of Bain and Spencer was
appointed. De Morgan considered that the old standard of religious
neutrality had been hauled down, and forthwith resigned. He was now 60
put \textit{hors de combat} by pebbles from a sling. If Goliath had
crept into a snail shell, David would have cracked the Philistine with
his foot. There is something like modesty in the implication that the
crack-shell pebble has not yet taken effect. it might have been thought
that the slinger would by this time have been singing---And thrice [and
one-eighth] I routed all my foes, And thrice [and one-eighth] I slew
the slain.''

In the region of pure mathematics De Morgan could detect easily the
false from the true paradox; but he was not so proficient in the field
of physics. His father-in-law was a paradoxer, and his wife a paradoxer;
and in the opinion of the physical philosophers De Moroan himself
scarcely escaped. His wife wrote a book describing the phenomena of
spiritualism, table-rapping, table-turning, etc.; and De Morgan wrote a
preface in which he said that he knew some of the asserted facts,
believed others on testimony, but did not pretend to know
\textit{whether} they were caused by spirits, or had some unknown and
unimagined origin. From this alternative he left out ordinary material
causes. Faraday delivered a lecture on \textit{Spiritualism}, in which
he laid it down that in the investigation we ought to set out with the
idea of what is physically possible, or impossible; De Morgan could not
understand this.
\begin{flushleft}
From A~Macfarlane, \textit{Lectures on Ten British Mathematicians of the
Nineteenth Century}, New York: Wiley and London: Chapman and Hall 1916,
pp.\,19--33.
\end{flushleft}

\end{document}

% `