Professionalization of Physics and Mathematics in the
Nineteenth Century
Marco Tompitak
May 25, 2012
Introduction
At the dawn of the nineteenth century, science was still very much a business attended to by
wealthy gentlemen who had the spare time to devote to research interests. By the turn of that
century, science had been professionalized; scientists had grouped themselves together in closed-off
professions, requiring restrictive qualifications from anyone seeking to enter their ranks, and were
making a living off of their science.
Science and Religion
To reach this point, science had to be emancipated from religious influence. For a long time,
science and religion had been inextricably linked. Researching nature meant researching God’s
creation and in uncovering the laws of nature, man learned of the wisdom with which God had
designed the universe.
In the nineteenth century, however, science and religion started to clash. Church authority
was already no longer deemed infallible. Criticism had arisen about inconsistencies within the
Bible and there were doubts as to whether the Bible should be taken literally. In 1835, German
theologian David Strauss provoked a storm of controversy with his book Das Leben Jesu, in which
he set forth his idea that Jesus was merely an historical figure and that the miracles ascribed to
him in the Bible are likely mythical. In his preface, Strauss writes, ”It is not by any means meant
that the whole history of Jesus is to be represented as mythical, but only that every part of it is
to be subjected to a critical examination, to ascertain whether it have not some admixture of the
mythical . . . and the enquiry must . . . be made whether in fact, and to what extent, the ground on
which we stand in the gospels is historical.”1
With Christian faith already somewhat on the defense, a fierce discussion immediately followed
Charles Darwin’s publication of his theory of evolution in 1859, dividing the faithful (clergy and
men of science alike). A new generation of scientists, lead by biologist T. H. Huxley and physicist
John Tyndall, took up arms against religious interference with science amidst these discussions.
Characterizing the church as conservative, closed-minded and overly concerned with their own
power, they championed science as the opposite: progressive in earnest search of the truth.
The issue underlying these ideological debates was in essence a struggle for power. Scientists
believed they had a rightful claim to status and influence in society. Their knowledge of the world
made them the proper advisors in most practical matters. The church undermined this claim,
however, having traditionally wielded this influence and being reluctant to give it up.
In 1872, Henry Thompson, a surgeon from London, dared to propose even to put the power
of prayer to the test. He suggested that the entire nation pray for the recovery of patients of a
specific hospital for a period of time and compare the mortality rate of these patients to those of
patients not excessively prayed for. Thus they could measure the efficacy of prayer. Thompson
meant to apply the scientific method to something thoroughly a matter of faith; such an idea was
unprecedented.
Thompson did not suggest this experiment out of spite for faith in prayer, nor did he likely
believe the experiment would ever be carried out. His article was mostly an exercise in polemics
1 David Strauss and Marian Evans. The Life of Jesus, Critically Examined. Vol. 1. New York: Calvin Blanchard,
1860, p. 3.
1
against the church and not without provocation. It was a common habit of the clergy to prescribe
prayer as the solution to a great many problems. When epidemics broke out or harvests threatened
to fail, dedicated days of prayer, on which the populace was to utter a specific prayer, were often
called for by the clergy to ask God to remedy the disasters. In doing so, they undermined the
authority of scientists, who knew e.g. that improved hygiene could prevent outbreaks of disease
and believed that the weather was not caused by the random whims of God, but was a system
governed by ordered, though extremely complex, laws of nature. To them, then, praying for
relief in these matters meant asking God to suspend the laws of nature for man, which seemed
unacceptable hubris. More importantly, the church’s calling for prayer rather than rational action
directly undermined the scientists’ efforts and the value of their knowledge.
Thus science and religion vied for power. John Tyndall, in his address to the assembly of the
British Association in Belfast in 1874, famously proclaimed,2
“What we should resist, at all hazards, is the attempt made in the past, and now
repeated, to found upon [man’s need for the emotional as well as the intellectual] a
system which should exercise despotic sway over his intellect. I have no fears as to
such a consummation. Science has already to some extent leavened the world: it will
leaven it more and more; and I should look upon the light of science breaking in upon
the minds of the youth of Ireland, and strengthening gradually to the perfect day, as
a surer check to any intellectual or spiritual tyranny which now threatens this island,
than the laws of princes or the swords of emperors. We fought and won our battle even
in the Middle Ages: should we doubt the issue of another conflict with our broken foe?
The impregnable position of science may be described in a few words. We claim, and
we shall wrest, from theology the entire domain of cosmological theory. All schemes
and systems, which thus infringe upon the domain of science, must, in so far as they do
this, submit to its control, and relinquish all thought of controlling it. Acting otherwise
proved disastrous in the past, and it is simply fatuous today. . . . The lifting of life is
the essential point; and as long as dogmatism, fanaticism, and intolerance are kept
out, various modes of leverage may be employed to raise life to a higher level.”
Tyndall’s words are combative and telling: science is the great liberator, the improver of life
and the proper authority in physical matters; the church is an oppressive, dogmatic, intolerant
tyrant, working against the intellect, a foe of the progress of mankind.
Men like Tyndall and Huxley wittingly kept this conflict between science and religion in place;
they realized that this was necessary in order to fully emancipate science. After all, if science
and religion were not at odds, there would be no need to separate them and respect science as an
authority in itself.
In his book, On the Genesis of Species (1871), St. George Jackson Mivart attempts to reconcile
Darwin’s theory of evolution with Christian doctrine. He writes, “The general theory of evolution
has indeed for some time past steadily gained ground, and it may be safely predicted that the
number of facts which can be brought forward in its support will, in a few years, be vastly
augmented. But the prevalence of this theory need alarm no one, for it is, without any doubt,
perfectly consistent with strictest and most orthodox Chrstian theology.”3 Mivart argued that
there was really no controversy between Christian beliefs and evolution, though of course the
Bible must not be taken literally, and that evolution could well be part of God’s design.
Mivart’s work met with a scathing review by Huxley, who decried the idea of reconciling
evolution with religion, warning that it was impossible to be “both a true son of the Church and
a loyal soldier of science.”4 What Mivart had failed to perceive was that Huxley and other fellow
scientists meant to keep the controversy in place in service to the emancipation of science from
the church.
2 John Tyndall. Address Delivered Before the British Association Assembled at Belfast: With Additions. London:
Longmans, Green, and Co., 1874, p. 61.
3 St. George Mivart. On the Genesis of Species. London: MacMillan and Co., 1871, p. 4.
4 Quoted in Frank M. Turner. “The Victorian Conflict between Science and Religion: A Professional Dimension”.
In: Isis 69.3 (1978), pp. 356–376. issn: 0021-1753, p. 370.
2
A Professional Countenance
Perhaps the foremost arena where science and religion clashed was in the educational systems.
These were traditionally under control of the clergy and science was not considered a valid area of
study in itself. Scientists sought to change this; they felt that educating people in science would
greatly benefit society. They argued that taking advantage of scientific knowledge provided an
edge in warfare and benefited public health and the economy, among other things. Scientists in
this way tried to link themselves in the view of the public and the state with the welfare of the
nation.
For science itself, a claim over education also provided job opportunities for its practitioners
and the chance to spread scientific ideas to a larger part of society. This was especially important
for the process of professionalization. Scientists laid claim to positions in education that would
come with prestige, power and income, as well as the opportunity to acquaint a broader audience
with their modes of thought, securing for science a higher place in society.
They further worked on their air of professionalism by forming scientific societies and starting
scientific magazines, from which any non-scientist was barred. Only practicing scientists with the
proper credentials were allowed into the societies and were accepted to publish in the magazines.
This excluded clergy and amateur scientists from becoming a part of the scientific community
and strengthened the positions of scientists as authorities: not just anyone could call themselves
a scientist and true science should be left in the hands of capable professionals.
This process of professionalization had greatly changed the face of science by the end of the
nineteenth century. Firstly, it became possible to make a living as a scientist; no longer did
one need to be independently wealthy to become a man of science. Secondly, science became
secularized, shunning direct interference from any religious considerations.
The description presented of the general process of professionalization might suggest that it
was by deliberate design that scientists enforced this change. This is a classic view put forward
by Frank M. Turner in 1978.5 However, as will be apparent from the more specific accounts in
the following sections, this view does require some nuance. A number of factors played a role in
enabling science to change as it did as well as in pushing it in the direction it took. Furthermore,
different fields of science reached their professionalized state through different paths. A clear
distinction can be seen between the paths travelled by mathematics and physics, two closely
related sciences, through the nineteenth century, which will be the topics of the rest of this essay.
Mathematics and Faith
At the beginning of the nineteenth century, the science of mathematics was strongly linked to faith
and continued to be for some time. Mathematicians reveled in viewing their science as the language
in which God had written the laws of nature. By the end of the century, however, mathematics
was thoroughly secularized. Mathematicians even went further than most other scientists, not
only withdrawing themselves from matters of faith and metaphysics, but also from the physical
world, instead viewing mathematics as a closed logical system, with no necessary relevance to
describing anything physical.
God’s Equations
In 1846, astronomer Johann Gottfried Galle discovered Neptune. The discovery of this eighth
planet was something special: for the first time ever, a celestial body had been discovered as a
result of a theoretical prediction of its existance and location. John Couch Adams in Britain and
Urbain Le Verrier in France had both independently studied distortions in the orbit of Uranus
and concluded that these anomalies must be caused by another planet. They had even managed
to predict, by mathematical means, where this planet must be.
The discovery of Neptune was a spectacular mental achievement and many scientists sang its
praise. It was pure, disembodied thought, independent of the mundane senses. In such terms,
the discovery became something philosophical and spiritual as well. It proved to many that the
universe was controlled by mathematical laws imposed by God. Mathematicians, then, were
5 Turner,
“The Victorian Conflict between Science and Religion”, see n. 4.
3
directly partaking in the mind of God and knowledge of mathematics was the path to divine
insight. Mathematicians were likened to clairvoyants and William Rowan Hamilton, the prominent
mathematician, went so far as to write verse to praise the accomplishment.
Mathematicians liked to quote Plato when glorifying their field. In Plato’s view, the world
is divided into a noumenal realm of perfect shapes, ideas and concepts and the phenomenal
realm we live in. The things we see in the phenomenal realm are imperfect images of perfect
noumenal shapes. Mathematicians likened their abstract conceptions to this noumenal realm and
liked to view mathematics as a way of exploring it, providing a bridge between the phenomenal
and the noumenal. For these early nineteenth century mathematicians, mathematics had strong
metaphysical connotations.
In retrospect, the discovery of Neptune owed significantly to luck. In their predictions, Adams
and Le Verrier used Bode’s law, which states that the distance of the n-th body in our solar system
from the sun goes as 4 + 3(2n ) and which isn’t a rigorous law of nature at all. It only happened
to point them in approximately the right direction. However, this reality did nothing to dampen
to social impact of the discovery: contemporary intellectuals saw the discovery of Neptune as a
complete triumph for pure mathematics.
This view of mathematics as a divine endeavor also tied in well with the religious ideas of
Unitarians and the upcoming movement of Transcendentalism. Unitarians, besides also having a
desire for a more reason-driven religion, put the focus of their faith on the relationship between
man and God, a more personal relationship than that established through any institutionalized
chuch. Mathematics, as a bridge to the mind of God, provided the means for such a relationship.
Transcendentalists held the belief that man and nature were inherently good and not a priori
corrupt and imperfect. They viewed the fact that God had given man the gift of mathematics as
an affirmation of this idea: God meant for humans to come to know his divine mind.
A prominent promotor of the congruence of mathematics and faith is found in Benjamin Peirce,
who was professor of mathematics at Harvard from 1831 until his death in 1880. Peirce was a
strong believer in the transcendental nature of mathematics. Especially after the discovery of
Neptune, the field of geometry was easily put upon a pedestal as a transcendental science. Having
been president of the American Association for the Advancement of Science in 1853, he spoke,
upon retiring from this position, about the transcendence of geometry. “But ascend with me
above the dust, above the cloud, to the realms of the higher geometry, where the heavens are
never obscured; where there is no impure vapor and no delusive or imperfect observation; where
the new truths are already arisen, while they are yet dimly dawning upon the earth below,”6 he
extolled. He went on to provide a thoroughly divine picture of mathematics.7
“Long before Bacon and Galileo, before observation had begun to penetrate the veil
under which Nature has hidden her mysteries, the restless mind sought some principle
of power, strong enough, and of sufficient variety, to collect and bind together all the
parts of a world. This seemed to be found, where one might least expect it, in abstract
number. Everywhere the exactest numerical proportion was seen to constitute the
spiritual element of the highest beauty. It was the harmony of music, and the music
of song; the fastidious eye of the Athenian required the delicately curved outlines
of the temple in which he worshipped his goddess to conform to the exact law of the
hyperbola, and he traced the graceful features of her statue from the repulsive wrinkles
of Arithmetic. Throughout nature, the omnipresent beautiful revealed an all pervading
language spoken to the human mind, and to man’s highest capacity of comprehension.
By whom was it spoken? Whether by the gods of the ocean and the land, by the
ruling divinities of the sun, moon, and stars, or by the nymphs of the forest and the
dryads of the fountain, it was one speech, and its written cipher was cabalistic. The
cabala were those of number, and even if they transcended the gematric skill of the
Rabbi and the hieroglyphical learning of the priest of Osiris, they were, distinctly and
unmistakably, expressions of thought, uttered to mind by mind; they were the solutions
of mathematical problems of extraordinary complexity. The bee of Hymettus solved
6 Benjamin Peirce. Address to the American Association for the Advancement of Science. 1853. url: http:
//www.spirasolaris.ca/Peirce1853.html, paragraph 3.
7 Ibid., paragraph 5.
4
its great problem of isoperimetry8 on the morning of creation; and the sword which
threatened the life of Damocles vibrated the elliptic functions two thousand years
before Legendre, Abel, and Jacobi had gained immortality by their discussion.”
Visionaries of Logic
It wasn’t only in matters of metaphysics and faith that mathematicians fancied themselves authorities: also in social matters, they had lofty plans for mathematics. In a society plagued by
religious factionalism, British mathematicians tended towards strongly ecumenical views. Two
prime examples of such mathematicians who longed for harmony and unity in society are George
Boole and Augustus De Morgan.
Boole, from the very beginning of his career, was confronted with the factionalism that ran
strong in Victorian society. He held his first teaching position at a Methodist school in the 1830s.
The Methodists were displeased, however, when they discoverd that Boole was not a Methodist
himself and they began to pray for his conversion. To avoid becoming the centre of controversy,
Boole quickly resigned.
Wherever he went, Boole, to his distaste, was faced with clashing religious factions. In 1849,
he found a spark of hope. He secured a position at Queen’s College in Cork, Ireland. QCC
was founded to be a nondenominational school where students from any religious background
were welcome and where factionalism was to be checked at the door. Boole viewed QCC as an
opportunity to promote unity among the different factions and also as a proving ground, to see
how well those factions could get along with each other and his hopes were high as he travelled to
Ireland.
Things were not quite so simple, Boole found when he arrived. Arriving in the middle of the
Great Famine, which kindled nationalistic sentiments among the populace, Boole found himself
alienated from the Irish. Nonetheless, Boole and QCC seemed to thrive. Though many of the
Irish viewed the new school with suspicion, it was accepted as a part of higher education and,
although the Catholics in the area hardly approved of the college, half of the students enrolling
at the school in the first year were Catholics.
Boole’s optimism soon started to fade, however. The new Irish Primate, Paul Cullen, began to
speak out against QCC and the rest of the Catholic church followed suit, denouncing the school
in their sermons and condemning the Catholic students for attending it. Student numbers started
to dwindle. Among growing religious tensions both in Ireland and back in England, QCC was
not faring well. Things took a turn for the worst when the Pope outright condemned the Queen’s
College and the pressure on its Catholic students to abandon it increased tremendously.
Perhaps surprisingly, Boole never decided to leave QCC and head back to England. In his
view, the situation in his home land was no better. He never would see the unity he so longed for
and never did find a place or religious denomination where he truly felt at home.
Not with religion, then, did Boole satisfy his longing for harmony, but with mathematics.
While working on his system of logic, published in his An Investigation of the Laws of Thought in
1854, Boole’s motivation was not primarily the advancement of mathematics but the development
of a proper language for discussion – particularly religious discussion. Boole hoped, perhaps overly
optimistically, that through developing logic, mathematicians would be able to find a system to
objectively test the veracity of any conceivable statement and thus structure the religious debates
and ultimately produce the unbiased truth of the matter. This would wipe out the religious
factionalism, which appalled him so, or so Boole dreamed.
Unsurprisingly, the first matters Boole applied his formal logic to were not mathematical issues,
but matters of religion and passages in the Bible. He hoped to show people how his logic could
be used to settle disputes and to, in the end, lead to a universal faith.
Augustus De Morgan was similarly interested in logic. He, too, could not see himself at home
within any of the religious denominations and deplored the friction between the different factions.
To understand just how broad was the ecumenism of De Morgan specifically and of mathematics
in general, we might look at the logo De Morgan designed for the London Mathematical Society,
founded in 1865, of which he served as the first president. He inscribed it with the motto Vis
unita fortior (a united force is stronger) and the numbers 1865, 5625 and 1281. All three numbers
8 Bees are thought to create their hexagonal honeycomb structures because the hexagons use the least amount
of material to span a given volume.
5
represent the year in which the LMS was founded, in the Christian, Jewish and Islamic calendars,
respectively. De Morgan was implying that people of all cultures and religions could unite under
the banner of transcendental mathematics.
In 1828, when he was only 21, De Morgan managed to land himself a coveted position as
the first professor of mathematics at University College, London. UCL, like QCC, was founded
to be a nonsectarian, secular university. Students from any faith were admitted. De Morgan
was optimistic about the influence of such a school on sectarian society and readily engaged in
promoting unity, befriending people from different backgrounds as he went.
Like Queen’s College, however, UCL was unable to keep sectarian controversy off of its campus
for long. From its inception, University College was derided as a godless and infidel institution.
Soon after its creation, UCL became mired in power struggles and began to forget its founding
principles. Leonard Horner, the college warden, tried in 1830 to appropriate more power for
himself, while De Morgan argued that faculty needed their autonomy. He went so far a year later
as to threaten to resign if the teachers were not granted more freedom. The administration was
unconvinced, however, and De Morgan resigned from UCL.
In 1837, De Morgan rejoined University College and for a while, sectarianism seemed to be
kept at bay as UCL greatly expanded. Unlike the unfortunate Boole, De Morgan had relatively
little to complain about. He did hear of his colleague’s predicament and sympathized, writing to
him in 1849, “I sincerely hope . . . that by keeping out of their squabbles, you may be able to live
in peace.”9
Eventually, though, controversy returned to campus. In 1853, UCL accepted a large donation
for the purchase of books. The benefactor imposed a condition that conflicted with the secular
principles of the school, however: only Anglican professors were allowed on the purchasing committee. De Morgan attempted to fight this compromising decision, but the library, tasked with
building a collection from nothing, eagerly wanted the money. The UCL council accepted the
donation on the technicality that the restriction had nothing to do with the hiring of professors
or with their regular duties and thus did not conflict with the school principles, greatly angering
De Morgan.
Like Boole, De Morgan also saw promise in logic to rid society of sectarian frictions. He
produced his own system of logic, which he published in his book Formal Logic in 1847. For
De Morgan, the problem lay in language. Human language was confused and vague and De
Morgan especially attacked the hazy use of words by theologians. Even basic concepts like “belief”
and “worship” meant different things to different factions and had taken on different meanings
throughout history.
In logic, De Morgan saw the way forward towards creating a precise language, using which one
could have a clear and meaningful debate. He wanted the statements and arguments in social and
theological debates to be as precise as those in matters of geometry. In his address to the London
Mathematical Society at its first meeting in 1865, De Morgan tells his fellow mathematicians how
important it is to study language, in addition to mathematics.10
“We have also questions of Language. If we do not attend to extension of language, we
are shut in and confined by it. Of this Euclid is a good example. He was stunted by
want of extension. When we come to study language in connection with Logic, we find
a great many things which would hardly have been expected, and by which we may
learn how we may best extend the meanings of our terms. Would any one suppose, at
first sight, that “of” and “but” are connected together in the manner of positive and
negative? ‘All of men,’ or ‘all men,’ including everything that is in the term ‘man.’
‘All but man’ including all that is not in the term ‘man.’ Thus, when we are speaking
of animals, the first phrase means all men; the second, all animals except men. ‘But’
thus contains the absolute opposite of ‘of.’ . . . When we begin to see the like of such
things as are here pointed out, we begin for the first time to have a rational power of
extending the meanings of words.”
9 Quoted in Daniel J. Cohen. Equations from God: Pure Mathematics and Victorian Faith. The Johns Hopkins
University Press, 2007. isbn: 0801885531, p. 116.
10 “Speech of Professor De Morgan”. In: Proceedings of the London Mathematical Society s1-1.1 (Jan. 1865),
pp. 1–9. issn: 0024-6115, 1460-244X, p. 8.
6
Pure Mathematics
As the nineteenth century wore on, however, the lofty view of mathematics that reigned at its
dawn seemed less and less tenable. As professionalization swept through the scientific world,
mathematics was inevitable caught in the flow. With religious factionalism raging on in Victorian
society and intensifying rather than subsiding, the ideals of unity held by mathematicians like
Augustus De Morgan and George Boole seemed less and less realistic.
In 1866, the UCL sought a new professor of psychology and one of the candidates was philosopher James Martineau. Though he was well-qualified, a dispute over his candidacy erupted when
council members learned that he was a Unitarian. Eventually, his opponents managed to keep
Martineau from landing the position.
The affair outraged De Morgan, who saw it as an indication that sectarianism had infiltrated
his secular university. It eventually drove him to resign his position once more, this time for good.
His hopes for unity were shattered. When in 1869 Martineau, together with his colleague Rev.
J. J. Tayler, came up with the idea of establishing a new brotherhood, the Free Christian Union,
where all monotheistic believers would be welcome to come together, set aside their differences
and become one under God, De Morgan, as much as he would have loved to see this endeavor
realized, had little hope for its success. To his eyes, society seemed too polarized for anything so
harmonic to flourish. “Supposing the intermediates could fraternise with the extremes, could the
extremes fraternise with one another? . . . You have your sand, and you aspire to make rope.”11
Resigned to the fact that sectarianism was a weed not easily stamped out, mathematicians began to distance themselves from theological debate, rather than try to overcome it. In the process,
they had to form a much more modest philosophy of mathematics and let the transcendental nature of the field go. Where in 1828, the young De Morgan had extolled the virtues of mathematics,
which would provide “the truths of metaphysics[,] of jurisprudence, or of political economy,”12 in
the 1860’s he set forth a much more modest view of mathematics, stripped of divine connotations.
Mathematics was a human endeavor: “Laws are mental enunciations . . . the names of diseases are
not known to nature–nor are laws.”13
Getting rid of the transcendental and divine view of mathematics was necessary for the proper
professionalization of the science. After all, if mathematics was a divine language, then certainly
the clergy and, in fact, any good Christian, had business learning about it and trying to advance
it. Professionalizing mathematicians, however, had to draw distinct lines: mathematics was to be
done by capable, professional mathematicians, not by amateurs or clergy. Therefore, the divinity
of mathematics had to go.
By making their science an earthly one, they made it less threatening as well as less alluring to
others. Mathematicians made no claim to metaphysical authority or even absolute knowledge. In
his book, The Principles of Science (1874), William Stanley Jevons, one of De Morgan’s students,
writes of the limitations of scientific knowledge and specifically, “Even mathematicians make statements which are not true with absolute generality.”14 In lowering the value of scientific knowledge
and draining certainty from science, Jevons explicitly tries to make it a non-threat to the religious
establishment. Near the end of his book one finds the following conclusion.15
“My purpose, as I have repeatedly said, is the purely negative one of showing that
atheism and materialism are no necessary results of scientific method. From the preceding reviews of the value of our scientific knowledge, I draw one distinct conclusion,
that we cannot disprove the possibility of Divine interference in the course of nature.”
Developments in several branches of mathematics itself shook its foundations and hurried
the loss of the transcendental view of the science along. For example, the Victorian era saw
the development of non-Euclidean geometry, which would ultimately allow Albert Einstein to
formulate his general theory of relativity. Euclid’s fifth postulate, the idea that for any line and
a point not on that line, there is a unique line through the point that is parallel to the first
11 Quoted
in Cohen, see n. 9, p. 159.
in ibid., p. 133.
13 Quoted in ibid., p. 136.
14 William Stanley Jevons. The Principles of Science: a Treatise on Logic and Scientific Method. London: MacMillan and Co., Limited, 1913, p. 43.
15 Ibid., p. 766.
12 Quoted
7
line and never intersects it, turned out not to be a necessary axiom. A consistent geometry
could be constructed in which parallel lines do intersect. When the famous mathematician Georg
Riemann established that non-Euclidean geometries could be realized in higher-dimensional spaces,
geometry became so abstract that it had little to do anymore with its common-sense origins.
Similar developments occurred in other branches of mathematics. As Georg Cantor studied
the real numbers in the context of set theory, they became an abstract mathematical construction
and there was less focus on using them to describe anything in the physical world.
These developments helped reshape the view of mathematics. It lost its divine appearance and
even started to remove itself from the physical world and became an abstract system unto itself.
The completion of this process came around the turn of the century at the hands of Bertrand
Russel. Russell was an enormous fan of pure mathematics and made it his mission to divorce
mathematics once and for all from the material world. His work on formal logic eventually lead
him to the realization that mathematics and logic were actually the same thing: mathematics
could be constructed out of a logical basis. When he put these ideas forth in The Principles of
Mathematics (1903), his book was about mathematics and mathematics alone; there was nothing
in his pages that might imply an advance in understanding of the physical universe.
Russell put forth his view of mathematics as an abstract system, removed from physical science,
in his essay Recent Work on the Principles of Mathematics, published in International Monthly
in 1901 and intended for a broad audience. Tellingly and explicitly, he casts out any reference to
anything physical whatsoever.16
“Pure mathematics consists entirely of assertions to the effect that, if such and such a
proposition is true of anything, then such and such another proposition is true of that
thing. It is essential not to discuss whether the first proposition is really true, and not
to mention what the anything is, of which it is supposed to be true. Both these points
would belong to applied mathematics. We start, in pure mathematics, from certain
rules of inference, by which we can infer that if one proposition is true, then so is some
other proposition. These rules of inference constitute the major part of the principles
of formal logic. We then take any hypothesis that seems amusing, and deduce its
consequences. If our hypothesis is about anything, and not about some one or more
particular things, then our deductions constitute mathematics. Thus mathematics
may be defined as the subject in which we never know what we are talking about, nor
whether what we are saying is true.”
The enormous contrast between Russell’s view of mathematics and the lofty conceptions of earlier nineteenth century mathematicians like Benjamin Peirce can hardly be exaggerated. Mathematicians faced the sunrise at the dawn of the twentieth century thoroughly professionalized,
secularized and retreated into a bubble of abstractness. Because the mathematicians readily retreated into this bubble and relinquished all claim to physical or metaphysical authority, their
interests did not clash greatly with the clergy. This allowed mathematics to fairly easily claim a
larger role in church-dominated education.
Squaring the Circle
As the level of abstraction of mathematics increased, a side effect was that amateur mathematicians found themselves more and more unable to keep up with the field. This set up a barrier
between professional mathematicians and aspiring amateurs. To some, however, this was not a
deterrent. They eagerly argued with professional mathematicians, some very publicly, and accused
the professional community of all sorts of conspiracy when they failed to be heard.
One example of a tenacious and very public amateur mathematician was one James Smith,
who was obsessed with the problem of squaring the circle. This ancient geometric problem of
constructing, for a given circle, a square with the same area, was highly alluring to amateur
mathematicians. The statement of the problem is extremely simple, which circumstance might
offer hope of a simple solution. That professional mathematicians believed there was no solution
did not deter James Smith from endeavoring to find one and, believing he had indeed found one,
defending it fiercely against the (invariable dissenting) opinions of professionals.
16 Bertrand Russell. Recent Work on the Principles of Mathematics, reprinted as Mathematics And The Metaphysicians. 1901. url: http://www.readbookonline.net/readOnLine/22895/, paragraph 3.
8
In 1861, Smith publiced a book, The Quadrature of the Circle, in which he published his
correspondence with an “Eminent Mathematician” (Augustus De Morgan) about the quadrature
of the circle. In the introduction, he laments his treatment at the hands of the British Association
for the Advancement of Science. Smith had come up with the theory that π = 25
8 and believed he
could prove it. He wrote a paper on the subject and submitted it to the Association, requesting
that he might read it to the assembly.
Though he was ultimately allowed to read his paper, Smith’s theory was discarded out of
hand by the mathematicians. During a meeting of the Association, Smith met George Biddell
Airy, mathematician and Astronomer Royal of England at the time. Upon being asked to discuss
Smith’s theory about the quadrature of the circle, Airy replies, ”It would be a waste of time, Sir,
to listen to anything you could have to say on such a subject.”17
The reason the mathematicians weren’t interested in what Smith had to say was that nearly
a century ago, the Swiss mathematician Johann Heinrich Lambert proved that π is an irrational
number. Though this did not yet prove conclusively that it was impossible to square the circle
(this would be proven in 1882, when Ferdinand Lindemann would show that π is transcendental),
most mathematicians believed that it was. In any event, it ruled out Smith’s theory that π = 25
8 .
Smith, however, believed the mathematicians were being thickheaded at best and consciously
conspiring against the truth at worst. He believed he had a valid contribution to science and felt
the mathematicians were keeping him from making that contribution. He proceeded to enter into
correspondence with several mathematicians, among whom the famous physicist and mathematicians William Rowan Hamilton; professor of mathematics at Queen’s College, Liverpool, William
Allen Witworth; and Augustus De Morgan. The latter two engaged in a lengthy correspondence
with Smith, pointing out the fallacies of his proofs, to little avail.
The case of James Smith is telling of the professionalization that had occurred in the mathematical community. There was a barrier around the professional mathematics, which the amateur
could not penetrate (for good reason). When Smith informs him that he means to publish their
correspondence, De Morgan replies, “What can be the object of the publication . . . I confess I am
unable to see. The mathematical world does not want to be reminded of a familiar proof, and the
non-mathematical will not understand a word.”18 De Morgan makes a clear distinction between
the professional mathematicians and the rest of the world.
Physics, Queen of the Sciences
Of course, not all of mathematics started to shun the physical world. Mathematics was fundamental to many other fields of science, especially physics, but also in engineering, industry
and economics. De Morgan’s student William Stanley Jevons would turn his attention towards
theoretical economics, applying mathematics to economic problems.
Mathematics and physics are especially intimately related fields. So much so that, at the
beginning of the nineteenth century, much of what we now consider to be physics actually fell
under the domain of mathematics. Additionally, any physical experiments were actually performed
at chemical laboratories; there were no laboratories designed specifically for physics research yet.
In fact, there was no such discipline as physics. It was during the nineteenth century that the
segmentation of science into different disciplines, which is still in place today, was established.
As discussed in the previous section, mathematics grew more and more abstract as the nineteenth century wore on and mathematicians drew themselves away from the physical world completely as it turned. Mathematical and theoretical physics was left to the physicists. Furthermore,
as the descriptions of electricity, magnetism, heat, light and the like became more and more mathematical, many chemists, whose field tended to employ different modes of thought, began to lose
interest in these fields, allowing physics to scoop them up.
The rising discipline of physics fared well as its practitioners carved out professional careers
for themselves and by the century’s close, physics was not only, like other sciences, secularized
and professionalized, it was also the dominant science and physicists the ultimate authority on
the nature of the universe. Where at the beginning of the century, mathematics had been deemed
17 James Smith and Augustus De Morgan. The Quadrature of the Circle: Correspondence Between an Eminent
Mathematician and James Smith, Esq. London: Simpkin, Marshall & Co., 1861, p. xiv.
18 Ibid., p. 146.
9
the fundamental science, manifestly divine, a hundred years later physics had taken the mathematician’s crown.
The Quest for Unity
The end of the eighteenth century saw the rise of the cultural movement of Romanticism. This
movement is usually associated with literary and artistic interest in human emotions and imagination and picturesque natural scenes, in opposition to the emphasis on the rational that prevailed
during the Enlightenment. However, the Romantic ideas also had a profound influence on the
natural sciences.
In contrast to the scientific view that the universe was a clockwork mechanism that could
be understood by taking it apart and examining the different cogs separately, Romantic natural
philosophers believed that nature must be one harmonic whole; nature must possess unity, they
thought. It was the task of the natural philosopher to try to find this unity, to look under the
surface of mere phenomena and come to understand the underlying meaning.
This lead to a new direction of scientific thought in the first decades of the nineteenth century.
As quick progress was made in different fields of natural philosophy, researching the phenomena of
light, heat, electricity, magnetism, motion and chemical affinity, there rose also the urge to unify
these areas, to find one basic principle that underlay all these different phenomena.
This pervasive idea of unity in nature turned out to be highly successful. Numerous experiments
performed by natural philosophers showed again and again how forces from one of these field could
be used to generate a different kind of force. When the chemist Humphry Davy rubbed together
two sheets of ice and noted that the friction caused them to melt, he came to the suggestion that
heat was not, as was thought at the time, some kind of intangible fluid, but actually just a form
of motion. A highly visible example, thanks to the Industrial Revolution, of the converse process
was also available. The steam engine clearly turned heat into motion.
In 1818, Scottish chemist Andrew Ure applied electricity to the nerves of a recently executed
criminal, causing the body’s muscles to contract. It showed that electricity was a fundamental
property of the human body and also that electricity could be used to effect motion. In 1820,
Hans Christian Oersted found that a magnetized needle was deflected when put in the vicinity
of a current-carrying copper wire, establishing a link between electricity and magnetism. Later,
Michael Faraday would build extensively upon this first link between the two phenomena, discovering magnetic induction and many more relations that would be of great inspiration to the famous
physicist James Clerk Maxwell when he conjured up his unified theory of electromagnetism.
Similar relationships were found between essentially all the different forces. Heat could be
turned into electricity by heating metals in a specific configuration. Inquiries into the effect of
different colours of light on the temperature of black bulbs by William Herschel showed interesting
links between solar light and heat (and lead to the discovery of infrared radiation). The new
technology of photography made very explicitly visible how light could effect chemical reactions.
In 1842, William Robert Grove invented the gas battery, precursor to the modern fuel cell, in which
he combined hydrogen and oxygen into water, producing electricity in the process; it produced
electricity from chemical affinity.
All these links seemed proof to many that there must be some underlying scheme uniting all
these forces. In 1846, Grove published his On the Correlation of the Physical Forces, in which he
set forth the idea that all the forces must be interrelated and can be converted into one another.
In the introduction, he writes,19
“The position which I seek to establish in this Essay is, that the various affections
of matter which constitute the main objects of experimental physics, viz. heat, light,
electricity, magnetism, chemical affinity, and motion, are all correlative, or have a
reciprocal dependence; that neither, taken abstractedly, can be said to be the essential
cause of the others, but that either may produce or be convertible into, any of the
others: thus heat may mediately or immediately product electricity, electricity may
produce heat; and so of the rest, each merging itself as the force it produces becomes
developed.”
19 William
Robert Grove. The Correlation of Physical Forces. London: Longman, Green, Longman, Roberts, &
Green, 1862, p. 10.
10
Grove frequenty lectured at the London Institution and often presented experiments that exemplified the correlation of the forces. His gas battery was a great favourite: Grove could merge
oxygen and hydrogen into water, producing electricity, and then use that electricity to split water into oxygen and hydrogen once more. For him, it was one of the greatest examples of the
mutability of the physical forces.
Eventually, not the correlation of physical forces would unite different areas of natural sciences,
but the more abstract concept of conservation of energy, which is still a basic tenet of physics today.
It would form an important part of Maxwell’s highly successful theory of electromagnetism and
would explain the correlations of the different fields of electricity, magnetism, heat, light, motion
and chemical affinity not through a direct correlation of the forces involved, but as the conversion
of one type of energy into another.
This search for unity and finally the discovery of that unity in the principle of the conservation
of energy allowed physics by the end of the nineteenth century to have established itself as the
most fundamental of the sciences and physicists to proclaim themselves the ultimate arbiters on
the nature of the physical universe.
Progenitors of Progress
Physicists also made an effort during the nineteenth century to make themselves useful and visible
to society. This did as much as, if not more than, the scientific merits of the field to cement the
view of the discipline of physics as greatest of all the sciences in the public eye.
Physics was not only a grand scientific quest to uncover the workings of nature, it had myriad
applications in society as well. With the industrial revolution in full swing, machines that worked
thanks to physical principles were abundantly visible and propelling economies forward. Advances
in astronomy allowed for more accurate navigation at sea, highly valuable for trade and warfare.
Perhaps most visible, however, was the science of electricity. Because it lent itself readily to
spectacular shows as well as to useful applications, electricity easily captured people’s imagination.
The first successful commercial technique to come from the field of electricity was electroplating.
It was noted that in a certain type of battery, a layer of metal would coat one of the electrodes as
the battery was drained. It was possible to use this phenomenon to coat a cheaper metal with a
thin layer of a more expensive metal and for mass-producing, for example, cheap silverware.
The most spectacular electrical invention of the nineteenth century, however, was the electric
telegraph. Though the concept of the telegraph is simple – an electrical circuit, a switch and a
way to make it known to the user when current is running – getting it to work over very large
distances was not quite so trivial. Breaks in the cables and dealing with noise and interference
posed serious challenges to the electrical engineers working on the telegraph systems that were
meant to cross oceans. The concept of instantaneous long-distance communication was also still
somewhat foreign to the world, although mid-length telegraphs were already operational, and
many potential investors were skeptical of the projects. When the first few attempts at laying
transatlantic cables failed, this greatly undermined public interest in the projects. It would take
some convincing to get public support for the transatlantic telegraph and it was only through
social engagement and promotion that engineers were able to achieve this support.
One such engineer was Cromwell Fleetwood Varley, a prominent telegraph engineer who invented several novel electrical devices for such purposes as finding breaks in cables, which helped
in realizing working long-distance telegraph systems. Varley’s method for promoting his telegraphy projects seems somewhat bizarre, viewed with modern eyes: he linked telegraphy with
Spiritualism.
It was very much in vogue in the nineteenth century to attend séances and to attempt to
communicate with the dead. Mediums, who seemed to be able to put the living in touch with
the deceased, were much sought after society. Varley drew a parallel between telegraphy and
talking to the dead. Another prominent telegraph engineer, William Thomson (Lord Kelvin),
described telegraphy as “the art of interchanging ideas by means of dead matter occupying space
between two intelligent beings,”20 a description which might as well have been written about spirit
communications. The parallel was easily drawn. During a séance, spirits would generally make
their messages known by rapping noises, signifying a sort of code, just like the telegraph was used
20 Quoted in Richard J. Noakes. “Telegraphy is an occult art: Cromwell Fleetwood Varley and the diffusion of
electricity to the other world”. In: British Journal for the History of Science 32 (1999), pp. 241–459, p. 422.
11
to transmit messages using Morse code. Mediums promised communication with invisible spirits,
like telegraphy companies promised communication with invisible people on the other side of the
Atlantic Ocean.
Varley was a firm believer in Spiritualism and devoted significant time to studying the matter,
attempting to prove scientifically that mediums were not charlatans, but really were in communication with spirits. He used electrical circuitry to scrutinize the practices of one particularly
popular medium, Florence Cook. Miss Cook purported to be able to actually materialize a spirit.
There was skepticism as to the veracity of these claims; during Miss Cook’s séances, the medium
herself sat in an adjacent room, out of view of her guests and the spirit she materialized bore
physical resemblances to Miss Cook herself. Varley attached electrodes to the medium’s body,
connecting her to circuitry that would be able to measure whether or not she moved from her
chair or removed the electrodes. When the materialized spirits came into the room, she wore no
electrodes and the circuitry showed nothing out of the ordinary; Varley was convinced that Miss
Cook was in the adjacent room the whole time, while the spirit was in the same room as he,
convincing him of Florence Cook’s powers.
At first, Spiritualism itself benefited most from the parallel with telegraphy to make its claims
plausible; if one can communicate with people across large distances, then why not with people
separated from us by death? Scientific proof such as that produced by Varley provided it with great
credibility. However, Varley subtly reversed the benefit to convince a broad audience – Spiritualism
was widely popular – of the soundness of the idea of building transatlantic telegraphs.
An important role in Varley’s scheme was played by William Henry Harrison, editor of the
Spiritualist, a popular magazine devoted to Spiritualism. Harrison had once been Varley’s personal
secretary and readily accepted his influence on the pages of his magazine. For Harrison, input from
a man of science like Varley boosted the credibility of his beliefs and of the writings he published
and he encouraged his readers to learn about scientific principles to better understand that input.
For Varley, the Spiritualist offered him just the audience he wanted: the readers were interested
in learning about science and telegraphy as well as Spiritualism and Varley could present himself
as an authority on both matters.
If believers in spirits wanted to use Varley’s scientific – specifically, electricity based – proofs
of the veracity of Spiritualist claims, they would have to accept that his electrical devices and
circuitry worked as he told them. They had to accept that he was an authority on those matters.
Varley used this authority to also sell them the idea of transatlantic telegraphy; after all, the
techniques he had used to scrutinize Miss Cook were essentially the same as those telegraphy
companies employed in their endeavors.
When transatlantic communication was eventually realized, the link with Spiritualism was
no longer necessary to sell telegraphy and science distanced itself from such notions. Varley’s
experiments with Florence Cook had a semblance of scientific method strong enough to cater
to believers, but they were strongly contested in academic circles. Having moved telegraphy
firmly out of speculation and into the realm of reality, physics readily dropped any Spiritualist
connotations and turned to its purely scientific explanations as the real and only reasons to trust
in telegraphy.
Once proven to be achievable, transatlantic telegraphy provided a highly visible step forward
in the progress of man. The leap in communication speed was unprecedented, shrinking the world
like no other invention ever had. For the science of electricity, it was a huge achievement and for
its practitioners, it provided a commercially viable application.
Electricity seemed an endless source of inspiration for nineteenth century inventors. Further
examples of electrical technology are the electric motor and electric lights, which would similarly
represent quick progress of man’s triumph over nature. The economic potential of electricity
seemed vast and its promise for human prosperity was hailed enthusiastically. William Robert
Grove praised its power in a speech addressed at the London Institution in 1842: ”Had it been
prophesised at the close of the last century that, by the aid of an invisible, intangible, imponderable
agent, man would in the space of forty years, be able to resolve into their elements the most
refractory compounds, to fuse the most intractable metals, to propel the vessel or the carriage, to
imitate without manual labour the most costly fabrics, and, in the communication of ideas almost
to annihilate time and space;–the prophet, Cassandra-like, would have been laughed to scorn.”21
21 Quoted
in Iwan Rhys Morus. When Physics Became King. University Of Chicago Press, 2005. isbn: 0226542017,
12
Electrical Entertainment
Physicists also busied themselves with providing the public with entertainment, further popularizing their field. For many physicists, giving lectures to a general audience was an important
source of income. Michael Faraday presided over weekly discourses where scientists were invited
to present the latest progress to London’s scientific, but also social, elite.
Of great importance, however, were the shows and exhibitions that were a popular part of
nineteenth century culture. The most well known exhibition is perhaps the 1889 World’s Fair in
Paris, which sported the Eiffel Tower. There were many of these kinds of exhibitions in Europe
and in the United States, where the public could come to marvel at the advances of art, science,
engineering and natural wonders. At these exhibitions, electricity was often well represented.
New marvels of electrical engineering, like the electrical telegraph and the electrical motor, were
displayed there and electrical inventors came to promote their inventions.
The first of these huge World’s Fairs, where international exhibitionists were welcomed to
display their wonders, was the Great Exhibition of the Works of Industry of all Nations in London
in 1851. Among the wonders of science, industry and art exhibited at the Great Exhibition,
electricity made a sizable appearance. On display were several electrical telegraphs, art produced
through electroplating, electric motors and an electromagnet made by the physicist James Prescott
Joule, which ”produces such a powerful attraction between the electromagnet and its armature,
that a weight of more than one ton has to be applied in order to draw them asunder.”22
More such exhibitions followed. At the Philidelphia Centennial Exhibition of 1876, Graham
Bell’s telephone was first displayed. By 1893, at the World Columbian Exposition in Chicago, the
Electricity Building was illuminated with 120,000 electric lights and visitors could travel around
the exhibition by electric railway. These exhibitions provided a showcase for electricity and made
it part and parcel of culture in the nineteenth century.
More small-scale showmanship, often flamboyant, also contributed to the public image of electricity. A well known example is Nikola Tesla, a Serbian immigrant in the United States who
made a name for himself as an inventor and showman. With his inventions, he was able to dazzle
crowds with enormous artificial lightning bolts and other amazing effects, showing his audience
his mastery over nature.
Through all these forms of entertainment, from the lectures of Faraday to the grand exhibits
and the spectacular electrical shows of men like Tesla, a wide audience got to know electricity
during the nineteenth century and thus it helped propel physics towards becoming the foremost
scientific discipline.
Comparison
When we compare the development of physics in the nineteenth century with that of mathematics,
we find some striking differences. The broad movement towards secularization and professionalization is similar: both sciences, by the end of the nineteenth century, are more heavily organized
into demarcated professions, offering their scientists career possibilities quite unavailable a century
earlier, and have got rid of church influences. The paths they take to reach this point are quite
different, however.
Mathematicians have high hopes for their science in the first half of the nineteenth century,
likening their science to a divine language in which God has written the laws of nature and
hoping it will also provide a common, objective language for human discourse that would lead
mankind to theological truth and, consequently, unity. As the century progressed, however, these
ideals started to crumble. New insights into the fundamentals of mathematics – specifically,
finding that those fundamentals were not as sturdy as had been thought – undermined the idea
that mathematics was something divine. As sectarian disputes raged only stronger, logic seemed
impotent to realistically provide a solution. Towards the end of the century, mathematics slowly
drew away, not only from its notions of godliness but also from any claim to authority over the
physical world and mathematicians redefined their field; mathematics was a human construct, a
p. 112.
22 The Great Exhibition of the Works of Industry of all Nations Official Descriptive and Illustrated Catalogue.
Vol. 1. London: Spicer Brothers, 1851, p. 432.
13
human system of logic based upon a set of human axioms; a closed logical system, whose only
requirement was internal consistency: any bearing on the real world was no longer a priority.
Because of the lack of any claims to authority by mathematicians, they had little conflict with
the clergy and were able to relatively easily climb up to a higher position within church-dominated
educational systems. Mathematics was a valued part of the training of the minds of the future
ruling class.
Physicists didn’t have the luxury of being able to withdraw themselves from conflicts over
authority; their science was necessarily about the nature of the cosmos. Eventually they gained the
authority they still hold today as the ultimate arbiters of the fundamentals of physical existance,
but only with considerable effort. Physics as a discipline had to acquire its domain of authority
from parts of mathematics and chemistry and its place in society and its image as the dominant
science had to be conquered.
Different factors went into establishing physics as the dominant science. If not for the Romantic
longing for beauty and unity in nature, the concept of conservation of energy might never have
been discovered and physics might not have attained its image as most fundamental of the sciences.
If not for the enormous applicability and marketability of the results of research in the fields of
e.g. electricity, thermodynamics and astronomy, physics would not have had the impact that it
did on societies and economies and would not have been viewed as the great producer of progress.
If not for the spectacular exhibits and shows that the science of electricity allowed electricians to
set up, physics might not have captured the public’s imagination quite so strongly.
The appearance of physics on the map relied on all these efforts. Physicists, to obtain the
position they found themselves in at the turn of the century, had to be active in society and
entrepeneurial, selling their science and the idea that they were the ultimate authorities on what
nature was like. The nineteenth-century efforts paid off, however, when physics had conquered the
throne and it was physics, rather than mathematics, which was viewed as queen of the sciences.
Comparing these accounts of the changes mathematics and physics went through with Turner’s
idea of deliberate professionalization, we see that this explanation, though clear-cut and elegant,
is not quite satisfactory. The professionalization of science was directed by numerous factors and
subject to the forces of society: industrialisation, sectarian strife, Romanticism and Spiritualism were all cultural trends that scientists and therefore science were not immune to. Profound
changes within the sciences themselves also contributed. Increasing abstractness was likely the
main reason amateurs were shunned from mathematics, not mathematicians’ desire to professionalize themselves. The advances in the science of electricity provided material highly suitable for
promoting physics to the public and the concept of energy allowed physics to snatch the title of
most fundamental science.
We see that Turner’s account needs to be nuanced: though perhaps some scientists, such as
Huxley and Tyndall, were to some extent conscious of the changes occurring and actively tried to
further them, it was certainly not a collective effort by all of science. Men of science worked with
what they had, to make of their science what they could and what they thought it should be, and
to carve out careers for themselves, but to suppose that the effect – professionalized science – was
their goal would be placing the cart before the horse.
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