Table Of ContentMATHEMATICIANS
AND THEIR GODS
Interactions between mathematics
and religious beliefs
Edited by
snezana lawrence
and
mark m cartney
c
1
1
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preface
The overlap between mathematics and theism may seem at first sight
an unpromising topic for a book. But as the many contributors to this
volume show, the intersection between the two provides fertile ground
both for historians of mathematics and of theology, and for the interested gen-
eral reader. The chapters have been written by a range of subject experts, who
have given willingly of their time and their knowledge. They have also submitted
with good humour and patience to our various editorial queries, suggestions,
and proddings, and we thank them for their enthusiasm for, and commitment
to, the project.
The chapters of the book are ordered broadly chronologically and thus the
work can be read beginning with the Pythagoreans and then meandering
through a range of times, places, and people, to end with Kurt Gödel. However,
each chapter is independent of the others and so the reader can feel free to ‘dip
in’ to the book at whichever point he or she finds most interesting. Hopefully,
such a reader will then be enticed into the other chapters.
As is noted in the introductory chapter, this book makes no attempt to be
comprehensive. The most glaring omission is of Islamic mathematics, with the
centre of gravity of the book being within the Christian West. The bias is benign
and can be accounted for by the interests of the editors, and the desire to keep
the scale of the book within manageable proportions. If there is a benefit of this
bias, it is that it illustrates that even within such a restricted field of study the
interactions between religion and mathematics are surprisingly rich.
Snezana Lawrence & Mark McCartney
March 2015
CONTENTS
1. Introduction 1
mark mccartney
2. The Pythagoreans: number and numerology 21
andrew gregory
3. Divine light 51
allan chapman
4. Kepler and his Trinitarian cosmology 77
owen gingerich
5. The Lull before the storm: combinatorics in the Renaissance 89
robin wilson and john fauvel
6. Mystical arithmetic in the Renaissance: from biblical
hermeneutics to a philosophical tool 105
jean-pierre brach
7. Newton, God, and the mathematics of the two books 121
rob iliffe
8. Maria Gaetana Agnesi, mathematician of God 145
massimo mazzotti
9. Capital G for Geometry: Masonic lore and the history of geometry 167
snezana lawrence
10. Charles Dodgson’s work for God 191
mark richards
11. P.G. Tait, Balfour Stewart, and The Unseen Universe 213
elizabeth f. lewis
12. Faith and Flatland 249
melanie bayley
13. Gödel’s ‘proof’ for the existence of God 279
c. anthony anderson
Author biographies 290
Index 293
vi | CONTENTS
CHAPTER 1
Introduction
mark mccartney
It is unfortunate that in popular thought the prevailing description of the
interaction between science and religion is one of warfare. God, in some
circles it seems, is the enemy of progress, the person we lazily appeal to in
order to fill the gaps in our current scientific knowledge, an outdated idea, a
delusion, an intellectual non-subject. At best, religious belief is seen as a matter
of private devotion which has nothing to do with public life. At worst, some
quarters seem to want to take what may be called an Orwellian ‘Animal Farm’
approach to the matter, replacing Snowball the pig’s ‘four legs good, two legs
bad’, with a version of scientism which states ‘science good, religion bad’.
And yet, dig down a little below the surface of popular assessment to schol-
arship on the history and philosophy of science, and a very different picture
begins to appear. In academic circles the nineteenth-century ‘conflict model’
to describe the interaction between science and religion has been rejected and
replaced with what Andrew Gregory in Chapter 2 of this book describes as the
‘complexity model’. The complexity model recognizes that there is a spectrum of
interactions, ranging from conflict or mutual non-engagement to dialogue and
synthesis. It recognizes that there are indeed conflicts, but there are also connec-
tions and consonances, and that these interactions have cultural and historical
contexts. Academics such as John Polkinghorne (1930–) and Alister McGrath
(1953–) are examples of two scholars trained both in science and theology who
have written widely on the links between those disciplines from a Christian per-
spective.1 But they are only two from a long list of scholars, some of faith, some
INTRODuCTION | 1
of none, who feel that there is much more to be said, and that much more needs
to be said, than the Orwellian ‘science good, religion bad’.2
However, move from science to mathematics and the suggestion that there is
an overlap with theism is likely to lead to puzzled looks. Linking algebra with
the Almighty seems as sensible as trying to find common ground between bot-
any and basketball. The famous story of Leonhard Euler (1707–83) confronting
Denis Diderot (1713–84) at the court of Catherine the Great springs to mind:
Diderot arrived at the Russian court in the 1770s and, it is said, spoke freely
of his atheism. While Catherine was amused, her advisors suggested Diderot
should have his atheistic wings clipped. Hence Euler, then at the St Petersburg
Academy, was brought before the court and publically confronted Diderot with
the statement ‘Sir, (a + bn)/n = x; hence God exists – Respond!’ Diderot, unable
to answer, and humiliated by the laughter from all sides, left the court and
immediately returned to France.
The tale is, of course, apocryphal.3 It is amusing to imagine that the brilliant
mathematician Euler would say such a thing, even more amusing that Diderot,
editor of the Encyclopédie and well versed in mathematics, should have been
taken in by it, and positively ridiculous that any such ‘argument’ could make
an impression on anyone. We may seek for links between God and the scien-
tific description of the created order, but surely any connections we might wish
to make between God and our equations will be as weak as Euler’s fictitious
remark?
However, it is precisely with the phrases ‘scientific description’ and ‘our equa-
tions’ that potential links between mathematics and theism are to be found.
The scientific description of nature
Galileo Galilei (1564–1642), in his book The Assayer, famously stated that
‘Philosophy is written in this grand book – I mean the universe – which stands
continually open to our gaze, but it cannot be understood unless one first learns
to comprehend the language and interpret the characters in which it is written.
It is written in the language of mathematics, and its characters are triangles,
circles, and other geometrical figures, without which it is humanly impossible
to understand a single word of it; without these one is wandering about in a
dark labyrinth.’4 Galileo’s insight that mathematics is the language of the uni-
verse has grown in significance since he penned it in 1623. It is not simply
that mathematics is the language of nature, but also that, as the Nobel laureate
2 | MARK McCARTNEY
Eugene Wigner (1902–95) pointed out in a famous essay, there is an ‘unreason-
able effectiveness of mathematics in the natural sciences’.5 In his essay he notes
that in theoretical physics, complex and independently discovered branches of
mathematics often turn out to be the appropriate language of nature. Thus, in
quantum mechanics the use of complex numbers is ‘far from natural or simple
and they cannot be suggested by physical observations. Furthermore, the use
of complex numbers in this case is not a calculational trick of applied math-
ematics but comes close to being a necessity in the formulation of the laws of
quantum mechanics.’6
He goes on to quip that:
A possible explanation of the physicist’s use of mathematics to formulate his laws of
nature is that he is a somewhat irresponsible person. As a result, when he finds a
connection between two quantities which resembles a connection well-known from
mathematics, he will jump at the conclusion that the connection is that discussed in
mathematics simply because he does not know of any other similar connection. It is
not the intention of the present discussion to refute the charge that the physicist is a
somewhat irresponsible person. Perhaps he is. However, it is important to point out
that the mathematical formulation of the physicist’s often crude experience leads in
an uncanny number of cases to an amazingly accurate description of a large class of
phenomena. This shows that the mathematical language has more to commend it than
being the only language we can speak; it shows that it is, in a very real sense, the correct
language.
Closely linked to the effectiveness of mathematics in the physical sciences is
what many mathematicians see as the intrinsic beauty of good quality mathem-
atics. Thus G.H. Hardy (1877–1947), one of the greatest British pure mathemat-
icians of the twentieth century, stated that ‘The mathematician’s patterns, like
the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the
words, must fit together in a harmonious way. Beauty is the first test; there is no
permanent place in the world for ugly mathematics.’7
When asked during a lecture at Moscow University in 1957 to give his phil-
osophy of physics, the Nobel prize winner Paul Dirac (1902–84) wrote, in
capitals, on the blackboard ‘PHYSICAL LAWS SHOULD HAVE MATHEM-
ATICAL BEAUTY’.8
Anyone who has dealt with Maxwell’s equations of electromagnetism, or the
Schrödinger equation, cannot fail to be impressed with the concise elegance of
the formulae. Their compact beauty is made all the more stark when one consid-
ers the very broad range of phenomena they ultimately explain and encapsulate.
INTRODuCTION | 3
