Abstract

Science and education is based on an assumption/belief, that the physical World ultimately is governed by mathematical laws imposed by the Creator of the World, which scientists can uncover by digging into the machinery of the World. This view is can be decribed as logical empirism, where the assumption is justified a posteriori by a perceived/observed mathematical nature of the World. In postmodern philosophy this is turned around and the mathematical nature is seen instead rather as a construction following from an a priori stipulation that nature has to be mathematical.

If there is a God, he’s a great mathematician. (Dirac)

The laws of nature are but the mathematical thoughts of God. (Euclid)

Bits of propaganda

Heaven or Hell?

The idea the Nature has a mathematical structure is deeply rooted in Western civlization from the early Greeks over the Scholasticism to the Enlighment and Scientific Revolution into our days of the physicists dream of Grand Unification Theory and Large Hadron Collider as if God is mathematician:

God ever geometrizes. (Plato)

Let no one ignorant of geometry enter here. (Inscription above Plato’s Academy)

The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. (Aristotle)
For the things of this world cannot be made known without a knowledge of mathematics. (Bacon)
The bird is an instrument functioning according to mathematical laws, and man has the power to reproduce an instrument like this with all its movements (da Vinci).
Geometry is the only science that it hath pleased God hitherto to bestow on mankind. (Hobbes)
I believe the geometric proportion served the creator as an idea when He introduced the continuous generation of similar objects from similar objects. (Kepler)
I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. (Leibniz)
God created everything by number, weight and measure. (Newton)
The latest authors, like the most ancient, strove to subordinate the phenomena of nature to the laws of mathematics. (Newton)
All the pictures which science now draws of nature and which alone seem capable of according with observational fact are mathematical pictures … From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician. (Jeans)
An equation means nothing to me unless it expresses a thought of God. (Ramanujan)
God exists since mathematics is consistent, and the devil exists since we cannot prove the consistency. (Morris Kline)
Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever. (Einstein)
But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed. (Einstein)
God used beautiful mathematics in creating the world. (Dirac)
The universe is an enormous direct product of representations of symmetry groups. (Weyl)
The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. (Wigner)
Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? (Hawking)

Newton playing God

Some believe that it is instead the Devil who is mathematician:

The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell. (St. Augustine)

and there are also (some) doubts:

A mathematician is a blind man in a dark room looking for a black cat which isn’t there. (Darwin)
I have hardly ever known a mathematician who was capable of reasoning. (Plato)
Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different. (Goethe)
Mathematics has the completely false reputation of yielding infallible conclusions. (Goethe)
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. (Einstein)
Mathematicians, who are only mathematicians, have exact minds, provided all things are explained to them by means of definitions and axioms; otherwise they are inaccurate and insufferable, for they are only right when the principles are quite clear. (Pascal)

Altogether, there is an over-whelming concert of voices connecting God with mathematics, or mathematics with God. Or Mathematics with Infinity and Infinity with God as exposed in a the BBC series Dangerous Knowledge propagating an idea of dark religious mysticism, way beyond Harry Potter, in our time of rationality based on mathematics: “What is the system everything has to adhere to if there is no God?”

When Napoleon teasingly remarked to Laplace that God is not mentioned in his treatise on Celestial Mechanics Laplace replied: “Sire, I did not need that hypothesis”. When Napoleon later reported this reply to Lagrange, the latter remarked, “Ah, but that is a fine hypothesis. It explains so many things.”

Bits of propaganda

The Doctrine of School Mathematics

The school system propagates this idea, or rather doctrine, that mathematics is everywhere present, in nature and society, which however unfortunately cannot be seen and properly understood most people; only by some professional mathematicians. The propaganda is effective: most people including all the people in different occupations and professions using only simple economy arithmetics, believe that mathematics is universal as if God is Mathematician or vice versa. The proof that this is so is thought to be convincing: 12 years of mathematics study or more for everybody. If God is not mathematician this would not be justified, and thus by simple logic the 12 years of school prove that God is Mathematician. Right?

So, is it possible to question such a generally held belief? And why should it be questioned? What´s wrong with letting people believe that God is Mathematician? Isn’t that helpful in mathematics education?

Maybe, but there can also be disadvantages. Before identifying them let us first remark that the question if God is Mathematician or not, probably has no answer. Maybe He is, maybe not, or maybe something in between like an applied or computational mathematician. This is related to the question if mathematics

is something you discover or invent, or both, which probably neither has an answer.

If we use a sociological approach it is natural to ask if there can be some hidden purpose behind the idea of God as Mathematician? We recall that before the democratic revolution the idea of the King as being godlike was propagated by the King’s men, as a way to keep control over souls and bodies. In Sweden there was a close alliance between religion and state in the form of a State Church until the separation in 1998 after 400 years of happy marriage. Until the reform of public schools in 1842 the education was in the hands of the Church as an extension of the State. Why is school today, after the separation of church from state, preaching the idea of God as Mathematician?

Transmitting the Doctrine.

Science as Religion

The reason can be that the religion of our time is rational science, and since mathematics is considered to be the basis of rational science, rationality requires that people believe in the religion of rational science, that is believe that God is Mathematician.

But does not the belief in science as our religion come from undeniable evidence that the only thing we can rely on in this unstable World, is science? Isn’t global warming something we must deal with using science?

And aids and Big Bang and The Financial Crisis? Maybe yes, and just because of this yes, it can be important to secure that the idea of God as Mathematician is not harmful, to people, society and science.

God as Mathematician

Darwin’s Mathematical Theory of Evolution

Darwin’s explains evolution as a result of natural selection from (genetic) variation, which is essentially a mathematical explanation, comparable to a minimization principle in mathematical physics or optimization algorithm in economics.

Richard Dawkin’s The God Delusion replaces God with Darwin’s mathematics.

Physicist´s Grand Unification Theory

Physicist’s pretentions of a Theory Of Everything (TOE) is expressed by Stephen Hawking as follows:

my goal is simple, it is a complete understanding of the universe, why it is as it is and why it exists at all

if we do discover a complete theory, it should be in time understandable in broad principle by everyone
then we shall all, philosophers, scientists, and just ordinary people be able to take part in the discussion of why we and the universe exist.

Calabi-Yau manifold The Holy Kabba in Mekka

A candidate to TOE is the Calabi-Yau manifold depicted above and defined by the following mathematical properties:

M has vanishing first real Chern class.

M has a Kähler metric with vanishing Ricci curvature.

M has a Kähler metric with local holonomy contained in SU(n).

A positive power of the canonical bundle of M is trivial.

M has a finite cover that has trivial canonical bundle.

M has a finite cover that is a product of a torus and a simply connected manifold with trivial canonical bundle.

A TOE or GUT with the entire Universe coming out as the solution to one mathematical equation is a deeply mystical idea of religious dimension with the theoretical physicist/pure mathematician playing the role of God of a religion demanding belief from taxpayers and educators, like Darwin’s mathematical theory.

The Large Hadron Collider

The Large Hadron Collider built in collaboration of 10.000 scientists from over 100 countries at a cost

of up to 100 billion dollars with the intention of testing the existence of the hypothesised Higgs boson of the Standard Model. Stephen Hawking again:

I think it will be much more exciting if we don’t find the Higgs. That will show something is wrong, and we need to think again. I have a bet of one hundred dollars that we won’t find the Higgs.
whatever the LHC finds, or fails to find, the results will tell us a lot about the structure of the universe.

It is easy to get the impression that the objective of LHC is to force nature, by bombarding matter

with protons accellerated to 9999991% of the speed of light, into a given mathematical form, like forcing non-believers into a certain belief, rather than allowing nature and people to express whatever they seek to express. LHC can be seen as a church of a religion of science of our time with universal ambitions.

Like the cathedral Notre Dame de Paris the very dimension of the project helps to support belief.

Inside the Large Hadron Collider Inside Notre Dame

Climate Change and Destiny of Civilization

The Panel on Climate Change states:

There is considerable conﬁdence that climate models provide credible quantitative estimates of future climate change, particularly at continental scales and above.increasing skill in representing many important mean climate features, such as the large-scale distributions of atmospheric.

Climate models are mathematical representations of the climate system, expressed as computer codes and run on powerful computers. One source of confidence in models comes from the fact that model fundamentals are based on established physical laws, such as conservation of mass, energy and momentum, along with a wealth of observations.

The future of humanity rests on mathematical modeling…based on established physical laws…what else can we believe in…confidence…despair…hope…

Disadvantages of God as Mathematician

The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit. (Whitehead)

The school system in the words of National Council of Mathematics Teachers (NCTM) preaches that

all students, regardless of their personal characteristics, backgrounds, or physical challenges, must learn significant mathematics with depth and understanding
the underpinnings of everyday life are increasingly mathematical … making purchasing decisions, choosing insurance or health plans, and voting knowledgeably all call for quantitative sophistication
citizens should develop an appreciation and understanding of mathematics as one of the greatest cultural and intellectual achievements of human-kind, including its aesthetic and even recreational aspects,

while the National Mathematics Advisory Panel observes that the significant mathematics and understanding effectively being transmitted, does not even reach fractions nor recreational satisfaction:

fractions are especially troublesome for Americans…the catchword for math teachers today should be “fractions”:

Learning to appreciate fractions

The net result of 12 years of mathematics education thus seems to be very small, for everybody, very far from the “quantitative mathematical sophistication” and “appreciation” required by all citizens of society according to NCTM, in particular for the group of students with potential interest in science and mathematics.

The school message of mathematics as the basis of the religion of science of our time, thus appears to be contra productive:

students interested in math/science get put off by dogmatic trivialization
students not interested in math get a bad start to lives where math is not needed nor beneficial.

The disadvantages of this situation are exposed in more detail in Why School Mathematics? and Why/What Engineering Mathematics?

Mathematics as Craftsmanship

Would it be beneficial for people and society if science was dethroned from its role as a religion with God as Mathematician into a more democratic function into different forms of craftsmanship without the ideological superstructure imprinted in the present school system?
Would it be beneficial with God as Craftsman with specific skills rather than God as Controller with the only skill of control?
Could such a reform help attracting students to science and/or help scientists to do their job better?
Could this ease the burden on all those students who have other interests than science and math?