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?
- 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)
- 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)
- 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)
- 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.”
The Doctrine of School Mathematics
Science as Religion
Darwin’s Mathematical Theory of Evolution
Physicist´s Grand Unification Theory
- 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.
- 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.
The Large Hadron Collider
- 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.
Climate Change and Destiny of Civilization
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)
- 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,
- fractions are especially troublesome for Americans…the catchword for math teachers today should be “fractions”:
- 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.
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?