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. Bertrand Russell, Mysticism and Logic, 1918
Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth. Brian Greene, The Fabric of the Cosmos
We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it. Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved. Paul Dirac
The methods of theoretical physics should be applicable to all those branches of thought in which the essential features are expressible with numbers. Paul Dirac
I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one’s trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics. Paul Dirac
Consequently he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics. Maimonides
Mathematics becomes very odd when you apply it to people. Copenhagen 2002 starring Stephen Rea & Daniel Craig & Francesca Annis et al, director Howard Davies, Heisenberg to Bohr
Sense is mathematics. ibid. Heisenberg
There is a strange and unexpected relationship between order and chaos. Jim Al-Khalili, The Secret Life of Chaos, BBC 2011
Alan Turin was a remarkable man – one of the greatest mathematicians who ever lived. He discovered many of the fundamental ideas that underpin the modern computer. Also during the second world war he worked here at Bletchley Park. ibid.
Chaos is one of the most overused words in English. But in science it has a very specific meaning. It says that a system that is completely described by mathematical equations is more than capable of being unpredictable without any outside interference whatever. ibid.
The Butterfly Effect ... started turning up everywhere. ibid.
Unpredictability was hardwired into every aspect of the world we live in. ibid.
To be scared of chaos in pointless. It is woven into the basic laws of physics. ibid.
The discovery of chaos was a real turning point in the history of science. As it tore down the Newtonian dream, scientists began to look more favourably at Turin and Bellusov’s work on spontaneous pattern formation. And perhaps more importantly as they did so they realised something truly astonishing: that there was a very deep and unexpected link – a truly cosmic connection – between Nature’s strange power to self organise and the chaotic consequences of the butterfly effect. ibid.
They discovered that the natural world could be deeply, profoundly unpredictable. That the very same things that make it unpredictable also allow it to create pattern and structure. Order and chaos – seems the two are more deeply linked than we could have ever imagined. ibid.
Underlying nearly all the shapes in the natural world is a mathematical principle known as Self Similarity. ibid.
Turin’s patterns, Bellusov’s reactions and Mandelbrot’s fractals are all signposts pointing to a deep underlying natural principle. ibid.
Muhammad ibn Musa al-Khwarizmi showed Europeans that there’s a better way of doing arithmetic. In his book entitled The Hindu Art of Reckoning he describes a revolutionary idea: you can represent any number you like with just ten simple symbols. Jim Al-Khalili, Science & Islam: The Language of Science, BBC 2009
They invented the decimal point. ibid.
A language that was specially developed to be precise and unambiguous which made it ideal for scientific and technical terms. ibid.
Algebra ... That sort of knowledge wins wars. ibid.
Algebra has helped create the modern world. ibid.
Baghdad (9th century) in this period was like Florence during the Renaissance or Silicon Valley in the age of the Internet. Jim Al-Khalili, Revolutions: The Ideas that Changed the World V: Telescope, BBC 2019
What if there is no math that unifies the universe? Through the Wormhole with Morgan Freeman s1e1: Is There a Creator? Science 2010
Throughout history humankind has struggled to understand the fundamental workings of the material world. We’ve endeavoured to discover the rules and patterns that determine the qualities of the objects that surround us, and their complex relationship to us and each other. Over thousands of years societies all over the world have found that one discipline above all others yields certain knowledge about the underlying realities of the physical world. That discipline is mathematics. Marcus du Sautoy, The Story of Maths I, BBC 2008
We needed to find a way of making sense of these natural patterns. The most basic concepts of Maths – Space & Quantity – are hardwired into our brains. ibid.
The earliest mathematical innovators: the Egyptians needed some way to record the results of their calculations. ibid.
The Egyptians were using a decimals systems motivated by the ten fingers on our hands. ibid.
The Egyptians were brilliant problem-solvers. ibid.
The Egyptians have understood the power of binary ... Today the whole technological world depends on the same principles that were used in ancient Egypt. ibid.
Suddenly new numbers are on the scene: fractions. ibid.
In a four-thousand-year-old document called the Moscow Papyrus we find the formula for the volume of a pyramid with its peak sliced off which shows the first hint of calculus at work. ibid.
Damascus ... They became masters at managing and manipulating numbers ... You can blame those ancient Babylonians for all those tortuous problems you had at school. ibid.
They were using powers of sixty. ibid.
The Babylonian calendar was based on the cycles of the moon. ibid.
This is the first time zero in any form had appeared in a mathematical universe. ibid.
The use of Quadratic Equations: one of the greatest legacies of Babylonian mathematics. ibid.
Quadratic Equations involved things where the unknown quantity you are trying to identify is multiplied by itself. ibid.
The Greeks were passionate about mathematics ... They gave us the power of proof. ibid.
Pythagoras is a controversial figure. ibid.
Experimenting with a stringed instrument Pythagoras discovered that the intervals between harmonious musical notes were always represented by whole number ratios. ibid.
The Academy: Plato founded this school in Athens in 387 B.C. ibid.
We know very little about Euclid’s life, but his greatest achievements were as a chronicler of mathematics. Around 300 B.C. he wrote the most important textbook of all time: The Elements. ibid.
Hypatia was exceptional – a female mathematician ... She was in fact a brilliant theorist and teacher. ibid.
This is the untold story of the mathematics of the East which would transform the West and give birth to the modern world. Marcus du Sautoy, The Story of Maths II: The Genius of the East
A decimal place value system ... It makes calculations very quick. ibid.
Without a zero the written number was very limited. ibid.
Equations are a little bit like cryptic crosswords: you’re given a certain amount of information about some unknown numbers, and from that information you’ve got to deduce what the unknown numbers are. ibid.
Quadratic equations involve numbers that are squared or to the power of two, say five times five. ibid.
We may never know how the Indians came up with their number system, but we do know that they refined and perfected it creating the ancestors for the nine numerals we use across the world today. Many rank the Indian system of counting as one of the greatest intellectual innovations for all time. ibid.