As a mathematician who focuses his attention on a field called dynamics, I am often asked when queried about my area of specialty, exactly what is a dynamical system? I usually answer something like: “I study the mathematics underlying what is means to model something mathematically.” And this seems to work as most people have a basic understanding that mathematics is used in science and engineering to model either a physical or an abstract process and to mine it for information.
When a group of people collectively solve a jigsaw puzzle, who gets the credit? The person who puts the final piece in the puzzle? The person who sorted out the edge pieces at the beginning? The person who realised what the picture was of? The person who found the puzzle pieces and suggested trying to put them together? The person who managed the project and kept everyone on track? The whole group?
“What connects archaeology and statistical physics?”, we asked ourselves one evening in The Marquis Cornwallis, a local Bloomsbury pub in London back in 2014, while catching up after more than a decade since our paths crossed last time. While bringing back the memories of that time we first met when we were both 16, it hit us that our enthusiasm for research we did as teenagers had not faded away
Mathematics is more than the memorization and application of various rules. Although the language of mathematics can be intimidating, the concepts themselves are built into everyday life. In the following excerpt from A Brief History of Mathematical Thought, Luke Heaton examines the concepts behind mathematics and the language we use to describe them.
Chinese scientists have recently announced the use of a satellite to transfer quantum entangled light particles between two ground stations over 1,000 kilometres apart. This has been heralded as the dawn of a new secure internet. Should we be impressed? Yes – scientific breakthroughs are great things. Does this revolutionise the future of cyber security? No – sadly, almost certainly not.
Alan Turing was one of England’s most influential scientists of the twentieth century. He is best remembered as having cracked the codes used in the Enigma machines, enabling the Allies to defeat the Nazis in many important battles, particularly in the Atlantic Ocean. While this achievement which arguably helped to bring the Second World War to a quicker end has been brought to the fore through popular histories
There is a concern that too many scientific studies are failing to be replicated as often as expected. This means that a high proportion is suspected of being invalid. The blame is often put on confusion surrounding the ‘P value’ which is used to assess the effect of chance on scientific observations. A ‘P value’ is calculated by first assuming that the ‘true result’ is disappointing
Game theory is considered to be one of the most important theories not simply within the field of economics, but also mathematics, political science, biology, philosophy, and ecology, just to name a few. It has been developed over the many years since the term was first coined to what it is now: a theory used to “understand the strategic behaviour of decision makers who are aware that their decisions affect one another.”
In fact the idea really goes back to Michael Faraday, who gave Christmas lectures about science for young people at The Royal Institution of Great Britain in London in 1826. Sir Christopher Zeeman, following upon Porter’s initiative, gave the first series of six one-hour lectures (Mathematics Masterclasses) to young people at The Royal Institution in 1981, about “The Nature of Mathematics and The Mathematics of Nature”.
The unreasonable popularity of pseudosciences such as ESP or astrology often stems from personal experience. We’ve all had that “Ralph” phone call or some other happening that seems well beyond the range of normal probability, at least according to what we consider to be common sense. But how accurately does common sense forecast probabilities and how much of it is fuzzy math? As we will see, fuzzy math holds its own.
Prime numbers have now become a crucial part of modern life, but they have been fascinating mathematicians for thousands of years. A prime number is always bigger than 1 and can only be divided by itself and 1 – no other number will divide in to it. So the number 2 is the first prime number, then 3, 5, 7, and so on. Non-prime numbers are defined as composite numbers (they are composed of other smaller numbers).
It is still possible to learn mathematics to a high standard at a British university but there is no doubt that the fun and satisfaction the subject affords to those who naturally enjoy it has taken a hit. Students are constantly reminded about the lifelong debts they are incurring and how they need to be thoroughly aware of the demands of their future employers. The fretting over this within universities is relentless.
If a social conversation turns to the history of navigation – a turn that is not so unusual as once it was – the most likely episode to be mentioned is the search for a longitude method in the 18th century and the story of John Harrison. The extraordinary success of the book by Dava Sobel has popularised a view of Harrison as a doughty and virtuous fighter, unfairly disadvantaged by the scientific establishment.
Once reframed in its historical context, mathematics quickly loses its intimidating status. As a subject innately tied to culture, art, and philosophy, the study of mathematics leads to a clearer understanding of human culture and the world in which we live. In this shortened excerpt from A Brief History of Mathematical Thought, Luke Heaton discusses the reputation of mathematics and its significance to human life.
Alan Turing’s personal mathematical notebook went on display a few days ago at Bletchley Park near London, the European headquarters of the Allied codebreaking operation in World War II. Until now, the notebook has been seen by few — not even scholars specializing in Turing’s work. It is on loan from its current owner, who acquired it in 2015 at a New York auction for over one million dollars.
What is the biggest whole number that you can write down or describe uniquely? Well, there isn’t one, if we allow ourselves to idealize a bit. Just write down “1”, then “2”, then… you’ll never find a last one.