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.
Before looking at the person-less variant of the Bernedete paradox, lets review the original: Imagine that Alice is walking towards a point – call it A – and will continue walking past A unless something prevents her from progressing further.
When people think of elementary school mathematics, they usually bring to mind number facts, calculations, and algorithms. This isn’t surprising, as these topics tend to dominate classroom work in many elementary schools internationally. There is little doubt that elementary students should know the multiplication tables, be able to do simple calculations mentally, develop fluency in using algorithms to carry out more complex calculations
My first degree was in mathematics, where I specialised in mathematical physics. That meant studying notions of mass, weight, length, time, and so on. After that, I took a master’s and a PhD in statistics. Those eventually led to me spending 11 years working at the Institute of Psychiatry in London, where the central disciplines were medicine and psychology. Like physics, both medicine and psychology are based on measurements.
This week we are celebrating the 500th title in the Very Short Introductions series, Measurement: A Very Short Introduction, which will publish on 6th October. Our expert authors combine facts, analysis, new ideas, and enthusiasm to make often challenging topics highly readable. To mark its publication editors Andrea Keegan and Jenny Nugee have put together a list of Very Short Facts about the series.
Just because everyone is on Twitter doesn’t mean they’ve all got interesting things to say. I vaguely recall reading that late 19th-century curmudgeons expressed similar scepticism about the then much-hyped technology of the telephone.
The capacity to work in teams is a vital skill that undergraduate and graduate students need to learn in order to succeed in their professional careers and personal lives. While teamwork is often part of the curriculum in elementary and secondary schools, undergraduate and graduate education is often directed at individual effort and testing that emphasizes solitary performance.
The subject of combinatorial analysis or combinatorics (pronounced com-bin-a-TOR-ics) is concerned with such questions. We may loosely describe it as the branch of mathematics concerned with selecting, arranging, constructing, classifying, and counting or listing things.
So, what is crystallography? Put simply, it is the study of crystals. Now, let’s be careful here. I am not talking about all those silly websites advertising ways in which crystals act as magical healing agents, with their chakras, auras and energy levels. No, this is a serious scientific subject, with around 26 or so Nobel prizes to its credit. And yet, despite this, it remains a largely hidden subject, at least in the public mind.
For people suffering from recurrent epileptic seizures, one of the most burdensome aspects of their condition is the unpredictability of their seizures. While medications, surgery, and novel neurostimulation methods can eliminate seizures seizures in some cases, many people with epilepsy face the possibility of a seizure at any time, even when they occur only rarely.
I’m sure you’ve had this experience. You want to get somewhere, say a concert, or a public building, and all the people are stopped by security officials, who ask to search your bag. They open it, maybe take out one or two items, then glance around inside the rest, before giving it back to you and letting you go.
The scientific method has long reigned as the trusted way to test hypotheses so as to produce new knowledge. Shaped by the likes of Francis Bacon, Galileo Galilei, and Ronald A. Fisher, the idea of replicable controlled experiments with at least two treatments has dominated scientific research as a way of producing accepted truths about the world around us. However, there is growing interest in design thinking, a research method which encourages practitioners to reformulate goals, question requirements, empathize with users, consider divergent solutions.
A theory is inconsistent if we can prove a contradiction using basic logic and the principles of that theory. Consistency is a much weaker condition that truth: if a theory T is true, then T consistent, since a true theory only allows us to prove true claims, and contradictions are not true. There are, however, infinitely many different consistent theories that we can construct.
Mary Somerville: the new face on Royal Bank of Scotland’s ten-pound note is worthy of international recognition
From 2017, ten-pound notes issued by the Royal Bank of Scotland will feature a new face: that of the great nineteenth-century science communicator Mary Somerville. Her book on mathematical astronomy, Mechanism of the Heavens — published in 1831, when she was fifty years old — was used as an advanced textbook at Cambridge for a hundred years. This is a phenomenal achievement for a woman who taught herself science and mathematics.
We are living with a climate system undergoing significant changes. Scientists have established a critical mass of facts and have quantified them to a degree sufficient to support international action to mitigate against drastic change and adapt to committed climate shifts. The primary example being the relation between increased atmospheric carbon dioxide concentrations and the extent of warming in the future.