Why do we teach students how to prove things we all know already, such as 0.9999••• =1? Partly, of course, so they develop thinking skills to use on questions whose truth-status they won’t know in advance. Another part, however, concerns the dialogue nature of proof.
Why study paradoxes? The easiest way to answer this question is with a story: In 2002 I was attending a conference on self-reference in Copenhagen, Denmark. During one of the breaks I got a chance to chat with Raymond Smullyan, who is amongst other things an accomplished magician, a distinguished mathematical logician, and perhaps the most well-known popularizer of `Knight and Knave’ (K&K) puzzles.
A large variety of complex systems in ecology, climate science, biomedicine, and engineering have been observed to exhibit so-called tipping points, where the dynamical state of the system abruptly changes. Typical examples are the rapid transition in lakes from clear to turbid conditions or the sudden extinction of species after a slightly change of environmental conditions. Data and models suggest that detectable warning signs may precede some, though clearly not all, of these drastic events. This view is also corroborated by recently developed abstract mathematical theory for systems, where processes evolve at different rates and are subject to internal and/or external stochastic perturbations.
One of the highest points of the International Congress of Mathematicians, currently underway in Seoul, Korea, has got to be the announcement of the Fields Medal prize winners. The prize is awarded every four years to up to four mathematicians under the age of 40, and is viewed as one of the highest honours a mathematician can receive
By Luciano Floridi
Philosophy is a bit like a computer with a memory leak. It starts well, dealing with significant and serious issues that matter to anyone. Yet, in time, its very success slows it down. Philosophy begins to care more about philosophers’ questions than philosophical ones, consuming increasing amount of intellectual attention.
By Franc Klaassen and Jan R. Magnus
Suppose you are watching a tennis match between Novak Djokovic and Rafael Nadal. The commentator says: “Djokovic serves first in the set, so he has an advantage.” Why would this be the case? Perhaps because he is then ‘always’ one game ahead, thus serving under less pressure. But does it actually influence him and, if so, how?
David J. Hand
Nowadays it appears impossible to open a newspaper or switch on the television without hearing about “big data”. Big data, it sometimes seems, will provide answers to all the world’s problems. Management consulting company McKinsey, for example, promises “a tremendous wave of innovation, productivity, and growth … all driven by big data”.
By Subrata Dasgupta
Politically, socially, and culturally, the 1960s were tumultuous times. But tucked away amidst the folds of the Cold War, civil rights activism, anti-war demonstrations, the feminist movement, revolts of students and workers, flower power, sit-ins, Marxist and Maoist revolutions – almost unnoticed — a new science was born in university campuses across North America, Britain, Europe and even, albeit tentatively, certain non-Western parts of the world.
By Kenneth Falconer
Fractal shapes, as visualizations of mathematical equations, are astounding to look at. But fractals look even more amazing in their natural element—and that happens to be in more places than you might think.
By Jason Rosenhouse
With the arrival of the new year, you can be certain that the annual extravaganza known as the Joint Mathematics Meetings cannot be far behind. This year’s conference is taking place in Baltimore, Maryland. It is perhaps more accurate to say that it is a conference of conferences, since much of the business to be transacted will take place in smaller sessions devoted to this or that branch of mathematics
By Stephen Blyth
Almost exactly twenty years ago, on 19 October 1993, the US House of Representatives voted 264 to 159 to reject further financing for the Superconducting Super Collider (SSC), the particle accelerator being built under Texas. $2bn had already been spent on the Collider, and its estimated total cost had grown from $4.4bn to $11bn; a budget saving of $9bn beckoned. Later that month President Clinton signed the bill officially terminating the project.
By Kenneth Falconer
“This is not maths – maths is about doing calculations, not proving theorems!” So wrote a disaffected student at the end of my recent pure maths lecture course. Theorems, along with their proofs, have gotten a bad name.
By James Nicholson
Statistics to me has always been about trying to make the best sense of incomplete information and having some feeling for how good that ‘best sense’ is. At a very crude level if you have a firm employing 235 people and you randomly sample 200 of these on some topic, I would feel my information was pretty good (even though it is incomplete).
In July, the first issue of the Journal of Survey Statistics and Methodology (JSSAM) will come out. The launch of a new journal is always a source of great anticipation in the academic publishing world. We face many concerns about a proliferation of unnecessary journals, reduced library budgets, and creating valuable publications in a digital world.
By Andrew Gelman
There’s a prevailing notion that communicating science is difficult, and it is therefore difficult to engage the general public. People can be fazed by statistics in particular, so how can we convey the importance of this science effectively?
By Ian Stewart
Symmetry has been recognised in art for millennia as a form of visual harmony and balance, but it has now become one of the great unifying principles of mathematics. A precise mathematical concept of symmetry emerged in the nineteenth century, as an unexpected side-effect of research into algebraic equations. Since then it has developed into a huge area of mathematics, with applications throughout the sciences.