Mathematics Rising

I am increasingly fascinated by the mathematics of fundamental cognitive processes – like creatures finding their way to and from significant locations, or foraging for food, or foraging with the eyes, or comprehending the duration of an event. I’m excited by the fact that there are cognitive neuroscientists that have become focused on the architecture [...]

I recently got a copy of Daniel Tammet’s latest book, Thinking in Numbers. As you may know, Daniel Tammet has been described as a high functioning autistic savant.   He gained some notoriety in 2004, when he recited the decimal expansion of pi to 22,514 places in just over 5 hours.  You can see him do [...]

In June The Guardian posted an interesting piece on finger counting and numbers.  The main content of the article concerns the work of cognitive scientists Andrea Bender and Sieghard Beller which explores the cultural diversity in finger counting.  It tells us that if asked to use you hands to count to 10, these variations will [...]

When I first became interested in studying mathematics an artist friend of mine expressed his disapproval by characterizing mathematicians as people who made bombs.  Although I didn’t know very much mathematics at the time, I knew enough to know that he was wrong.  But I was reminded today of one of the ways his mistake [...]

I listened to three short talks today and found that they had something nice in common – they each show us how sensory experience (often vision) gives rise to mathematics that provides access to what cannot be seen, and clarifies what is seen. The first of these talks was called Symmetry, reality’s riddle presented by [...]

A number of websites have reported on a recent study, that correlated innate number sense with mathematical ability.  A concise report of the study can be found in the Johns Hopkins University Gazette, published by the institution where the study was done.  The study’s results confirm a correlation between the strength of ones number sense [...]

The essence of mathematics lies precisely in its freedom. This statement from Georg Cantor is quoted so very often, and perhaps this is because of the surprise coupling of the words mathematics and freedom, or because of the implications of the word essence, which calls to mind other words like intrinsic, inherent or something that [...]

I would like to go back today to Riemann, and the significance of his generalized notions of space and magnitude, but with an eye on what neuroscience may be adding to how mathematics gains its effectiveness. In a recent post, I pointed to the influence the philosopher Herbart had on Riemann’s 1854 lecture in which [...]

I would like to follow up on Alain Connes’ statement in my last blog. The weave of mathematical thought is tight.  The seeds of mathematics are found in early explorations of number relationships and in observations of what we call space. But symbol, stripped of content, has led to heightened powers of thought and discernment.  [...]

For me, one of the more intriguing things that happened in mathematics is what is called the arithmetization of the Calculus.  This is not because it contributes to my understanding of fundamental concepts (because it doesn’t).  Nor is it because the ideas are exotic (they’re not). I’m captivated, instead, by what it may demonstrate about [...]