1) At some point recently, the following tweet crossed my screen and I copied it down only to later re-look at it and be intrigued…:
"OK. So mathematics is the science of patterns. I can dig that. But what, exactly, is a pattern?"
As someone interested in semantics, words, meaning, and tautology, this struck me as a fair and deeper question than it appeared at first glance… how does one define pattern without falling into some tautological trap? Anyway, that led me to a few pages worth passing along:
First of course, was the always handy Wikipedia, which essentially defined a pattern as 'elements repeating in a predictable manner'… that's probably about as good as it gets, even if it evokes the further questions of what actually constitutes an "element" and when is something precisely corroborated as "predictable"?
Anyway, it turns out that the Mathematics Assoc. of America has also previously tackled this topic a bit in a multi-part series here:
…the theme of the piece is that the notion of math as the 'science of patterns' is actually a modern approach to mathematics (Keith Devlin has certainly been a popular exponent of it) and that early mathematics was quite a different kind of study.
a quick excerpt:
"It is in view of this, I want to consider the often-heard definition of mathematics as the “science of patterns.” Specifically, I want to show, by comparing Euclid and Steiner, that while this is presented to students as a timeless—that is, non-historical—definition, in fact, it represents a modern view of mathematics. I shall show that Greek mathematics, for example, is not a search for patterns but for concrete properties of concrete mathematical objects; and I shall show, conversely, that it is when mathematics becomes symbolic that patterns, as such, are suggested to mathematicians and become objects of their thought."2) Almost exactly a year ago, renowned mathematician Tim Gowers launched a broadside at (and boycott of) journal publisher Elsevier, and probably, to his own surprise, struck a nerve with a great many other academics (not just mathematicians) who joined the fray with their own pent-up feelings about glossy publishers. I won't replay all the discussion that took place over the matter, except to say that arguments against the stranglehold of expensive professional journals versus more open-access forms of publishing in the digital age continue, and Gowers (with others) remains at the forefront with his announcement of new open-access journals on the way.
This Aperiodical article summarizes what Gowers is up to (with direct links back to Gowers' latest posts on it):
...and Nature has good coverage of the effort as well, here:
Even for those of us not involved in research and its publish-or-perish world, watching this inevitable evolution play out in the open is fascinating.