On Numbers (2000-)

 "As archetypes of our representation of the world, numbers form, in the strongest sense, part of ourselves, to such an extent that it can legitimately be asked whether the subject of study of arithmetic is not the human mind itself. From this a strange fascination arises: how can it be that these numbers, which lie so deeply within ourselves, also give rise to such formidable enigmas? Among all these mysteries, that of the prime numbers is undoubtedly the most ancient and most resistant." (Gerald Tenenbaum & Michael M France, "The Prime Numbers and Their Distribution", 2000)

"Mathematics has given us dazzling insights into the power of exponential growth and how the same patterns recur in numbers, regardless of the phenomena being observed." (Richar Koch, "The Power Laws", 2000)

"One of the most fundamental notions in mathematics is that of number. Although the idea of number is basic, the numbers themselves possess both nuance and complexity that spark the imagination." (Edward B Burger, "Exploring the Number Jungle", 2000)

"We analyze numbers in order to know when a change has occurred in our processes or systems. We want to know about such changes in a timely manner so that we can respond appropriately. While this sounds rather straightforward, there is a complication - the numbers can change even when our process does not. So, in our analysis of numbers, we need to have a way to distinguish those changes in the numbers that represent changes in our process from those that are essentially noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"[…] you simply cannot make sense of any number without a contextual basis. Yet the traditional attempts to provide this contextual basis are often flawed in their execution. [...] Data have no meaning apart from their context. Data presented without a context are effectively rendered meaningless." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Big numbers warn us that the problem is a common one, compelling our attention, concern, and action. The media like to report statistics because numbers seem to be 'hard facts' - little nuggets of indisputable truth. [...] One common innumerate error involves not distinguishing among large numbers. [...] Because many people have trouble appreciating the differences among big numbers, they tend to uncritically accept social statistics (which often, of course, feature big numbers)." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Mathematics is not just about numbers. As well as numbers, modern mathematics also looks at the relations between them. The passage from pure numerology to this new vision has derived from the realization that the most profound meaning is not in the numbers but in the relations between them. Mathematical investigation is precisely the exploration and the study of the different possible relations; some of them find a concrete and immediate application in the environment in which they are immersed, others just ‘live’ in the minds of those that conceive them." (Cristoforo S Bertuglia & Franco Vaio, "Nonlinearity, Chaos and Complexity: The Dynamics of Natural and Social Systems", 2003)

"One can be highly functionally numerate without being a mathematician or a quantitative analyst. It is not the mathematical manipulation of numbers (or symbols representing numbers) that is central to the notion of numeracy. Rather, it is the ability to draw correct meaning from a logical argument couched in numbers. When such a logical argument relates to events in our uncertain real world, the element of uncertainty makes it, in fact, a statistical argument." (Eric R Sowey, "The Getting of Wisdom: Educating Statisticians to Enhance Their Clients' Numeracy", The American Statistician 57(2), 2003)

"[…] statistical thinking, though powerful, is never as easy or automatic as simply plugging numbers into formulas. In order to use statistical methods appropriately, you need to understand their logic, not just the computing rules." (Ann E Watkins et al, "Statistics in Action: Understanding a World of Data", 2007)

"Equations are the mathematician's way of working out the value of some unknown quantity from circumstantial evidence. ‘Here are some known facts about an unknown number: deduce the number.’ An equation, then, is a kind of puzzle, centered upon a number. We are not told what this number is, but we are told something useful about it. Our task is to solve the puzzle by finding the unknown number." (Ian Stewart, "Why Beauty Is Truth", 2007)

"Our culture, obsessed with numbers, has given us the idea that what we can measure is more important than what we can't measure. Think about that for a minute. It means that we make quantity more important than quality." (Donella Meadows, "Thinking in Systems: A Primer", 2008)

"Mathematical ideas like number can only be really 'seen' with the 'eyes of the mind' because that is how one 'sees' ideas. Think of a sheet of music which is important and useful but it is nowhere near as interesting, beautiful or powerful as the music it represents. One can appreciate music without reading the sheet of music. Similarly, mathematical notation and symbols on a blackboard are just like the sheet of music; they are important and useful but they are nowhere near as interesting, beautiful or powerful as the actual mathematics (ideas) they represent." (Fiacre 0 Cairbre, "The Importance of Being Beautiful in Mathematics", IMTA Newsletter 109, 2009)

"The value of having numbers - data - is that they aren't subject to someone else's interpretation. They are just the numbers. You can decide what they mean for you." (Emily Oster, "Expecting Better", 2013)

"We tend to think of maths as being an 'exact' discipline, where answers are right or wrong. And it's true that there is a huge part of maths that is about exactness. But in everyday life, numerical answers are sometimes just the start of the debate. If we are trained to believe that every numerical question has a definite, 'right' answer then we miss the fact that numbers in the real world are a lot fuzzier than pure maths might suggest." (Rob Eastaway, "Maths on the Back of an Envelope", 2019)

"Numbers can easily confuse us when they are unmoored from a clear definition." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)