A prominent feature of comparative life histories in fish (and other indeterminate growers) is the approximate invariance across species of certain dimensionless numbers made up from reproductive and timing variables. The two best known are the age at maturity (alpha) divided by the average adult lifespan (E), and the proportion of a body mass given to reproduction per year (c) multiplied by E....

Humans prioritize the processing of threats over neutral stimuli; thus, not surprisingly, the presence of threats has been shown to alter performance on both perceptual and cognitive tasks. Yet whether the quantification process is disrupted in the presence of threat is unknown. In three experiments, we examined numerical estimation and discrimination abilities in adults in the context of threa...

The notion of a number is as old as mathematics itself, and their developments have been inseparable. Usually a new set of numbers included the old set, or, as we often say, extended it. In this way, the set {1, 2, 3, ...} of natural numbers, has been extended by adding zero to it, negative integers, rational numbers (fractions), irrational numbers, complex numbers. The actual extensions happen...

A bout 120 new Mesopotamian mathematical cuneiform texts, all from the Norwegian Schøyen Collection, are published in the author’s book A Remarkable Collection of Babylonian Mathematical Texts, Springer (2007). Most of the texts are Old Babylonian (1900–1600 BC), but some are older (Sumerian), or younger (Kassite). In addition to the presentation and discussion of these new texts, the book cont...

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and...

We present a range of mathematical theorems whose proofs require unexpectedly strong logical methods, which in some cases go well beyond the usual axioms for mathematics. ************************************************ There are a variety of mathematical results that can only be obtained by using more than the usual axioms for mathematics. For several decades there has been a gradual accumulat...

Children use numbers every day and typically receive formal mathematical training from an early age, as it is a main subject in school curricula. Despite an increase in children neuroimaging studies, a comprehensive neuropsychological model of mathematical functions in children is lacking. Using quantitative meta-analyses of functional magnetic resonance imaging (fMRI) studies, we identify conc...

A significant feature of contemporary science is the widespread use of mathematics in several of its subfields. In many instances, the content of scientific theories cannot be formulated without reference to mathematical objects (such as functions, numbers, or sets). In the hands of W. V. Quine and Hilary Putnam, this feature of scientific practice was invoked in support of platonism (the view ...

bilevel linear programming  is a decision making problem with a two-level decentralized organization. the textquotedblleft leadertextquotedblright~ is in the upper level and the textquotedblleft followertextquotedblright, in the lower. making a decision at one level affects that at the other one. in this paper, bilevel linear programming  with inexact parameters has been studied and a method is...

The mathematical concept of infinity, in the sense Cantor, is rather far from applied mathematics and statistics. These fields can be linked. We comment on properties infinite numbers relate them to some operations with random variables. existence statistical parametric models studied terms cardinal numbers. Some probabilistic interpretations Gödel’s theorem, Turing’s halting problem, Banach-Ta...