A simple mathematical example concerns the number of holes in a 3-dimensional Euclidean surface.
The philosophical analysis of mathematical explanations concerns itself with two different, although connected, areas of investigation.
Much of Descartes' output at this time is both highly mathematical and concerns only specific physical problems, not unlike the work of his contemporary Galileo.
Since permanence is one of the most important topics in the study of population dynamics, one of the most interesting questions in mathematical biology concerns the survival of species in ecological models.
These include causal structuralism concerning the individuation of properties, mathematical structuralism concerning the nature of mathematical objects, and structuralism about laws and dispositions.
The earliest extant mathematical result concerning perfect numbers occurs in Euclid's Elements (c.
Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry, and probability theory).
In 2004, Lan paid two hundred and forty thousand dollars for two of the Vatican books — first editions of Galileo's "Discourses and Mathematical Demonstrations Concerning Two New Sciences" and "The Assayer" — and a 1611 copy of Johannes Kepler's "Refraction".
So, in the wake of his 80th birthday celebrations, perhaps we can expect new mathematical problems concerning the geometry of torn wrapping paper, the variability of birthday cake crumb size and the maximally efficient arrangement of cards on a finite horizontal surface.
The Second Day lays out the mathematical principles concerning how bodies break.
