In 1972, Theodosius Dobzhansky addressed the convention of the National Association of Biology Teachers on the theme “Nothing in biology makes sense except in the light of evolution”. The title of that address (published in The American Biology Teacher, Vol. 35, pp. 125-129) might serve as an epigram of Dobzhansky’s worldview and life, although it is limited in scope, for Dobzhansky believed an...

Let U ⊆ H(OP1×P1 (2, 1)) be a basepoint free four-dimensional vector space. The sections corresponding to U determine a regular map φU : P1 × P1 −→ P3. We study the associated bigraded ideal IU ⊆ k[s, t;u, v] from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free resolution. These resolutions play a key role in determinin...

...Teilhard de Chardin described the world as if he were outside of it. He was sure that every change, every new bifurcation, was going in the right direction – in the direction of increased spirituality. On the contrary, I am more impressed by the existence of multiple time horizons. A bifurcation can lead us to the best or to the worst. We are participating in an evolution whose outcome isn’t...

We unveil in concrete terms the general machinery of the syzygybased algorithms for the implicitization of rational surfaces in terms of the monomials in the polynomials defining the parametrization, following and expanding our joint article with M. Dohm. These algebraic techniques, based on the theory of approximation complexes due to J. Herzog, A, Simis and W. Vasconcelos, were introduced for...

We show optical evidence that demonstrates artists as early as Jan van Eyck and Robert Campin (c1425) used optical projections as aids for producing their paintings. We also have found optical evidence within works by later artists, including Bermejo (c1475), Lotto (c1525), Caravaggio (c1600), de la Tour (c1650), Chardin (c1750) and Ingres (c1825), demonstrating a continuum in the use of optica...