In a famous lecture in 1900, David Hilbert listed 23 difficult problems he felt deserved the attention of mathematicians in the coming century. His conviction of the solvability of every mathematical problem was a powerful incentive to future generations: ``Wir müssen wissen. Wir werden wissen.'' (We must know. We will know.) Some of these problems were solved quickly, others might never be completed, but all have influenced mathematics. Later, Hilbert highlighted the need to clarify the methods of mathematical reasoning, using (...) a formal system of explicit assumptions, or axioms. Hilbert's vision was the culmination of 2,000 years of mathematics going back to Euclidean geometry. He stipulated that such a formal axiomatic system should be both `consistent' (free of contradictions) and `complete' (in that it represents all the truth). Hilbert also argued that any wellposed mathematical problem should be `decidable', in the sense that there exists a mechanical procedure, a computer program, for deciding whether something is true or not. Of course, the only problem with this inspiring project is that it turned out to be impossible. (shrink)

The sequencing of the human genome and decreasing costs of sequencing technology have led to the notion of ‘personalized medicine’. This has been taken by some authors to indicate that personalized medicine will provide individualized treatments solely based on one’s DNA sequence. We argue this is overly optimistic and misconstrues the notion of personalization. Such interpretations fail to account for economic, policy and structural constraints on the delivery of healthcare. Furthermore, notions of individualization based on genomic data potentially take us (...) down the road of genetic reductionism obscuring the role of environmental factors in disease and ill health. We propose that one should see personalized medicine as a way of using personal genomic information to stratify individuals into subpopulations and suggest that personalized medicine be seen within a broader idea of personalized healthcare, reflecting healthcare that integrates personal genomic data into cultural, environmental and personal contexts. (shrink)

By considering the irreducible representations of the Lorentz group, an analysis of the different spin-2 waves is presented. In particular, the question of the helicity is discussed. It is concluded that, although from the point of view of representation theory there are no compelling reasons to choose between spin-2 waves with helicity σ=±1 or σ=±2, consistency arguments of the ensuing field theories favor waves with helicity σ=±1.