HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

ORIGIN AND PREVALENCE OF HUMAN T-LYMPHOTROPIC VIRUS TYPE 1 (HTLV-1) AND TYPE 2 (HTLV-2) AMONG INDIGENOUS POPULATIONS IN THE AMERICAS

Human T-lymphotropic virus type 1 (HTLV-1) is found in indigenous peoples of the Pacific Islands and the Americas, whereas type 2 (HTLV-2) is widely distributed among the indigenous peoples of the Americas, where it appears to be more prevalent than HTLV-1, and in some tribes of Central Africa. HTLV-2 is considered ancestral in the Americas and is transmitted to the general population and injection drug users from the indigenous population. In the Americas, HTLV-1 has more than one origin, being brought by immigrants in the Paleolithic period through the Bering Strait, through slave trade during the colonial period, and through Japanese immigration from the early 20th century, whereas HTLV-2 was only brought by immigrants through the Bering Strait. The endemicity of HTLV-2 among the indigenous people of Brazil makes the Brazilian Amazon the largest endemic area in the world for its occurrence. A review of HTLV-1 in all Brazilian tribes supports the African origin of HTLV-1 in Brazil. The risk of hyperendemicity in these epidemiologically closed populations and transmission to other populations reinforces the importance of public health interventions for HTLV control, including the recognition of the infection among reportable diseases and events.