Current Work on Mathematical Truth

The overall aim of this paper is to serve as an introduction to the work currently being done on the topic of mathematical truth. It provides an overview of the major developments concerning mathematical truth and also evaluates those developments as potential contributions to mathematician’s understanding of the subject

Proof and Intution

This paper discusses various perspectives on proof and intuition by examing two epistemic systems, Intuition Intensive and Logic Intensive, and Jules Henri Poincaré\u27s objections to the latter

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

新機能性物質設計の基礎的研究 : 熱力学量と構造の関係について

博士（理学）神戸大

Intraoperative Ultrasound: A Tool to Support Tissue-Sparing Curative Pancreatic Resection in Focal Congenital Hyperinsulinism

Background: Focal congenital hyperinsulinism (CHI) may be cured by resection of the focal, but often non-palpable, pancreatic lesion. The surgical challenge is to minimize removal of normal pancreatic tissue.Aim: To evaluate the results of intraoperative ultrasound-guided, tissue-sparing pancreatic resection in CHI patients at an international expert center.Methods: Retrospective study of CHI patients treated at Odense University Hospital, Denmark, between January 2010 and March 2017.Results: Of 62 consecutive patients with persistent CHI, 24 (39%) had focal CHI by histology after surgery. All patients had a paternal ABCC8 or KCNJ11 mutation and a focal lesion by 18F-DOPA-PET/CT. Intraoperative ultrasound localized the focal lesion in 16/20 patients (sensitivity 0.80), including one ectopic lesion in the duodenal wall. Intraoperative ultrasound showed no focal lesion in 11/11 patients with diffuse CH (specificity 1.0). The positive predictive value for focal histology was 1.0, negative predictive value 0.73.Tissue-sparing pancreatic resection (focal lesion enucleation, local resection of tail or uncinate process) was performed in 67% (n = 16). In 11/12 having tissue-sparing resection and intraoperative ultrasound, the location of the focal lesion was exactly identified. Eight patients had resection of the pancreatic head or head/body, four with Roux-en-Y, three with pancreatico-gastrostomy and one without reconstruction. None had severe complications to surgery. Cure of hypoglycaemia was seen in all patients after one (n = 21) or two (n = 3) pancreatic resections.Conclusion: In focal CHI, tissue-sparing pancreatic resection was possible in 67%. Intraoperative ultrasound was a helpful supplement to the mandatory use of genetics, preoperative 18F-DOPA-PET/CT and intraoperative frozen sections

How much detail and accuracy is required in plant growth sub-models to address questions about optimal management strategies in agricultural systems?

The amount of detail and accuracy required in plant growth sub-models within agricultural systems management models depends strongly on the question being addressed. Taking an ‘as-simple-as-possible’ approach has advantages such as keeping models transparent and easy to analyse while remaining appropriate to the question of interest

LiverScreen project: study protocol for screening for liver fibrosis in the general population in European countries

Background: The development of liver cirrhosis is usually an asymptomatic process until late stages when complications occur. The potential reversibility of the disease is dependent on early diagnosis of liver fibrosis and timely targeted treatment. Recently, the use of non-invasive tools has been suggested for screening of liver fibrosis, especially in subjects with risk factors for chronic liver disease. Nevertheless, large population-based studies with cost-effectiveness analyses are still lacking to support the widespread use of such tools. The aim of this study is to investigate whether non-invasive liver stiffness measurement in the general population is useful to identify subjects with asymptomatic, advanced chronic liver disease. Methods: This study aims to include 30,000 subjects from eight European countries. Subjects from the general population aged ≥ 40 years without known liver disease will be invited to participate in the study either through phone calls/letters or through their primary care center. In the first study visit, subjects will undergo bloodwork as well as hepatic fat quantification and liver stiffness measurement (LSM) by vibration-controlled transient elastography. If LSM is ≥ 8 kPa and/or if ALT levels are ≥1.5 x upper limit of normal, subjects will be referred to hospital for further evaluation and consideration of liver biopsy. The primary outcome is the percentage of subjects with LSM ≥ 8kPa. In addition, a health economic evaluation will be performed to assess the cost-effectiveness and budget impact of such an intervention. The project is funded by the European Commission H2020 program. Discussion: This study comes at an especially important time, as the burden of chronic liver diseases is expected to increase in the coming years. There is consequently an urgent need to change our current approach, from diagnosing the disease late when the impact of interventions may be limited to diagnosing the disease earlier, when the patient is asymptomatic and free of complications, and the disease potentially reversible. Ultimately, the LiverScreen study will serve as a basis from which diagnostic pathways can be developed and adapted to the specific socio-economic and healthcare conditions in each country

The Creative Ideal in Mathematics

International audienc

A Brief Introduction to Gödel’s Theorems

Gödel’s two famous incompleteness theorems are results that have come up a number of times in the discussions at the 1977 ACMS conference. This paper provides a brief and relatively non-technical statement on these results and of their significance for the foundations of mathematics