“孪生素数猜想”提出后的一百多年间，从数学家到民科都对其表现出了浓厚的兴趣。而在2013年，时年58 岁的数学家张益唐证明了一个弱形式的孪生素数猜想：存在无穷多个之差小于7000万的素数对。一时间轰动整个数学界。张益唐的成果让很多追求这个终极目标的数学家们又重新燃起了希望，此后，数学家们迅速将70,000,000降到了246。 张益唐的生活从此改变：学校从合同制讲师立马把他提升到正教授，各种奖励接踵而来， 各大名校纷纷邀请他加盟，中国数学界对其盛情邀请。常人们则把话题的焦点集中在了张益唐这样做是否值得的问题上：万一他一辈子都做不出这样的结果来，那他一辈子可能就是一个大学合同制讲师。在我们回答这个问题之前，先请读者来看另一个人的故事。这个人也试图攻下孪生素数猜想，曾经以为自己成功了，但终究以失败而告终。如果他地下有知张益唐的研究成果会作何感想呢？他就是美国范德堡大学的数学家阿仁斯道夫（Richard Arenstorf）教授。

Abstract Euler developed a program which aimed to transform analysis into an autonomous discipline and reorganize the whole of mathematics around it. The implementation of this program presented many difficulties, and the result was not entirely satisfactory. Many of these difficulties concerned the integral calculus. In this paper, we deal with some topics relevant to understand Euler’s conception of analysis and how he developed and implemented his program. In particular, we examine Euler’s contribution to the construction of differential equations and his notion of indefinite integrals and general integrals. We also deal with two remarkable difficulties of Euler’s program. The first concerns singular integrals, which were considered as paradoxical by Euler since they seemed to violate the generality of certain results. The second regards the explicitly use of the geometric representation and meaning of definite integrals, which was gone against his program. We clarify the nature of these difficulties and show that Euler never thought that they undermined his conception of mathematics and that a different foundation was necessary for analysis. Communicated by Jesper Lützen.

ABSTRACT There are many ways to consider the philosophy of history. In this article, I claim that one of the most viable approaches to the philosophy of history today is that of critical theory of history, inspired by Reinhart Koselleck. Critical theory of history is based on what I call known history, history as it has been established and expounded by historians. What it contributes—its added value, so to speak—is a reflection on the categories employed to think about historical experience at its different levels, not only as a narrative but also as a series of events: their origins, contexts, terminology, functions (theoretical or practical), and, finally, eventual relevance.

ABSTRACT Jouni-Matti Kuukkanen has written an important book. It directly confronts a key theoretical dilemma that has shadowed debate in historiography for several decades: histories cannot be written without using some narrative structure or other, but epistemological evaluation cannot be applied to narratives qua narrative. Thus, if empirical inquiry takes the form of a history, then it cannot be rationally evaluable, and if rationally evaluable, empirical inquiry cannot be in the form of a history. Kuukkanen's book both directly confronts and proposes a strategy for surmounting this tired and tiresome theoretical barrier. Kuukkanen deserves great credit for attempting to reshape a long-stalled debate in a way that enables the theoretical options to be imagined anew. Yet his structuring of the oppositional tendencies engenders some ongoing problems regarding how to understand the philosophical stakes and options. This review argues that achieving Kuukkanen's postnarrativist future requires going back to past epistemic concerns discarded because they were tied to conceptions of logic and explanation that could not be reconciled with narrative form. Kuukkanen practices postnarrativism but still preaches a prenarrativist conception of logic. To reach his promised future, to actually overcome the dilemma that he rightly seeks to transcend, one must actually have the courage of Kuukkanen's pragmatist convictions.

【摘要】 本文从我国基础研究发展面临的新形势出发,分析了我国财政科技投入支持基础研究的情况,包括我国财政科技投入及基础研究经费、中央支持基础研究的政策措施和地方支持基础研究的主要实践。通过调研,本文剖析了基础研究投入存在的主要问题:基础研究经费占R&D经费比例显著低于国际水平;中央财政占基础研究投入的绝大多数,仍有待进一步提高;地方财政基础研究经费投入稳步增长,但总量偏低;企业对基础研究的投入严重不足;稳定性支持不足;科研经费管理模式亟待完善;科研评价不够科学合理。最后,本文借鉴发达国家基础研究的投入机制,根据我国国情提出相关政策建议。 【关键词】 基础研究； 经费投入； 科技政策；