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By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…

度量几何 · 数学 2007-05-23 Thomas C. Hales

The solar system has changed dramatically since its birth, and so did our understanding of it. A considerable research effort has been invested in the past decade in an attempt to reconstruct the solar system history, including the earliest…

地球与行星天体物理 · 物理学 2015-07-17 D. Nesvorny , F. Roig

Generative adversary network (GAN) generated high-realistic human faces have been used as profile images for fake social media accounts and are visually challenging to discern from real ones. In this work, we show that GAN-generated faces…

计算机视觉与模式识别 · 计算机科学 2022-06-01 Hui Guo , Shu Hu , Xin Wang , Ming-Ching Chang , Siwei Lyu

We revisit the discovery and implications of the first candidate systems to contain multiple transiting exoplanets. These systems were discovered using data from the Kepler space telescope. The initial paper, presenting five systems…

地球与行星天体物理 · 物理学 2022-02-01 Jason H. Steffen , Jack J. Lissauer

The Kepler map was derived by Petrosky (1986) and Chirikov and Vecheslavov (1986) as a tool for description of the long-term chaotic orbital behaviour of the comets in nearly parabolic motion. It is a two-dimensional area-preserving map,…

混沌动力学 · 物理学 2013-12-30 Ivan I. Shevchenko

After mathematicians and physicists had learned that the structure of physical space was not necessarily Euclidean, it became conceivable that the global topological structure of space was non-trivial. In the context of the late 19th…

历史与综述 · 数学 2007-05-23 Moritz Epple

A hundred years ago, two British expeditions measured the deflection of starlight by the sun's gravitational field, confirming the prediction made by Einstein's General theory of Relativity. One hundred years later many physicists around…

物理学史与哲学 · 物理学 2020-01-15 Jorge L. Cervantes-Cota , Salvador Galindo-Uribarri , George F. Smoot

The scientific status of physical cosmology has been the subject of philosophical debate ever since detailed mathematical models of the Universe emerged from Einstein's general theory of relativity. Such debates have revolved around whether…

物理学史与哲学 · 物理学 2025-08-21 Pedro G. Ferreira , William J. Wolf , James Read

Deep fakes became extremely popular in the last years, also thanks to their increasing realism. Therefore, there is the need to measures human's ability to distinguish between real and synthetic face images when confronted with cutting-edge…

计算机视觉与模式识别 · 计算机科学 2022-01-12 Federica Lago , Cecilia Pasquini , Rainer Böhme , Hélène Dumont , Valérie Goffaux , Giulia Boato

A debate in the scientific literature has arisen regarding whether the orb depicted in Salvator Mundi, which has been attributed by some experts to Leonardo da Vinci, was rendered in a optically faithful manner or not. Some hypothesize that…

图形学 · 计算机科学 2019-12-10 Marco , Liang , Michael T. Goodrich , Shuang Zhao

The year 2012 will be the fourth centennial year of the Jesuit Christopher Clavius (1535-1612), known as the Euclid of XVI century and the collaborator of the Pope Gregory XIII for the calendar reformation. In the occasion of the year of…

物理学史与哲学 · 物理学 2011-06-14 Costantino Sigismondi

The Jacobian conjecture is thought to have been proposed by O. H. Keller in 1939. However, we have found that the statement of the conjecture is precisely the main result of a paper published by L. Kraus in 1884. Although the final step of…

代数几何 · 数学 2025-12-30 Lázaro O. Rodríguez Díaz

Lambert's theorem (1761) on the elapsed time along a Keplerian arc drew the attention of several prestigious mathematicians. In particular, they tried to give simple and transparent proofs of it (see our timeline \S 9). We give two new…

动力系统 · 数学 2020-10-29 Alain Albouy

The English optician John Dollond (1706-1761) performed a number of experiments with prisms of various transparent materials and concluded that an achromatic lens could exist. At that time, the dominant opinion about light refraction denied…

物理学史与哲学 · 物理学 2021-10-19 Igor Nesterenko

Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their history. The original error was made when a (startlingly)…

经典分析与常微分方程 · 数学 2007-05-23 Erik Talvila

Advances in face synthesis have raised alarms about the deceptive use of synthetic faces. Can synthetic identities be effectively used to fool human observers? In this paper, we introduce a study of the human perception of synthetic faces…

计算机视觉与模式识别 · 计算机科学 2021-11-09 Bingyu Shen , Brandon RichardWebster , Alice O'Toole , Kevin Bowyer , Walter J. Scheirer

One of the most famous drawings by Leonardo da Vinci is a self-portrait in red chalk, where he looks quite old. In fact, there is a sketch in one of his notebooks, partially covered by written notes, that can be a self-portrait of the…

计算机视觉与模式识别 · 计算机科学 2011-11-22 Amelia Carolina Sparavigna

A succinct chronology is given around Nov 1915, when the explicit field equations of General Relativity have been found. Evidence, unearthed by D.Wuensch, that a decisive document of Hilbert has been mutilated in recent years with the…

综合物理 · 物理学 2007-05-23 Dieter W. Ebner

An impressive bulk of multiple astronomical observations indicates that there are plenty of objects in the universe with the age which cannot be explained by the conventional theory. A model is considered which successfully describes all…

宇宙学与河外天体物理 · 物理学 2014-10-28 A. D. Dolgov

The 75th anniversary of Turing's seminal paper and his centennial year anniversary occur in 2011 and 2012, respectively. It is natural to review and assess Turing's contributions in diverse fields in the light of new developments that his…

计算复杂性 · 计算机科学 2014-02-10 Miguel-Angel Martin-Delgado