A pair of mathematicians has solved the first chunk of one of the most famous conjectures about the additive properties of whole numbers. Proposed more than 60 years ago by the legendary Hungarian mathematician Paul Erdős, the conjecture asks when an infinite list of whole numbers will be sure to contain patterns of at least three evenly spaced numbers, such as 26, 29 and 32. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research develop ments and trends in mathe matics and the physical and life sciences. Erdős posed thousands of problems over the course of his career, but the question of which number lists contain evenly spaced numbers (what mathematicians call arithmetic progressions) was one of his all-time favorites. "I think many people regarded it as Erdős' number-one problem," said Timothy Gowers of the University of Cambridge.
"You don't know that rock music exists in this age unless someone shows you," Jacob Faber told Rolling Stone in January. As Sunflower Bean, Faber, Nick Kivlen, and Julia Cumming propose a contemporary take on lo-fi psychedelia, wearing shrewd influences on stylish sleeves. They play their latest album, "Human Ceremony," at Music Hall of Williamsburg on Oct. 7, with its classic-rock chops, slick titles ("2013"), and New Wave aesthetics ("Easier Said"), delivered under Cumming's runway-ready voice.
Sebastian Barry has become the first novelist to win the prestigious Costa Book of the Year prize twice. Days Without End, a novel set in the 1850s, tells the story of two Irish soldiers who go to fight in the US. The Dublin-born author and playwright was inspired to write about the gay relationship at the heart of the story after his youngest son came out. The 61-year-old, who receives £30,000, won the same accolade in 2008 with The Secret Scripture. Prof Kate Williams, who chaired the judging panel, described the book as "a searing, magnificent and incredibly moving description of how the West was won".
Any questions about Paige VanZant's competitive nature and toughness were effectively answered by the bloody beating she took at the hands of Rose Namajunas a year ago this month. So when the 22-year-old recent "Dancing With the Stars" runner-up said this week in an interview that "I really haven't thought about" winning a UFC women's straw-weight title, the first reaction is to question her commitment. In light of the UFC's purchase this year by Beverly Hills talent agency WME-IMG and by considering VanZant's popularity noted in her main-event placement on Saturday's UFC Fight Night card on Fox from Sacramento, it quickly becomes apparent VanZant is deeply driven by a more universal definition of success. "I take fights as they come. The ultimate goal is to win and win, but I also have many other things outside fighting that I'm pursuing and I'm passionate about," VanZant told the Los Angeles Times while taking tiny bites from a kale salad in an interview at a hillside restaurant on the Westside.
Urijah Faber is one of the most popular lighter weight fighters in the history of the sport. The former WEC champion has built up that fan base with an entertaining fight style and outgoing personality. However, Faber appears to be reaching the end of his peak as a top fighter and hasn't looked as good in recent fights. Rivera is a fighter on the rise with a 19-1 record and is coming off an impressive win on Fox. This is a crucial crossroads fight, with Faber looking to remain in the top mix of the division and Rivera attempting to break into that group with the biggest win of his career.