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Domain: kyoto-u.ac.jp
Stories and comments across the archive that link to kyoto-u.ac.jp.
Stories · 6
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Titans of Mathematics Clash Over Epic Proof of ABC Conjecture (quantamagazine.org)
Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years. Quanta Magazine: In a report [PDF] posted online Thursday, Peter Scholze of the University of Bonn and Jakob Stix of Goethe University Frankfurt describe what Stix calls a "serious, unfixable gap" within a mammoth series of papers by Shinichi Mochizuki, a mathematician at Kyoto University who is renowned for his brilliance. Posted online in 2012, Mochizuki's papers supposedly prove the abc conjecture, one of the most far-reaching problems in number theory. Despite multiple conferences dedicated to explicating Mochizuki's proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 pages, are written in an impenetrable style, and refer back to a further 500 pages or so of previous work by Mochizuki, creating what one mathematician, Brian Conrad of Stanford University, has called "a sense of infinite regress."
Between 12 and 18 mathematicians who have studied the proof in depth believe it is correct, wrote Ivan Fesenko of the University of Nottingham in an email. But only mathematicians in "Mochizuki's orbit" have vouched for the proof's correctness, Conrad commented in a blog discussion last December. "There is nobody else out there who has been willing to say even off the record that they are confident the proof is complete." Nevertheless, wrote Frank Calegari of the University of Chicago in a December blog post, "mathematicians are very loath to claim that there is a problem with Mochizuki's argument because they can't point to any definitive error." That has now changed. In their report, Scholze and Stix argue that a line of reasoning near the end of the proof of "Corollary 3.12" in Mochizuki's third of four papers is fundamentally flawed. The corollary is central to Mochizuki's proposed abc proof. "I think the abc conjecture is still open," Scholze said. "Anybody has a chance of proving it." -
How Would You Generate C Code Using Common Lisp Macros? (github.com)
Long-time Slashdot reader kruhft brings news about a new S-Expression based language transpiler that has the feel of C. This structure allows for the creation of code generation macros using the full power of the host Common Lisp environment, a language designed for operating on S-Expressions, also known as Lists. It is unknown exactly what power might come about from this combination of low level processing with high level code generation.
This has prompted some discussion online about other attempts to convert Lisp to C -- raising several more questions. How (and why) would you convert your Lisp code into C, and what would then be the best uses for this capability? -
Possible Proof of ABC Conjecture
submeta writes "Shinichi Mochizuki of Kyoto University has released a paper which claims to prove the decades-old ABC conjecture, which involves the relationship between prime numbers, addition, and multiplication. His solution involves thinking of numbers not as members of sets (the standard interpretation), but instead as objects which exist in 'new, conceptual universes.' As one would expect, the proof is extremely dense and difficult to understand, even for experts in the field, so it may take a while to verify. However, Mochizuki has a strong reputation, so this is likely to get attention. Proof of the conjecture could potentially lead to a revolution in number theory, including a greatly simplified proof of Fermat's Last Theorem." -
Top 100 Papers in Physics Ranked
Rob Carr writes "What do physicists care about most? Who are the greatest minds of our time? What physics papers have had the greatest impact? Sidney Redner attempts to answer that question by looking at the citations of all journals in the Physical Review Journals since 1893. He ranked the top 100 papers based on their 'impact': the number of citations times the average age of the citations. Einstein's Relativity papers, which were not in Physical Review journals, are the most stunning absence. 'Fan Favorites' are there - Einstein does make the list for the Einstein Podolsky Rosen paper. Feynman, Dirac, Bethe, Wheeler are on the list. Stephen Hawking does not make the list. Yet Nobel Prize winner Walter Kohn, who is virtually unknown to the general public, is an author on five of the 100 papers, including the top two and one of the top 15 'hot' papers. The paper goes into the statistics of the citations, a fascinating area in it's own right. Some papers make an immediate splash, while others might wait 50 years before their importance becomes apparent. The vast majority die a quick and quiet death. It's tempting to wonder if Redner's paper conclusively proves Sturgeon's Law." -
Preview of Java 1.5
gafter writes "An early access prototype implementation of the proposed new J2SE 1.5 language features is available. The prototype includes generics (JSR 14), typesafe enums, varargs, autoboxing, foreach loops, and static import (JSR 201). In other words, all the new language features planned for 1.5 except metadata (JSR 175). The prototype includes full sources for the compiler, written in the extended language. You can download the prototype from java.sun.com. It requires J2SE 1.4.1 and provides some examples of how to use the new language constructs. The prototype includes an experimental type system (variant type parameters) for Generic Java that is being considered for Tiger (1.5) based on a paper by Igarashi and Viroli at ECOOP 2002 . Comments and votes for the new type system are being gathered at bugParade." -
1TB In A Cubic Centimeter
rgetty writes "Inforworld posted this article describing the process used by a group of engineers and scientists from Kyoto University and Central Glass (Japan) to pack 1TB of data into a cubic centimeter of glass. Portable data warehousing is not too far off..."