The latest IPCC report
The latest draft edition of the UN’s Intergovernmental Panel on Climate Change (IPCC) report includes some rather stark language:
Continued emission of greenhouse gases will cause further warming and longlasting changes in all components of the climate system, increasing the likelihood of severe, pervasive and irreversible impacts for people and ecosystems.
Among the potential sources of havoc are rising sea levels, more frequent extreme temperatures, flooding, drought, harm to marine life and potentially violent conflicts arising from the changing agricultural and meteorological environment.
Skeptics of the scientific consensus have made great hay over the fact
Continue reading To frack or not to frack: That’s not the question
“Experimental mathematics” has emerged in the past 25 years or so to become a competing paradigm for research in the mathematical sciences. An exciting workshop entitled Challenges in 21st Century Experimental Mathematical Computation was held at the Institute for Computational and Experimental Research in Mathematics (ICERM), July 2125, 2014, which explored emerging challenges of experimental mathematics in the rapidly changing era of modern computer technology. This report summarizes the workshop findings (without mentioning any of the research presentations).
While several more precise definitions have been offered for “experimental mathematics,” we used the informal one given in the book The Computer
Continue reading Opportunities and challenges in experimental mathematics
Introduction
On 10 August 2014, a team led by Thomas Hales of the University of Pittsburgh, USA, announced that their decadelong effort to construct a computerverified formal proof of the Kepler conjecture was now complete. The project was known as Flyspeck, a rough acronym for “Formal Proof of Kepler.”
The Kepler conjecture is the assertion that the simple scheme of stacking oranges typically seen in a supermarket has the highest possible average density, namely pi/(3 sqrt(2)) = 0.740480489…, for any possible arrangement, regular or irregular. It is named after 17thcentury astronomer Johannes Kepler, who first proposed that planets orbited in
Continue reading Formal proof completed for Kepler’s conjecture on sphere packing
Background
Intellectual property law is complex and varies from jurisdiction to jurisdiction, but, roughly speaking, creative works can be copyrighted, while inventions and processes can be patented. In each case the intention is to protect the value of the owner’s work or possession.
For the most part mathematics is excluded by the Berne convention of the World Intellectual Property Organization WIPO. An unusual exception was the successful patenting of Gray codes in 1953. More usual was the carefully timed Pi Day 2012 dismissal by a US judge of a copyright infringement suit regarding Pi, since “Pi is a
Continue reading Can Pi be trademarked?
One of the present bloggers (Jonathan M. Borwein) has published an article in The Conversation on the proposed cuts to scientific research in the latest Australian federal budget. While some medical research has been spared, other sectors, notably basic science, are being cut severely.
The cuts include AUS$74 million cuts to the Australian Research Council (ARC), AUS$80 million cuts to the Cooperative Research Center (CRC) program, AUS$111 million cuts to the Commonwealth Scientific and Industrial Research Organization (CSIRO) and AUS$120 million cuts to the Defence Science and Technology Organization (DSTO).
Borwein observes that even if one grants that medical research
Continue reading Borwein on the Australian scientific research budget
In a dramatic announcement on March 16, 2014, a team of astronomers led by John Kovac of the HarvardSmithsonian Center for Astrophysics said that they have detected gravitational waves, confirming predictions made by mathematical physicists Alan Guth, Andrei Linde and others in the 1970s and 1980s.
Gravitational waves from inflation, with their distinctive twisting pattern, in the polarization of the cosmic microwave background radiation.
MIT physicist/cosmologist Max Tegmark assessed the discovery in these terms: “I think that if this stays true, it will go down as one of the greatest discoveries in the history of science.”
Similarly, Marc Kamionkowski
Continue reading Gravitational waves confirm mathematical prediction of inflationary big bang
Introduction
In a 2004 review in Science of Searle’s Mind a Brief Introduction, neuroscientist Christof Koch wrote
Whether we scientists are inspired, bored, or infuriated by philosophy, all our theorizing and experimentation depends on particular philosophical background assumptions. This hidden influence is an acute embarrassment to many researchers, and it is therefore not often acknowledged. Such fundamental notions as reality, space, time, and causality–notions found at the core of the scientific enterprise–all rely on particular metaphysical assumptions about the world.
This may seem selfevident, and was regarded as important by Einstein, Bohr and the founders of quantum theory a century
Continue reading Is philosophy needed in mathematics and science?
A special session “Software, Design and Practice in Random Walks” has been scheduled for the upcoming Fourth international Congress on Mathematical Software (ICMS2014), to be held in Seoul, August 59, 2014.
This session will examine interactions between software use/design and random walk research, in a broad sense. More details, including abstract submission guidelines, can be found at ICMS website.
Plenary speakers for the conference include:
Jonathan Borwein (one of the present bloggers), University of Newcastle, Australia. Bruno Buchberger, Johannes Kepler University, Linz, Austria. Wolfram Decker, Technische Universitat Kaiserslautern, Germany. Andrew Sommese, University of Notre Dame, USA. Lloyd Trefethen,
Continue reading Upcoming ICMS special session on random walks
Pi is very old
The number pi = 3.14159265358979323846… is arguably the only mathematical topic from very early history that is still being researched today. The Babylonians used the approximation pi ≈ 3. The Egyptian Rhind Papyrus, dated roughly 1650 BCE, suggests pi = 256/81 = 3.16049…. Early Indian mathematicians believed pi = √10 = 3.162277… Archimedes, in the first mathematically rigorous calculation, employed a clever iterative construction of inscribed and circumscribed polygons to able to establish that 3 < 10/71 = 3.14084... < pi < 3 1/7 = 3.14285... This amazing work, done without trigonometry or floating
Continue reading Pi day 3.14 (14)
Scientists through the ages have noted, often with some astonishment, not only the remarkable success of mathematics in describing the natural world, but also the fact that the best mathematical formulations are usually those that are the most beautiful. And almost all research mathematicians pepper their description of important mathematical work with terms like “unexpected,” “elegance,” “simplicity” and “beauty.”
Some selected opinions
British Mathematician G. H. Hardy (1877–1947), pictured below, expressed in his autobiographical book A Mathematician’s Apology what most working mathematicians experience: “Beauty is the first test; there is no permanent place in the world for ugly mathematics.”
Continue reading Why mathematics is beautiful and why that matters

