Mathematicians have traditionally dealt with convergent series and shunned divergent ones. But, long ago, astronomers found that divergent expansions yield valuable results. If these so-called asymptotic expansions are truncated, the error is bounded by the first term omitted. Thus, by stopping just before the smallest term, excellent approximations may be obtained.
Archive for December, 2019
Divergent Series Yield Valuable Results
Published December 26, 2019 Occasional ClosedTags: Analysis
Having your Christmas Cake and Eating it
Published December 19, 2019 Irish Times ClosedTags: Algorithms
As Christmas approaches, the question of fair sharing comes into focus. Readers can rejoice that there has been a recent breakthrough in cake-cutting theory. Cake cutting may sound limited, but it is important for many practical problems. A cake is a metaphor for a parcel of land to be divided, broadcast frequencies to be allocated, divorce settlements, chores to be done by flatmates, border resolutions or any other valuable or scarce resource to be shared [TM177 or search for “thatsmaths” at irishtimes.com].
Image from https://www.irishcentral.com/%5D
In 1985, cosmonaut Vladimir Dzhanibekov commanded a mission to repair the space station Salyut-7. During the operation, he flicked a wing-nut to remove it. As it left the end of the bolt, the nut continued to spin in space, but every few seconds, it turned over through 
Flipping nut [image from Veritasium].
A New Mathematical Discovery from Neutrino Physics
Published December 5, 2019 Irish Times ClosedTags: Physics
Although abstract in character, mathematics has concrete origins: the greatest advances have been inspired by the natural world. Recently, a new result in linear algebra was discovered by three physicists trying to understand the behaviour of neutrinos [TM176 or search for “thatsmaths” at irishtimes.com].
Neutrino trails in a bubble chamber [image from Physics World]
Continue reading ‘A New Mathematical Discovery from Neutrino Physics’
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