Cybermath column NZ Math Society Newsletter April 2017

This column takes a break from its recent heavy focus on publication reform to list a few interesting links more related to mathematical research and other professional issues. It is a partially fenced stream of consciousness, but may be useful all the same.

Laci Babai made a bold claim, which generated substantial publicity, that determining whether two graphs are isomorphic can be solved in quasipolynomial time. Harald Helfgott found a flaw while reading the paper deeply in order to present it to S\'{e}minaire Bourbaki, which I had no idea still existed. Babai retracted the claim on 4 January 2017, and reasserted it after fixing the proof on 7 January 2017. How long would this process have taken under the current journal system — would the error have been spotted at all? (sorry, couldn’t resist that). This is an important theoretical breakthrough and shows how well mathematics can work in the internet age.

Speaking of internet mathematics, there is a  journal of that name, devoted really to the mathematics of complex networks (what we used to call graphs before the marketers took over). Not only is the journal interesting and apparently well run, it uses the new platform  Scholastica (as does Tim Gowers’  Discrete Analysis). Another interesting fact is that the journal was formerly published by one of the traditional publishers (Taylor \& Francis), and they gave it up to the editors (not, however, before charging them for the back issues).

Getting back to mathematics on the internet, Polymath is still active, although generating less publicity than a few years ago. They are currently focusing on Rota’s basis conjecture:  if $B_1, B_2, \dots, B_n$ are disjoint bases of an $n$-dimensional vector space $V$  then there exists disjoint bases $C_1, \dots, C_n$ such that each $C_j$ contains one element from each $B_i$.

The arXiv has become very important to mathematicians. At my urging my university will become a financial supporter. I challenge other readers to get their institutions to do the same, rather than freeload as seems to be NZ policy in so many areas in recent years. Although it is cheap to run per paper, the total cost is nontrivial because there are so many papers. It is a challenge to keep up with new postings, so if you trust recommendation algorithms, try  arXivist (“your personal guide to the arXiv”) or Scirate to navigate it. An alternative is to visualise its million-plus papers as a complex network using Paperscape.

The arXiv idea has recently spread to disciplines with very little preprint tradition. The Center for Open Science has developed a preprint platform used by psychology, engineering, sociology and other fields. Maybe journals will change radically soon, after all.

Springer made many old volumes in its Graduate Texts in Mathematics series available for free download in late 2015. The direct links can be found easily by searching although they have apparently revoked the free deal. If they were serious, presumably they would remove the links.

If you want to attend a mathematical meeting in person rather than do everything via the internet, try MathMeetings.Net which aims to be a complete list.

I recently read (much of — far too many letters and namedropping for my taste to finish all of it) The Autobiography of Bertrand Russell. A controversial figure but certainly a mathematician (for part of his life) who followed his conscience wherever it took him. The American Mathematical Society is awarding the Bertrand Russell Prize every 3 years from 2018, for “research or service contributions of mathematicians or related professionals to promoting good in the world and recognizes (sic) the various ways that mathematics furthers human values.” Thomas Hales has apparently funded the prize. It would be good to see nominations (which close 30 June 2017) from this part of the world.

Of course, political activity by mathematicians can cause problems and muddy reputations, as the recently deceased great mathematician Igor Shafarevich found out. Other nonagenarians who have left us recently, in mathematics or related fields, include Kenneth Arrow, Joseph Keller, Howard Raiffa and Thomas Schelling. Going back a year, there is also Christopher Zeeman (whom I am sure visited NZ sometime), Fields Medallist Klaus Roth, while Felix Browder made it to 89. Best wishes to all readers aiming to make 100 while still doing mathematics! The longest-lived mathematician that I am aware of is Leopold Vietoris who not only lived during three centuries, has quite a few concepts named after him.

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