Posted by: Administrator | 25/01/2016

Professor Alexandre Borovik, University of Manchester

I have never published anything in the JCM and had never been involved
in its publication and therefore have no personal interest in its existence.

I wish to say a few words about the scope of the JCM. It seems to me
that Terry Lyons’ criticism of the Journal is based on an arbitrary
assumption that the Journal should publish quality papers from so-called
“experimental” mathematics and from numerical mathematics. But the JCM
is unlikely to be competitive in these areas are because there is plenty
of journals around already covering them.

But the JCM plays, and is in position to continue to play, a unique role
as the leading journal in specific, increasingly important,
cross section of pure mathematics: symbolic and/or absolute precision
arithmetic computations, frequently at the limits of capacity of modern
computers, in algebra, representation theory, combinatorics, number
theory, algebraic geometry, etc. The role of mathematical work of this
type will only increase in future.

Let us take look at a very recent paper which I picked on the very first
page of the JCM site hosted by CUP because the subject appeared familiar
to me:

John Ballantyne, Chris Bates and Peter Rowley, The maximal subgroups of
E_7(2), LMS J. Comput. Math. 18 (1) (2015) 323-371.

A few general words about the area : finite groups appear in mathematics as automorphism groups of mathematical structures. In particular, they act on sets. The so-called primitive actions are building blocks of actions of finite groups on sets. The so-called simple groups are building blocks of groups. To make Classification of Finite Simple Groups, one of the key results of 20th century, fully usable across mathematics, one needs to know primitive permutation representation representations of simple groups. It is an elementary fact that description of primitive permutation representations of a finite group is equivalent to description of maximal subgroups in the group. E_7(2) is one of finite simple groups; it is big, it contains contains about 10^40 elements. It is a very big haystack to search for the proverbial needle; 10^40 straws have the same mass as 1 million Suns. In the paper, a much more difficult problem is solved: in a haystack of that size, specific symmetric configurations of straws  are identified, and fully described.

And now is my assessment of the paper:

  1. The result may appear to be narrow and specific, but it will stay
    relevant for decades to come, because it is about a concrete, eternal,
    and important mathematical object.
  2. Methods are an intricate intertwining of subtle and difficult mathematics with hard but subtle computations.
  3. It is hard to find any other journal to publish this paper together with 51 MB (3.36 MB in compressed form) of electronic files supporting the calculations.
  4. Two younger authors of the paper  are brilliant young mathematicians with proven ability to compute in areas where no mathematician has computed before. In my opinion, this makes them pretty special,  As it has already been said in this discussion about similar situations, peer-reviewed publication of their papers is crucially important for the future career of young mathematicians.

This small case study explains, I think, why the JCM is a unique and special journal and why closing it is not in the interests of mathematics  and, in my humble opinion, not in the interests of the nation.

To conclude, a comment from Rob Wilson (placed here with his kind permission):

I am perhaps at the opposite extreme, having published ten papers in the
JCM over the past 14 years, with another one in press at the moment.
Some might say this is a ‘conflict of interest’ that disqualifies me
from speaking, but I fully endorse what Sasha has said about the type of
computation and mathematics that is represented in the JCM. It is a much
misunderstood and even despised area of mathematics, but in fact is hard
core computation on the edge of the impossible.

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