Normat 59:3-4, 97 (2011) 97

Galois 200 years

Ulf Persson

Department of Mathematics, Chalmers University of Technology

SE-412 96 Göteborg, Sweden

ulfp@chalmers.se

The brief life of Évariste Galois ending tragically as a consequence of an ill-advised duel

before he was even twenty-one must be known to all mathematicians. Never in the annals

of mathematics was there ever a more poignant tale of early brilliance cut short. It is

now two hundred years since he was born, and as those lines are being written more

than hundred and eighty since he died. His mathematics on the other hand is more alive

than ever. To celebrate Galois in a Normat issue in 2011 was a very natural thing to

do, and as my co-worker for this issue - Juliusz Brzezinski remarked, especially since the

bicenntennial anniversary largely seemed to go unnoticed as opposed to that of Abel ten

years ago (but Abel is the pride of a small nation, which takes well care of him).

Articles for this issue have been externally solicited as well as internally produced.

Although the initial ambition was for one issue, the amount of material turned out to

easily ﬁll out two, with extra m aterial to be published later in due time. Thus, maybe

for the ﬁrst time ever, a double issue is being produced by Normat. As the issue needed

to appear in 2011 (at least retroactively) this has held up production of Normat, but I

promise that subsequent issues will appear in quick succession. One ﬁnal remark: Although

all the authors are Scandinavian, it so happened that the language of choice for the authors

turned out to be English, and hence this introduction is for the sake of uniformity also

written in English. This is a deviation from the tradition, and maybe even the mission of

Normat, but circumstances are special.

Although he twice was barred from École Polytechnique and had to be satisﬁed with

École Normale from which he was eventually ex pelled due to the political turbulence of

the time, one should not cast him in the role of the misunderstood genius. True Cauchy

was more negligent in his duties than even his professorial position would have condoned,

but once the work was read its importance was never in doubt. But by then Galois was

already dead.

Galois is associated with criteria for solubility of polynomial equations, where he went

well beyond his somewhat elder contemporary - Abel, but Galois theory turns out to be

concerned with so much more in modern mathematics. Wiles proof of the Fermats Last

Theorem would be impossible without it.

In this modest issue on the theme of Galois theory, we have two elementary articles

on classical topics for introductory Galois theory, namely on cubics and quartics. We also

are happy to be able to include a survey by Christian Jensen, the foremost Scandinavian

expert on Galois theory, on the inverse problem. Given a group, can we ﬁnd an extension of

say Q, with that group of symmetries? Juliusz Brzezinski contributes a lengthy survey on

connections between Galois theory and number theory and is meant to be an elementary

introduction to the Langlands program. Finally Dennis Eriksson voluntered to write on

so called Dessins, elementary combinatorial encodings of coverings of P

only ramiﬁed at

three points. This shows how Galois actions also occur in geometric contexts.