# Nicolas Bourbaki and M. Lothaire - Two Prolific Mathematicians

In 1983, mathematician M. Lothaire wrote a book titled on Combinatorics on Words. Roger Lyndon of ‘Lyndon word’ wrote this in the foreword -

This is the ?rst book devoted to broad study of the combinatorics of words, that is to say, of sequences of symbols called letters. This subject is in fact very ancient and has cropped up repeatedly in a wide variety of subjects.

Lothaire was so much ahead of his time that it took 14 years for his book to get any attention. The 1983 book was reprinted in 1997, and he followed up with two other seminal books on the subject - “Lothaire, M. (2002), Algebraic combinatorics on words” and “Lothaire, M. (2005), Applied combinatorics on words”.

But here is the most fascinating aspect of today’s commentary. There was no mathematician named M. Lothaire.

Who wrote the books then? It was written by a number of mathematicians, and many of them were students of Marcel-Paul Schtzenberger, a well-known French mathematician, or was he?

Schtzenberger’s first doctorate, in medicine, was awarded in 1948 from the Facult de Mdecine de Paris. His doctoral thesis, on the statistical study of gender at birth, was distinguished by the Baron Larrey Prize from the French Academy of Medicine.[4]

Biologist Jaques Besson, a co-author with Schtzenberger on a biological topic,[5] while noting that Schtzenberger is perhaps most remembered for work in pure mathematical fields, credits him for likely being responsible for the introduction of statistical sequential analysis in French hospital practice.

“First doctorate” means he got a second doctorate, and it was indeed in mathematics. Schtzenberger continued to do great work in mathematics and express his disdain for geneticists. So, it is ironic that the genome scientists are finding mathematical theories developed by him and his students useful.

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M. Lotharie reminds us of another prolific and influential mathematician, Nicolas Bourbaki, who did not exist. This character was also created by the French mathematicians.

Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality. Their work led to the discovery of several concepts and terminologies still discussed.

While there is no Nicolas Bourbaki, the Bourbaki group, officially known as the Association des collaborateurs de Nicolas Bourbaki (Association of Collaborators of Nicolas Bourbaki), has an office at the cole Normale Suprieure in Paris.

**Books by Bourbaki**

Bourbaki’s main work is the Elements of Mathematics (lments de mathmatique) series. This series aims to be a completely self-contained treatment of the core areas of modern mathematics. Assuming no special knowledge of mathematics, it tries to take up mathematics from the very beginning, proceed axiomatically and give complete proofs.

Set theory (Thorie des ensembles)

Algebra (Algbre)

Topology (Topologie gnrale)

Functions of one real variable (Fonctions d’une variable relle)

Topological vector spaces (Espaces vectoriels topologiques)

Integration (Intgration)

and later

Commutative algebra (Algbre commutative)

Lie theory (Groupes et algbres de Lie)

Spectral theory (Thories spectrales)