Speech Given by Heisuke Hironaka at the Occasion of his Légion d’honneur Ceremony

Your Excellency, Mr Ambassador, Dear Madam,

Ladies and gentlemen representing the French government and various industries and organisations, Ladies, Misses, Gentlemen,

It is with great pleasure and undisguised emotion that I receive this high distinction from the French government, one of the greatest honours of my life. I offer you my warmest thanks.

Thank you also to all those who have taken the trouble to come today despite a busy schedule at the start of the year.

This decoration was, it is said, created by Napoleon Ist. I am all the more mindful of this because, when I was at school, I first became interested in mathematics upon learning of a geometric proposition known as ‘Napoleon’s theorem’.

I need hardly point out that he was a great man, a military leader who played a key role in restoring France’s international standing through his administrative skills and tactical acumen.

Moreover, as a man of science, I am particularly impressed by the fact that it was on his initiative that institutions – such as École Normale Supérieure and École Polytechnique – were established in the capitals of France and Italy, institutions that are still renowned throughout the world today.

Similarly, he did not merely build roads in every region of France, but also had trees planted along their edges, much to the delight of today’s travellers.

This clearly illustrates his long-term vision for science and landscape planning. I hope that Japan’s current leaders will take inspiration from Napoleon on this point.

But whilst I am delighted, from the bottom of my heart, to receive such an honour, it is certainly not because of any personal interest I have in Napoleon. Ever since my youth, I have been particularly drawn to the world of French mathematics. It was whilst I was a student at Kyoto University, whilst reading Laurent Schwartz’s (1915–2002) “Théorie des distributions”, that I decided to become a mathematician.

My first, very modest, article on mathematics was published in a very modest student journal: an essay devoted to L. Schwartz’s theory.

Similarly, reading three works by André Weil: “Foundations of Geometry”, “Abelian Varieties” and “Algebraic Curves and Varieties Derived from”, convinced me to specialise in Algebraic Geometry.

When I was a postgraduate student, it was through reading articles and books by Jean-Pierre Serre and Henri Cartan that I learnt about the theory of complex analytic functions of several variables.

It was also during this period that I experienced one of my first intellectual thrills upon discovering Jean Leray’s ideas on spectral sequences and sheaves.

When I was a student, the whole world regarded French mathematics as being at the very pinnacle of the field, and many mathematicians of that era dreamed of going to study in France. Indeed, many Japanese students, including mathematicians of my generation, went to study in Paris after receiving a scholarship from the French government.

In my case, due to my financial situation, it was not possible for me to go and study directly in France. In 1957, however, I was awarded an American scholarship, known as a Fulbright grant, which enabled me to go to Harvard University.

Two years later, I met Alexander Grothendieck there, who had come to Harvard as a visiting professor, and, at his invitation, I was finally able to go to Paris, the city I had always admired, to study at the Institut des Hautes Études Scientifiques (IHES).

To my knowledge, IHES was at the time the smallest research centre in the world. Yet, despite its size, it was a centre of attention for the global mathematical community.

The IHES rented just one floor of a small museum situated at Rond-Point Bugeaud, near l’Étoile.

Its staff consisted solely of the director, Mr Motchane, two professors, Jean Dieudonné and Grothendieck, and a secretary, Miss Rolland. Added to this was a visiting researcher: myself.

It is fair to say that this was undoubtedly a research centre on a ‘human scale’, placing great emphasis on the human element.

Jean Dieudonné was already a famous mathematician, whilst Alexander Grothendieck was a young mathematical genius. Renowned mathematicians, whether living in Paris or simply passing through, flocked to the seminars held there.

The seminar room was full.

Forty years later, the IHES, now housed in spacious premises in the Paris suburbs, has grown to become a Mecca for mathematicians, at the cutting edge of the discipline and among the world’s finest.

If we consider only the number of recipients among full professors of the Fields Medal, it is clear that IHES is unquestionably ranked first in the world.

Two French professors, Michael Gromov and, before him, André Weil, have received the Kyoto Prize, for which I am a member of the selection committee. Gromov is a Permanent Professor at IHES.

The Kyoto Prize was established by Mr Inamori, who, to my great delight, is here with us today.

Ultimately, is IHES not undoubtedly the best model in the world for such research centres?

It owes its development to a fundamental principle, namely “the importance placed on the human element”, as encapsulated in the phrase “start small and grow through education”.

As a mathematician, but also as an individual, everything I have learnt during my time abroad is invaluable.

What I have received from France is what has left the deepest impression on me. In addition to all the benefits I have enjoyed so far from France, it is therefore a great honour to be the recipient today of this highest French honour.

Finally, I would like to add that my work within the Japanese Association of Mathematical Sciences, which has enabled me to receive such an honour, is not the achievement of one man alone. It is also thanks to the friends, staff, mathematicians and industry representatives who have worked there in large numbers as supervisors, advisers or administrators.

I would like to take this opportunity to thank them from the bottom of my heart.

Thank you very much to everyone.

Heisuke Hironaka
Tokyo, French Embassy, 21 January 2004