D alexandre grothendieck biography

His birth was recorded under the name Alexander Raddatz since, at the time of his birth, his mother was marred to Alf Raddatz. Alf and Hanka were divorced in Alexander Schapiro who still called himself Alexander Tanaroff and Hanka lived with their son Schurik and his mother's daughter Maidi in Berlin from to There they had a photographic studio which provided the family income.

On 1 April there was the so-called "boycott day" when Jewish shops and businesses were boycotted. On 7 April the Nazis passed a law which, under clause three, ordered the retirement of civil servants who were not of Aryan descent. Although Alexander Schapiro was hiding his Jewish origins by using the name Tanaroff, he still considered that Berlin was too dangerous a place for a Jew and he returned to Paris in May Hanka and her son Alexander remained in Berlin until December when she arranged for five year old Alexander to be fostered by the pastor Wilhelm Heydorn and his wife Dagmar who lived in Hamburg.

She put her daughter Maidi into an institution in Berlin. Schurik, together with other foster children, lived with the Heydorns from the beginning of until April He attended elementary school and then began his studies at the Gymnasium. Meanwhile Hanka had joined Alexander's father in Paris and, after the outbreak of the Spanish Civil War - 39they both went to Spain where they supported the Republicans.

By the end of April the Heydorns, who were now in serious danger as part of the resistance against Hitler, considered that their home was too dangerous a place for young Schurik so, having located his parents in France, put him on a train to join his father. The law concerning 'undesirables' had been passed on 12 November which required all Germans living in France to be sent to special internment camps.

Hanka and Schurik were interned in the Rieucros Camp near Mende. However, Schurik was allowed to continue his education at the village school about 5 km from the Camp. He also was given some private tutoring. Schurik's father, Alexander, was interned at the Camp du Vernet. In the Rieucros Camp was closed so Schurik and his mother were sent to the Gurs concentration camp near Pau.

He would hide in the woods every time the authorities came round looking for Jews. Meanwhile, in August his father had been handed over by the French Vichy government to the Nazis who took him from the Camp du Vernet to the Auschwitz extermination camp where he perished. Let us note at this point that Maidi survived the war and eventually emigrated to the United States.

In Schurik, who we will now start to call Grothendieck, and his mother moved to the village of Maisargues near Montpellier where Grothendieck worked in the vineyards and also, with the aid of a small scholarship, studied mathematics at the University of Montpellier. While at school he had felt dissatisfied with some of the mathematics that had been presented to him see, for example [ 16 ] :- What was least satisfying to me in our high school mathematics books was the absence of any serious definition of the notion of length of a curve, of area of a surface, of volume of a solid.

I promised myself I would fill this gap when I had the chance. He didn't find his professors at Montpellier much help in filling these gaps so he had to work on his own [ 8 ] :- It was in Montpellier, during his undergraduate days, that he underwent his first real mathematical experience. He was very dissatisfied with the teaching he was receiving.

He had been told how to compute the volume of a sphere or a pyramid, but no one had explained the definition of volume. It is an unmistakable sign of a mathematical spirit to want to replace the "how" with a "why". A professor of Grothendieck's assured him that a certain Lebesgue had resolved the last outstanding problems in mathematics, but that his work would be too difficult to teach.

Alone, with almost no hints, Grothendieck rediscovered a very general version of the Lebesgue integral. The genesis of this first mathematical piece of work [ was ] accomplished in total isolation Let us note that the professor at Montpellier who believed that Lebesgue had solved all outstanding mathematics problems was a certain M Soula.

There he attended Henri Cartan 's seminar which was on algebraic topology and sheaf theory. One of Grothendieck's fellow students was Jean-Pierre Serre. In Grothendieck moved to the University of Nancy where he lived with his mother who was occasionally bedridden due to tuberculosis contracted in the internment camps. At this time Grothendieck had a son named Serge with the lady from whom they rented rooms.

His mother, Johanna Grothendieck, was a German-born anarchist who moved to Berlin to pursue her interests in avant-garde art and politics. Due to persecution under the Nazi regime, Grothendieck's parents sent him to live with a foster family in Hamburg, Germany, just before the start of World War II. Inboth of his parents were interned, with his father tragically dying in the Auschwitz concentration camp.

Grothendieck and his mother were sent to an internment camp in Rieucros, France, where he attended school in a nearby town. Despite the challenges of his upbringing, Grothendieck showed immense talent in mathematics. After the war, he studied at the University of Montpellier in France, where he faced financial hardships and worked as a grape picker to support himself and his mother.

Springer Lecture Notes in Mathematics Hamet Seydi : Under A. Grothendieck and P. Second period. Voisin and J. Under C. Pierre Damphousse : Cartographie topologique. Philippe Delobel : Combinatoire. Gordon Edwards : Primitive and group-like elements in symmetric algebras. Do you want to know more about the Grothendieck Institute? Subscribe to our Newsletter.

In Septemberalmost totally deaf and blind, he asked a neighbour to buy him a revolver so he could kill himself. Grothendieck was born in Weimar Germany. Inaged ten, he moved to France as a refugee. Records of his nationality were destroyed in the fall of Nazi Germany in and he did not apply for French citizenship after the war. Thus, he became a stateless person for at least the majority of his working life and he traveled on a Nansen passport.

Grothendieck was very close to his mother, to whom he dedicated his dissertation. She died in from tuberculosis that she contracted in camps for displaced persons. He had five children: a son with his landlady during his time in Nancy; [ 3 ] three children, JohannaAlexanderand Mathieu with his wife Mireille Dufour; [ 1 ] [ 41 ] and one d alexandre grothendieck biography with Justine Skalba, with whom he lived in a commune in the early s.

Grothendieck's early mathematical work was in functional analysis. His key contributions include topological tensor products of topological vector spacesthe theory of nuclear spaces as foundational for Schwartz distributionsand the application of L p spaces in studying linear maps between topological vector spaces. It is, however, in algebraic geometry and related fields where Grothendieck did his most important and influential work.

Homological methods and sheaf theory had already been introduced in algebraic geometry by Jean-Pierre Serre [ 81 ] and others, after sheaves had been defined by Jean Leray. Grothendieck took them to a higher d alexandre grothendieck biography of abstraction and turned them into a key organising principle of his theory. He shifted attention from the study of individual varieties to his relative point of view pairs of varieties related by a morphismallowing a broad generalization of many classical theorems.

Inhe applied the same thinking to the Riemann—Roch theoremwhich recently had been generalized to any dimension by Hirzebruch. This result was his first work in algebraic geometry. Grothendieck went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which at the time were in a state of flux and under discussion in Claude Chevalley 's seminar.

He outlined his programme in his talk at the International Congress of Mathematicians. His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions. He adapted the use of non-closed generic pointswhich led to the theory of schemes. Grothendieck also pioneered the systematic use of nilpotents. As 'functions' these can take only the value 0, but they carry infinitesimal information, in purely algebraic settings.

His theory of schemes has become established as the best universal foundation for this field, because of its expressiveness as well as its technical depth. In that setting one can use birational geometrytechniques from number theoryGalois theorycommutative algebraand close analogues of the methods of algebraic topologyall in an integrated way. Grothendieck is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation.

His influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules. Although lauded as "the Einstein of mathematics", his work also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems. Weil had realized that to prove such a connection, one needed a new cohomology theory, but neither he nor any other expert saw how to accomplish this until such a theory was expressed by Grothendieck.

This program culminated in the proofs of the Weil conjecturesthe last of which was settled by Grothendieck's student Pierre Deligne in the early s after Grothendieck had largely withdrawn from mathematics.

D alexandre grothendieck biography: Alexander Grothendieck, later Alexandre

Here the term yoga denotes a kind of "meta-theory" that may be used heuristically; Michel Raynaud writes the other terms "Ariadne's thread" and "philosophy" as effective equivalents. Grothendieck wrote that, of these themes, the largest in scope was topoi, as they synthesized algebraic geometry, topology, and arithmetic. The theme that had been most extensively developed was schemes, which were the framework " par excellence " for eight of the other themes all but 1, 5, and Grothendieck wrote that the first and last themes, topological tensor products and regular configurations, were of more modest size than the others.

Topological tensor products had played the role of a tool rather than of a source of inspiration for further developments; but he expected that regular configurations could not be exhausted within the lifetime of a mathematician who devoted oneself to it. Grothendieck is considered by many to be the greatest mathematician of the twentieth century.

Although mathematics became more and more abstract and general throughout the 20th century, it was Alexander Grothendieck who was the greatest master of this trend. His unique skill was to eliminate all unnecessary hypotheses and burrow into an area so deeply that its inner patterns on the most abstract level revealed themselves—and then, like a magician, show how the solution of old problems fell out in straightforward ways now that their real nature had been revealed.

By the s, Grothendieck's work was seen as influential, not only in algebraic geometry and the allied fields of sheaf theory and homological algebra, [ 89 ] but influenced logic, in the field of categorical logic. According to mathematician Ravi Vakil"Whole fields of mathematics speak the language that he set up. We live in this big structure that he built.

We take it for granted—the architect is gone". In the same article, Colin McLarty said, "Lots of people today live in Grothendieck's house, unaware that it's Grothendieck's house. Grothendieck approached algebraic geometry by clarifying the foundations of the field, and by developing mathematical tools intended to prove a number of notable conjectures.

Algebraic geometry has traditionally meant the understanding of geometric objects, such as algebraic curves and surfaces, through the study of the algebraic equations for those objects. Properties of algebraic equations are in turn studied using the techniques of ring theory. In this approach, the properties of a geometric object are related to the properties of an associated ring.

The space e. Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces "spectra" and associated rings the primary objects of study.

D alexandre grothendieck biography: Alexandre Grothendieck was a German

To that end, he developed the theory of schemes that informally can be thought of as topological spaces on which a commutative ring is associated to every open subset of the space. Schemes have become the basic objects of study for practitioners of modern algebraic geometry. Their use as a foundation allowed geometry to absorb technical advances from other fields.

His generalization of the classical Riemann—Roch theorem related topological properties of complex algebraic curves to their algebraic structure and now bears his name, being called "the Grothendieck—Hirzebruch—Riemann—Roch theorem". The tools he developed to prove this theorem started the study of algebraic and topological K-theorywhich explores the topological properties of objects by associating them with rings.

D alexandre grothendieck biography: Alexander Grothendieck was a German

Grothendieck's construction of new cohomology theories, which use algebraic techniques to study topological objects, has influenced the development of algebraic number theoryalgebraic topologyand representation theory. As part of this project, his creation of topos theorya category-theoretic generalization of point-set topologyhas influenced the fields of set theory and mathematical logic.

The Weil conjectures were formulated in the later s as a set of mathematical problems in arithmetic geometry. They describe properties of analytic invariants, called local zeta functionsof the number of points on an algebraic curve or variety of higher dimension. It did not provide the intended route to the Weil conjectures, but has been behind modern developments in algebraic K-theorymotivic homotopy theoryand motivic integration.

Grothendieck's emphasis on the role of universal properties across varied mathematical structures brought category theory into the mainstream as an organizing principle for mathematics in general. Among its uses, category theory creates a common language for describing similar structures and techniques seen in many different mathematical systems.

The book is a lightly fictionalized account of the world of scientific inquiry and was a finalist for the National Book Award. The "Istituto Grothendieck" has been created in his honor. Contents move to sidebar hide. Article Talk. Read Edit View history. Tools Tools. Download as PDF Printable version. In other projects. Wikimedia Commons Wikiquote Wikidata item.

French mathematician —