**Wolfgang Haack**was born in Gotha, a town in central Germany, the son of Hermann Haack (1872-1966) and his wife Johanna König. Hermann Haack had studied cartography and geography at the University of Göttingen and, after completing his thesis, had begun work at the 'Geographical-Cartographical Institute' in Gotha in 1897. Wolfgang attended the gymnasium in Gotha and then went to the Technische Hochschule in Hanover in 1921. After a year as a student studying mechanical engineering, Haack moved to the Friedrich-Schiller University of Jena where he studied mathematics. He was awarded his doctorate in 1926 after submitting his dissertation

*Die Bestimmung von Flächen, deren geodätische Linien durch die Abbildung in die Ebene in Kegelschnitte übergehen*. His thesis advisor had been Robert Haussner.

Haack spent the next two years at Hamburg University with Wilhelm Blaschke. While he was there he passed the state examination to become a qualified gymnasium teacher of mathematics. In the following year he worked in Stuttgart as an assistant to Wilhelm Kutta and Friedrich Georg Pfeiffer, then in the autumn of 1928 he went to the Technische Hochschule in Danzig as assistant to Julius Sommer. While in Danzig he submitted his habilitation thesis *Affine Differentialgeometrie der Strahlensysteme* in 1929 and, following this, he became a privatdozent in Danzig. He applied for a position as an assistant to Rudolf Rothe at the Technische Hochschule Berlin-Charlottenburg and on 31 May 1934 Ernst Pohlhausen, who was a former rector of the Technische Hochschule in Danzig, wrote a letter of recommendation [1]:-

Now, of course, by this time the Nazis had come to power and any appointments had to be approved politically. The political report discussed Haack's character saying that [1]:-... mentioning Haack's many excellences as a teacher and reputed fine scholarship.

It also appended a report on his political views which must have made him only marginally acceptable to the Nazis [1]:-... in straitened economic circumstances for three years, Haack has nevertheless been a successful teacher and productive scholar. ... Haack has a clear-thinking critical mind, whose very frank judgment and unconditional maintenance of what he has once recognized as correct have caused him multiple difficulties. On the other hand, exactly these qualities, together with his amiable nature, have won him attention among his colleagues.

Having been approved, in 1935 Haack took up his new post in Berlin. He married the physicist Marianne Blumentritt, a student of Friedrich Hund, Georg Joos and Peter Debye, in 1936. Her doctoral thesis had been presented to Jena University and published inAlthough during the time of struggle of the National Socialist movement, Herr Haack had been uncomprehendingly opposed to it, it is to be assumed that his entering the motorized SA, to which he has belonged for a long time, accompanies an inner conversion.

*Annalen der Physik*in 1928. Haack did not spend long in Berlin for in 1937 he was appointed to a lectureship in Mathematics and Geometry at the Technische Hochschule of Karlsruhe. He was promoted to an extraordinary professor in 1938 and, two years later, to full professor.

Up to this time Haack had produced many excellent papers on geometry, in particular on differential geometry. For example his papers included *Affine Differentialgeometrie der Strahlensysteme* (1929), *Affine Differentialgeometrie der parabolischen Strahlensysteme* (1931) and *Eine geometrische Deutung der Affin-Invarianten einer Raumkurve* (1934). However, around 1936, he began to work on problems in gas dynamics and differential equations, collaborating with his wife on these topics. He explained in later writings and interviews that, seeing the approaching war and realising that differential geometry was "not very much tuned to war purposes", he changed areas. In a 1991 interview he explained that he was [7]:-

The "Aeronautical Proving Ground Hermann Göring" in Braunschweig put forward a project to determine the optimum shape of missiles which was a problem involving ballistics and fluid dynamics. As soon as war had broken out Haack phoned the head of research at Göring's aviation ministry offering his services. The work, which he carried out in collaboration with his wife, led to a paper he presented in 1941. Hoyrup writes [7]:-... afraid to be called to the army as an ordinary soldier, because he had been classified as a 'driver only' in examination.

Although his report was top secret in 1941, it was translated into English and published in 1948 under the titleParticular mathematical activities of very different kinds and theoretical levels(pure analysis, numerical algorithms, graphical methods)were involved. There was a gradual approach of two different engineering disciplines, ballistics and aerodynamics, that were about to recognise what they had in common mathematically. There was a pure mathematician(Haack)who made use of his special expertise(differential geometry)...

*Projectile shapes for smallest wave drag*. W R Sears writes in a review:-

Haack's work was effective for the war effort [7]:-Using von Kármán's approximate theory of slender bodies in supersonic flow, the author determines the optimum shapes of projectiles for prescribed(i)calibre and length,(ii)volume and length,(iii)volume and calibre. Only wave drag is considered. The method of calculation is first to attack the single variational problem of minimum drag for given calibre, length and volume, by standard methods.

Hoyrup makes a point about Haack's mathematics being put to a deadly use [7]:-... there is no doubt that the job[Haack]did was urgent and his results were really used to produce anti-aircraft projectiles. With undisguised pride Haack reported on the "success" of his theory of projectiles which allowed for a considerable extension of reach of German anti-aircraft artillery.

Reader must think about this point, and form their own opinion, not just as it relates to Haack, but also to hundreds of mathematicians whose advances have been used for destructive purposes.Not just in the background of this story but rather dominant is, of course, the peculiar political situation of the war. One sees the indifference of an allegedly apolitical mathematician to the destructive and deadly aspect of the military use of his science.

Returning to Haack's career, we note that in 1944, the Technische Hochschule of Berlin tried to persuade him to accept a chair but his war work prevented a move at this time. After the war ended, Georg Hamel was appointed to a chair of Mathematics and Mechanics at the Technische Hochschule of Berlin but, in 1949, Haack succeeded to Hamel's chair. From 1945 to 1949 he had been working as an advisor to the "British Research Branch" in Bad Gandersheim. He had also had roles as a visiting professor at ETH Zürich and at the University of Göttingen. As well as his chair at the Technische Hochschule of Berlin, from 1950 Haack had an honorary position at the Free University of Berlin. In 1964 Haack was named professor of numerical mathematics in a new Department of Computational Mathematics which had been founded thanks largely to his efforts. He held this position for four years until he retired and was made professor emeritus. In fact perhaps Haack's most important contribution at the Technische Hochschule of Berlin was his successful effort to introduce electronic computers [5]:-

Let us now look briefly at some of Haack's publications. In 1948 he published the two volume workWhen, after the war, he found out more about electronic computers, he was seized by their future importance for science, and he founded a working group for electronic computing devices in1950. During the years to come, Haack tried to have a computer installed at the TU Berlin and to this end contacted Konrad Zuse. The biggest handicap was finance, and Haack was turned down by the Deutsche Forschungsgemeinschaft(German Research Council)as this body considered it perfectly satisfactory for Germany's Universities that Göttingen, Darmstadt and Munich were actively working in the area of electronic computers. In response he managed to obtain donations from a number of companies, finally acquiring the funds needed so that the TU Berlin's first computer could begin work in1958, thanks above all to his work.

*Differential-Geometrie*. A Schwartz writes in a review:-

In 1955 he publishedThe style is concise and clear, and the explanations and derivations are almost always motivated by intuitive geometric considerations.

*Elementare Differentialgeometrie*which used some of the same chapters as his 1948 book but contains three new chapters. One year earlier, he had published

*Darstellende Geometrie. I. Die wichtigsten Darstellungsmethoden. Grund- und Aufriss ebenflächiger Körper*and, in the same year of 1954, the second volume

*Darstellende Geometrie. II. Körper mit krummen Begrenzungsflächen. Kotierte Projektionen*. The third, and final, volume

*Darstellende Geometrie. III. Axonometrie und Perspektive*was published in 1957. As well as these books on geometry, he also continued his work on gas dynamics; for example in 1958 he published the paper (published jointly with his doctoral student Gerhard Bruhn)

*Ein Charakteristikenverfahren für dreidimensionale instationäre Gasströmungen*in which he derived the characteristic equations for the unsteady three-dimensional motion of inviscid perfect gas.

At the Technische Hochschule of Berlin, Haach lectured on systems of two linear partial differential equations of first order in two independent variables, in particular, elliptic systems. His course was written up in collaboration with Wolfgang Wendland (one of Haack's doctoral students) in 1966 as *Systeme linearer partieller Differentialgleichungen* . Three years later the same two authors published the 550-page book *Vorlesungen über Partielle und Pfaffsche Differentialgleichungen* . Schechter writes in the review [8]:-

Finally, we note that Haack was honoured by being elected president of the German Mathematical Society (Deutsche Mathematiker-Vereinigung) in 1961-62.This book combines the study of partial and Pfaff differential equations. The point of view is to consider partial differential equations in the framework of Pfaff equations. ... The presentation is clear and detailed. Various examples help to motivate the material. ... The reader interested in this subject will benefit much from the book.

**Article by:** *J J O'Connor* and *E F Robertson*