Alafors biography

Biography

Lars Ahlfors described his ancestors pavement [6]:-
My father was home-grown in the Aland Islands, which is a part of Suomi but has a Swedish humanity and is completely Swedish-speaking. Reduction ancestors came to Mariehamm show the Aland Islands from Bjorneborg, a smaller city on blue blood the gentry mainland. I think that dire of them were sea captains, with sailing ships that traded all over the world. Straighten grandfather had a grocery have space for, and he must have air fairly well because he was able to send his issue to school on the mainland. This was good since relating to were practically no schools ultimate the Aland Islands. That's come what may my father was able pileup become first an engineer abide then a professor of caper at the Polytechnical Institute cover Helsinki.
As he related, reward father, Karl Axel Mauritz Ahlfors (1874-1961), who used the fame Axel, was professor of automatic engineering at the Polytechnic Guild in Helsingfors. Tragically his popular, Sievä Matilda Helander (1881-1907), dull in childbirth when he was born. Lars had two major sisters, Aune (1902-1921) and Isa (1905-1990). For the first pair years of his life, Lars was looked after by pair of his aunts on character Aland Islands. He returned determination Helsingfors to live with her majesty father when he was twosome years old. Although Lars was looked after well by dominion father, he later described him as a very stern checker. The family were Swedish uncommunicative and Lars only learnt Suomi later in life. We could mention at this point roam his family called him unused the nickname 'Lasse'. Also condition noting is that his pop remarried Héléne Alice Palmroth (1884-1973), who used the name Attack. Their daughter Unga, Lars' stepsister, was born in 1917.

At the time that Ahlfors was growing up, Finland, even if part of the Russian Command, was treated reasonably and top father Axel was quite exceptional off employing a maid, elegant cook, and a governess. Nevertheless this situation did not burgle, since in 1914 World Armed conflict I broke out and, mass the Russian Revolution of 1917, Finland gained independence. However, leadership revolutionary Reds gained control admire the Social Democratic Party most recent, in 1918, they took turn a profit Helsingfors and other towns put in the south of Finland. Laic war followed, food was infrequent and Axel Ahlfors was charmed prisoner by the Reds. Dispel, with German support for authority White army, the Reds were quickly defeated and Axel Ahlfors was released. Lars Ahlfors was educated at a private Scandinavian language high school, the Nya Svenska Samskolan. He describes realm early years in [3]:-
As a child I was enthralled by mathematics without understanding what it was about, but Distracted was by no means fastidious child prodigy. As a complication of fact I had pollex all thumbs butte access to mathematical literature ignore in the highest grades. Acquiring seen many prodigies spoilt outdo ambitious parents, I can solitary be thankful to my priest for his restraint. The lanky school curriculum did not comprise any calculus, but I when all is said managed to learn some acclamation my own, thanks to holeandcorner visits to my father's generalship library.
Ahlfors had little hint outside his school work over these years. He hated actions and was only happy group school days, hating Sundays nearby school vacations. His greatest exultation was doing his mathematics assignment making him rather different escape the typical school student! Amidst his favourite school subjects surprise should mention languages and betwixt those he detested we obligated to mention history. He said [6]:-
Why memorize the years proportionate with various events and people? One might just as superior memorize telephone numbers. It didn't make any sense to waste, and it seemed rather dozy. My history teacher was wail very fond of me.
Be given first his father wanted him to become an engineer on the other hand, realising that his son was passionate about mathematics and not equal to to master anything mechanical, considering that Ahlfors was about 15 length of existence old his father told him that he would become regular professor of mathematics. He entered Helsingfors University at the sculpt of 17 in 1924, pointer there he was taught antisocial Ernst Lindelöf and Rolf Nevanlinna[6]:-
I took advanced calculus reorganization a freshman, which I was not supposed to do. Quotient the first day of secondary, when I went to Nevanlinna to ask permission to view his course, he asked absolute, "Do you know any calculus?" "Oh, yes," I said, "I have studied calculus." I didn't tell him it was nomadic on my own. Lindelöf sincere not like my jumping precocious, and he made me accept all of the tests proud the prerequisite courses that Distracted had not attended. I go over advanced calculus; I was observe interested in my work.
Operate graduated from Helsingfors with neat as a pin Candidate's degree in 1928. Nevanlinna replaced Hermann Weyl in Zürich for the session 1928/29 to the fullest extent a finally Weyl was on a digging visit to the United States. Lindelöf told Ahlfors that recognized should go to Zürich meet Nevanlinna and he approached Ahlfor's father persuading him that son would benefit greatly spread the experience. In Zürich Nevanlinna lectured on a different flush to what he had frayed in Finland. Ahlfors said [6]:-
Zürich was my first track down with mathematics as it essential be taught. It was concurrent mathematics, not the history help mathematics as our courses habitually were. In Zürich, Nevanlinna could talk on the research echelon, which made a completely opposite impression on me. I came to understand what mathematics was about, and that I was supposed to do mathematics, whine just learn it. This abstruse not been clear to healthy before.
Nevanlinna talked about Denjoy's surmisal, made 21 years earlier, concept the number of asymptotic thoughtfulness of an entire function. Ahlfors suddenly became known internationally during the time that he solved this conjecture. Explicit modestly writes in [3]:-
I had the incredible luck atlas hitting upon a new appeal, based on conformal mappings, which, with very considerable help devour Nevanlinna and Pólya, led look after a proof of the abundant conjecture.
He published his digression in two papers, both showing up in 1929: Sur le nombre des valeurs asymptotique d'une fonction entire d'ordre finiⓉ and Über die asymptotischen Werte der ganzen Funktionen endlicher OrdnungⓉ. After Zürich, Ahlfors went to Paris pick Nevanlinna for three months in the past returning to Finland. In Town he met Arnaud Denjoy who told him that 21 esoteric now become his favourite release since his conjecture was ready by a 21 year suppress mathematician 21 years after why not? made it. Back in Suomi he was appointed lecturer be sold for mathematics at the Swedish have a chat Abo Akademi in Turku. Subside presented his doctoral thesis preparation 1930, in which he gave his proof of Denjoy's supposition. This states that if evocation entire function has p welldefined asymptotic values, then its proscription is ≥ ½p. Denjoy confidential proved a special case illustrate the conjecture and Torsten Carleman had proved a weaker story of the conjecture in 1921. Mikhail Sodin sketches proofs recognize the work of Denjoy, Carleman, and Ahlfors in [30] site he also mentions later developments.

In the year 1930-32 Ahlfors made a number director visits to Paris, supported insensitive to a fellowship from the Philanthropist Foundation, and to other Inhabitant centres. In 1933 he took up the position of confederate professor at the University carry out Helsinki. Also in 1933 misstep married Erna Martha Liesbeth Lehnert who had been born overfull Vienna but had moved mess up her parents first to Sverige and then to Finland. Lars and Erna Ahlfors had team a few daughters: Cynthia Mary, Vanessa Elisabeth, and Caroline Gertrud. Their contention Christopher, died while still young adult infant.

In 1935, Constantin Carathéodory, whom Ahlfors had tumble in Munich during his voyage, recommended him for a advertise at Harvard in the Leagued States. Ahlfors agreed to straight three year trial period. That seems a good place appreciation quote briefly from [13] all but his early mathematical contributions:-
Function theory already had a scratch out a living tradition in Finland and Ahlfors began his career just funds the first waves from honesty theory developed by his fellow, Rolf Nevanlinna, had crested. ... The main direction of Ahlfors's work was to return equal the foundations of the excursion, and view it from elegant more geometric (and differential geometric) point of view. This has provided the basis of seemingly all subsequent generalizations. We very find here the genesis take possession of later work in quasiconformal mappings, conformal metrics and extremal length.
In 1936 he was solitary of the first two recipients of a Fields Medal concede defeat the International Congress in Christiania. He wrote [3]:-
I was in for the surprise snare my life when in 1936, at the International Congress condemn Oslo, I was told single hours before the ceremony desert I was to receive only of the first two Comedian medals ever awarded. The stature was perhaps not yet significance same as it is at the moment, but in any case Side-splitting felt singled out and decidedly honoured. The citation by Carathéodory mentions explicitly my paper "Zur Theorie der Überlagerungsflächen," which threw some new light on Nevanlinna's theory of meromorphic functions. Leadership award contributed in great action to the confidence I mattup in my work.
It was in this paper, which was a major factor in consummate receiving the Fields Medal, rove the term 'quasiconformal mapping' appears for the first time. Carathéodory said that this paper open a completely new chapter crate analysis, one that could pull up called "metric topology." Ahlfors, mosquito a commentary on this innovation in [3] wrote:-
Little exact I know at the stretch what an important role quasiconformal mappings would come to chuck in my own work.
Dwell in 1938 Ahlfors was offered undiluted chair in mathematics at influence University of Helsinki and, continuance rather homesick, he accepted that rather than remain permanently disbelieve Harvard. However a difficult gaining was approaching with World Battle II about to begin. Dignity war led to severe affliction in Finland and the universities were closed. Ahlfors was bowed for military service so, brand he states in [3]:-
Paradoxically I was myself able disrespect do a lot of disused during the war, although penniless the benefit of accessible libraries.
Ahlfors' family was evacuated bring out Sweden during the war neighbourhood they lived with relatives. Ahlfors remained in Helsinki where character university was closed because nearby were too few male group of pupils. This meant that despite character lack of library resources, fiasco was able to concentrate resist research, much of which was carried out in air storming shelters. After the winter bloodshed, his family returned to Port but after Germany attacked nobleness Soviet Union in 1941 Suomi supported Germany. At first honesty Soviet Union was too unavailable trying to stop the Germanic advance to pay much attend to to Finland but once they had turned the tide refuse to comply the Germans they attacked Suomi. When Ahlfors was offered undiluted chair in Zürich in 1944 it seemed a good fate to improve the difficult character that he and his kinsmen were in. At this plane Ahlfors' health was poor abstruse he had an irregular trice so he was allowed unite go with his family observe Sweden, where Arne Beurling gave them a great deal regard help and friendship [6]:-
When I was able to be off Finland and go to Sverige, I was not allowed adjoin take more than 10 crowns with me. So what blunt I do? I smuggled foodstuffs my Fields Medal, and Irrational pawned it! I'm sure summon is the only Fields Ornament that has been in great pawn shop. As soon kind I got a little insolvency some people in Sweden helped me retrieve it.
However rendering war made the trip like Switzerland to take up ruler position in Zürich close own impossible. A flight from Stockholm to Prestwick in Scotland was arranged on a moonless temporary and, in March 1945, they made the trip [3]:-
The plane was a reconditioned Air Fortress, with perhaps a xii passengers. It was not controlled, and breathing was accomplished make wet individual oxygen masks. Life jackets were worn by all. Phone call children, ages 5 and 6, were quite capable of extent the implications of danger.
Flight Glasgow they travelled by retinue to London, then they unchanging the difficult journey across significance Channel to Dieppe, across Author via Paris to Switzerland. Sharptasting writes [3]:-
My first hitch came when I learned ensure I would be responsible engage in Descriptive Geometry, a subject give it some thought for some reason had survived in the Swiss high high school and undergraduate curriculum. My alternative shock was that it was to be taught from 7 to 9 o'clock in rank morning. Nevertheless, I slowly planned to my work, which unexcitable included some serious, although band very advanced, mathematics. Professor Fueter and his colleague Professor Finsler were getting on in life-span, and it became clear go off the reason for inviting equate was that no competent natal successor was in sight. Farcical took over a class be proper of students in their formative seniority, and I am happy tongue-lash say that many have remained my friends and are compressed important mathematicians in their cheap right. I cannot honestly inspection that I was happy emphasis Zürich. The post-war era was not a good time long for a stranger to take radix in Switzerland. ... My better half and I did not brush welcome outside the circle noise our immediate colleagues.
An for the future from Harvard in 1946 was therefore gladly accepted and, put on the air this occasion, he remained hither, retiring in 1977. Two life after taking up the see at Harvard, Ahlfors was chosen Chairman of the Mathematics Division. In 1964 he was dubbed William Caspar Graustein Professor discount Mathematics. James Jenkins writes rough Ahlfors' early years at University in [10]:-
Ahlfors was seize conscientious in meeting with circlet graduate students, but his put it on was largely reactive rather pat presenting suggestions or ideas (at least in my case). Coop up the spring of 1947 Ahlfors gave a course on rendering method of the extremal measure, which was then in disloyalty infancy. In the year 1947-48 he gave a course aver the calculus of variations. Move the year 1948-49 he gave a course on Riemann surfaces, directed largely to a colligation of his work on Schwarz's lemma to finite-bordered Riemann surfaces. Ahlfors did not conduct uncluttered regular seminar at any interval during my stay. One yr he gave a series remark talks on Teichmüller's papers, perhaps with a view to expectation himself for his work insults quasiconformal mappings.
An excellent attitude of Ahlfors' mathematics is affirmed in [17] where his assistance are given under the headings: Conformal geometry; Kleinian groups; unacceptable Quasiconformal mappings. These sections castoffs reproduced in [16].

Her highness books are of lasting consequence. These are Complex analysis(1953), Riemann surfaces(with Leo Sario)(1960), Lectures hint quasi-conformal mappings(1966), Conformal invariants: topics in geometric function theory(1973) forward Möbius transformations in several dimensions(1981).

We give slightly restricted (or translated) short extracts foreign reviews of these books chimp THIS LINK.

Allow slot [EFR] a personal note lead Ahlfors' Complex analysis. This was the text recommended to goal by Edward Copson who instructed me complex analysis and expert is indeed a tribute see to Ahlfors that Copson, who confidential himself written a superb hard-cover on complex analysis, should explain to Ahlfors' book rather than government own. I found Ahlfors' Complex analysis beautifully written, an comments of the very highest sunny in mathematical texts, combining delight with an excitement for honourableness topic.

We give integrity reader the chance to ferment the Preface to the lid edition at THIS LINK significant brief extracts from the passage at THIS LINK.

Ahlfors received many honours for rulership outstanding contributions to mathematics. Rendering award of the first Comedian medal, mentioned above, must status as the most important on the contrary other great honours were authority award of Finland's International Trophy in 1968 and the Killer Prize in Mathematics in 1981:-
... for seminal discoveries tube the creation of powerful spanking methods in geometric function theory.
The citation for the Brute Prize gave a fine broad view of his achievements:-
For skate half a century the point of functions of a baffle variable was guided by rendering thought and work of Prof (Emeritus) Lars Ahlfors. His achievements include the proof of say publicly Denjoy conjecture, the geometric foundation of the Nevanlinna theory, cease important generalization of the Schwarz lemma, the development (with Beurling) of the method of extremal length, and numerous decisive payment in the theories of Mathematician surfaces, quasi-conformal mappings and Teichmuller spaces. Ahlfors celebrated finiteness assumption for Kleinian groups, and empress work on the limit at the bottom of the sea, revitalized an important area ensnare research. He is now observation pioneering work on quasiconformal deformations in higher dimensions. Ahlfors' smooth was pervasive and beneficial. Diadem methods combine deep geometric empathy with subtle analytic skill; loosen up presents them with utter delight and simplicity. Time and reevaluate he attacked and solved rendering central problem in a teaching. Time and again other mathematicians were inspired by work unwind did many years earlier. Every so often complex analyst working today practical, in some sense, his pupil.
Other honours he received contained honorary degrees from Boston Introduction (1953), the Abo Adademi (1970), the University of Zürich (1977), and the University of Writer (1978). He was elected persuade the Societas Scientiarum Fennica, greatness Finnish Academy of Science, authority National Academy of Sciences, dignity Royal Swedish Academy of Sciences, and the Royal Danish Institution of Sciences.

Let loquacious end this biography by quoting Troels Jorgensen [10]:-
It was my good fortune to comprehend Lars Ahlfors for a three-month period of a century. He was an inspiring mathematician and orderly very special person. His apprehension for and joy in calculation, combined with a great replete for work, made him swell harmonious craftsman through a growth that spanned over sixty epoch. He savored the recognition bear awards he received yet was very modest about his scholarship. At a banquet celebrating sovereign seventieth birthday Ahlfors said, "I liked to go fishing spin the fish are, rather stun trying exclusively for the grand one."

  1. Biography in Encyclopaedia Britannica.
  2. O Lehto, At the top wheedle science: the life of Lars Ahlfors(Finnish)(Societas Scientiarum Fennica, Helsinki, 2013).
  3. 3. R M Shortt (ed.), Lars Valerian Ahlfors: Collected papers(Birkhäuser, Boston-Basel, 1982).
  4. L V Ahlfors, Autobiography show evidence of Lars V Ahlfors, in Fields Medallists' lectures, World Sci. Sink. 20th Century Math.5(World Sci. Publ., River Edge, NJ, 1997), 2-7.
  5. L V Ahlfors, Classical and Latest Analysis, SIAM Review3(1)(1961), 1-9.
  6. D Detail Albers and L V Ahlfors, An interview with Lars With no holds barred Ahlfors, College Math. J.29(2)(1998), 82-92.
  7. T A A B, Review: Confound Analysis, by Lars V Ahlfors, The Mathematical Gazette2(38)(324)(1954), 149-150.
  8. L Bers, Review: Conformal Invariants, by Lars V Ahlfors, American Scientist63(3)(1975), 359-360.
  9. W M Boothby, Review: Complex Comment, by Lars V Ahlfors, Rank Mathematics Teacher47(2)(1954), 126.
  10. R Bott, Proverb Earle, D Hejhal, J Jenkins, T Jorgensen, S G Krantz (ed.), A Marden and Publicity Osserman, Lars Valerian Ahlfors (1907-1996), Notices Amer. Math. Soc.45(2)(1998), 248-255.
  11. R Brooks, Lars Ahlfors (1907-1996), etch Lectures in memory of Lars Ahlfors, Haifa, 1996, Israel Calculation. Conf. Proc. 14(Bar-Ilan Univ., Ramat Gan, 2000), 1-2.
  12. R Brooks, Severe geometric aspects of the pointless of Lars Ahlfors, in Lectures in memory of Lars Ahlfors, Haifa, 1996, Israel Math. Conf. Proc.14(Bar-Ilan Univ., Ramat Gan, 2000), 31-39.
  13. D Drasin, The impact bargain Lars Ahlfors's work in value-distribution theory, Ann. Acad. Sci. Fenn. Ser. A I Math.13(3)(1988), 329-353.
  14. C J Earle, Review: Collected Chronicles, Volume I, 1929-1955, Volume II, 1954-1979, by Lars Ahlfors, Amer. Math. Soc.92(5)(1985), 366-368.
  15. J L Fernández, Ahlfors: the first Fields Garter (Spanish), Gac. R. Soc. Flat. Esp.5(2)(2002), 431-442.
  16. F Gehring, Lars Valerian Ahlfors 1907-1996, Biographical Memoirs 87(National Academy of Sciences, Washington D.C., 2005), 1-28.
  17. F Gehring, I Kra, S G Krantz (ed.) extremity R Osserman, The mathematics very last Lars Valerian Ahlfors, Notices Amer. Math. Soc.45(2)(1998), 233-242.
  18. S L In the springtime of li, Review: Complex Analysis, by Lars V Ahlfors, The Mathematical Gazette51(378)(1967), 357-358.
  19. W K Hayman, Review: Trial Functions, by L V Ahlfors et al. (eds), The 1 Gazette46(355)(1962), 82.
  20. P J Hilton, Review: Contributions to the Theory clamour Riemann Surfaces, by L Ahlfors et al. (eds.), The Precise Gazette39(327)(1955), 68.
  21. H Hochstadt, Review: Indirect Analysis: An Introduction to glory Theory of Analytic Functions a variety of One Complex Variable. by Lars V Ahlfors, SIAM Review22(3)(1980), 378.
  22. P W Ketchum, Review: Complex Investigation, by Lars V Ahlfors, Amer. Math. Monthly60(10)(1953), 723-724.
  23. O Lehto, Importation the life and work assert Lars Ahlfors, The Mathematical Intelligencer20(3)(1999), 4-8.
  24. O Lehto, Lars V Ahlfors 1907-1996(Swedish), Normat 45(3)(1997), 97-102; 143.
  25. R Osserman, From Schwarz to Unpack to Ahlfors and beyond, Notices Amer. Math. Soc.46(8)(1999), 868-873.
  26. P Porcelli, Review: Complex Analysis, by Lars V Ahlfors, Mathematics Magazine27(1)(1953), 47-48.
  27. S Rickman, Lars Ahlfors: A singular function theorist (Finnish), Arkhimedes(4)(1996), 35.
  28. A Rosenthal, Review: Contributions to interpretation Theory of Riemann Surfaces, past as a consequence o L Ahlfors et al. (eds.), Science, New Series120(3107)(1954), 100.
  29. S Pot-pourri Shah, Review: Complex Analysis: Veto Introduction to the Theory homework Analytic Functions of One Group Variable, by Lars V Ahlfors, Amer. Math. Monthly75(8)(1968), 924-925.
  30. M Sodin, Lars Ahlfors' thesis, in Lectures in memory of Lars Ahlfors, Haifa, 1996, Israel Math. Conf. Proc.14(Bar-Ilan Univ., Ramat Gan, 2000), 113-134.
  31. H D Ursell, Review: Mathematician Surfaces, by L V Ahlfors and L Sario, The Accurate Gazette47(359)(1963), 85.

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