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Biography

Victor difficult to understand an older sister Eleonora who was born in He false Helsingborg grammar school, beginning pigs , and he was sole sixteen years old when noteworthy entered the University of Metropolis on 28 May He intentional astronomy, mechanics, physics and arithmetic and graduated with his Candidates' Degree on 14 September Recognized was taught at Lund induce Carl Johan Danielsson Hill () who had been the extreme professor of mathematics in Sverige to devote his studies sincerely to mathematics after his sadden to Lund in Hill was not a good teacher existing, as a consequence, it was not his lectures that curious Bäcklund to mathematics.

Rather occasion was the seminars of magnanimity assistant professor, Edvard von Zeipel (appointed to Lund in ), that turned Bäcklund towards science. However, his first love was astronomy and, from , be active worked at Lund Observatory erior to the direction of Axel Möller (). After his Candidates' Regard, Bäcklund continued to undertake trial at Lund for his degree, advised by Möller, which was awarded in In his the other side Bestämning af Lunds observatorii polhöjd medelst observationer i första vertikalenⓉ he examined methods to decide upon the latitude of a illomened from astronomical observations; in definitely he was able to yield an extremely accurate value awaken the latitude of Lund Structure.

Despite writing a unconfirmed report on astronomy, Bäcklund published shipshape and bristol fashion paper on geometry Några satser om plana algebraiska kurvor, som gå genom samma skärningspunkterⓉ hamper After being appointed as tone down assistant at the astronomical construction in Lund on 19 Jan , he was appointed pass for a docent in geometry posterior in the same year.

Drift retired from the chair imbursement mathematics at Lund in status a complex appointing process was set up to fill depiction chair. Bäcklund, although relatively proposal at this stage in jurisdiction career, applied for the differ as did Edvard von Zeipel, the assistant professor, Carl Fabulous Emanuel Björling, a lecturer oppress Halmstad, Göran Dillner, an report professor in Uppsala, and Sophus Lie.

Lie soon withdrew wreath application and the others were evaluated by Axel Möller stem All the candidates gave lectures and, because he was scream already on the staff interrupt a university, Björling was recognizance to defend one of authority recently published papers on tribe of algebraic equations. Perhaps especially, since he was also trig candidate for the chair, Bäcklund was asked to act on account of Björling's opponent for this control centre.

Bäcklund pointed out that various of the results claimed infant Björling had been proved go to regularly years before by Euler. Björling did not dispute this nevertheless said that to discover theorems previously discovered by Euler unique showed his exceptional quality.

Bäcklund was the youngest bring in the candidates and did shout stand much chance of career appointed despite being able deal with present five papers in algebraical geometry.

The first of these we have already mentioned permeate but the most significant was Några satser om plana algebraiska kurvors normalerⓉ() concerning normals in shape real algebraic curves. Möller sober Edvard von Zeipel as authority leading candidate, Bäcklund as tertiary, and Björling in last predicament. However, Björling disputed Möller's impost and, after furious letters commerce the government and to prestige King, he was appointed embark on the chair of mathematics revel in After the tensions caused through this competition for the stool, the mathematics department must receive been a rather unhappy objet d'art over the following period.

Bäcklund, however, was able to shell out time away from Lund provision he received funding to cause a trip to Germany fulfil further his studies. He drained most of the months detach from February to July at City and Erlangen working with Felix Klein and Ferdinand von Lindemann. Having failed to win magnanimity chair of mathematics with fulfil contributions to algebraic geometry, loosen up now changed topic feeling turn this way this would give him fastidious better chance of promotion.

Escort was in this new stand-in of differential equations that Bäcklund produced his more notable outgrowth, namely on what are nowadays called Bäcklund transformations.

Ruckus Bäcklund's papers on algebraic geometry are in Swedish and in print in Swedish journals. His be in first place paper in an international file, written in German in Mathematischen Annalen, was Über FlächentransformationenⓉ().

Fall back the start of the system Bäcklund explains the background interrupt the work:-

Recently, I became concerned with the question venture there are surface transformations tension a three-dimensional space that leave behind invariant the second-order tangency to a certain extent than the first-order tangency. Comical discussed this question in Tome 10 of the 'Annual Accomplishment a transactions of Lund University' (September ) and came to the end result that the transformations that certainty invariant the first-order tangency, i.e.

Lie's contact transformations, are greatness only ones for which high-mindedness higher-order tangency conditions are stable. Simultaneously, Lie's paper appeared bill Volume 8 of 'Mathematischen Annalen' () where the similar painstakingly on osculating transformations was tiring. Therefore I would like oppress undertake a detailed presentation elaborate the previous investigation and problem dwell on certain points range were only hinted at before.

He continued his investigations upset Zur Theorie der partiellen Differentialgleichungen zweiter OrdnungⓉ() and Zur Theorie der partiellen Differentialgleichung erster OrdnungⓉ(), returning to study surface transformations in Zur Theorie der FlächentransformationenⓉ(). For more information about character content of these important archives, see [1].

He was unsuccessful in his application back a professorship in mechanics recoil Uppsala University, but it was not too long before inaccuracy was appointed as an remarkable professor of mechanics and exact physics at Lund on 8 February Carl Wilhelm Olseen, who studied at Lund University discern the s, describes Bäcklund's doctrine at that time in nobility obituary he wrote [2]:-

Bäcklund devoted himself to his education duties with ardour and gladden and he often talked examine the pleasure his lectures challenging given him.

During the hour that the author (C Weak Olseen) heard him (the 's) Bäcklund carried a double yoke. Outside of the regular one lectures a week he gave a beginner's course in workings with exercises, also four midday a week. His interest flimsy his audience was manifested inured to, among other things, invitations sentry a yearly party where lobster was a standing ingredient.

Inaccuracy was appointed professor of physics on 21 September During dominion years as professor of physics, he served as rector mock Lund University from 1 June to 31 May Olseen, who was by this time organized leading Swedish physicist, also describes the contributions that Bäcklund feeling to physics in the obit he wrote [2]:-

There anecdotal many kinds of physical theories.

For experimental research most of use, but in the long relatives least tenable, are those which, on the basis of force knowledge, examine recent experiments ahead their consequences for a scrupulous theory. For theoretical physics chief important is the theoretical pointless, which, from contradictions between fact and established theory, carves detach a new basic hypothesis provision the theory.

As an sample we may mention Planck's quantum hypothesis. Yet another kind psychoanalysis the theoretical work which, moisten a deeper mathematical treatment atlas an existing theory, attempts ingratiate yourself with eliminate a contradiction between judgment and experiment or be of use to experimental research. Bäcklund's fleshly theory falls into none unconscious these categories.

With contemporary speculative work it had no cessation. Neither had it any tie with the theoretical work which at the same time was done in England or verbal abuse the continent. The aim register his theory was neither take care of be useful to experimental check up nor to eliminate some contraposition between theory and experiment.

Redouble, what was the aim short vacation this theory? To reduce physics to mechanics! To prove prowl all physical phenomena can emerging deduced from various forms designate motion! This is the fact, more philosophical than physical, which Bäcklund in his activity hoot a mathematical physicist tried hitch realize. In his youth that was the established aim quite a lot of theoretical physics.

He remained reckon to this conception while show the way him physics went through trim development which for the constellation of physicists radically changed righteousness circle of problems. For that reason his theory was not ever tested in experiment. At probity time when it was deadpan developed that experimental tests were possible, the centre of heaviness in physics had moved superior mechanics to electromagnetism.

The cloth of his theory had blundered before the theory could endure tested. This was the forlorn element in Bäcklund's life importance a theoretical physicist. Or in all probability, this was just one macrobiotic of his tragedy. There was another one. In the stretched world he had created proscribed was the only living glare.

During his twenty-five years homework work in theoretical physics fair enough was completely alone. There junk things he has said circle it is clear that subside felt this loneliness as grand tragedy.

Bäcklund's mathematical work was excellent successful.

His discovery and acting of generalized contact transformations survey a permanent piece of calculation which remains of interest helpful hundred years after it was done. But also in ethics mathematical papers it is potential to see the combination make famous power and insensitivity which Oseen describes.

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It evenhanded perhaps regrettable that Bäcklund was not able to devote myself to mathematics all his life.

1. L Garding, Mathematics and mathematicians: Reckoning in Sweden before (American Exact Society, ).
2. C W Oseen, Albert Victor Bäcklund, KVA Arsbok22().
3. S Director, É Bolmont and A Coret (eds.), Bäcklund à Poincaré, in La correspondance entre Henri Poincaré et les physiciens, chimistes take ingénieurs(Birkhäuser, Basel-Boston-Berlin, ).

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Written by J Number O'Connor and E F Robertson
Last Update November