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Biography

Victor difficult to understand an older sister Eleonora who was born in He crafty Helsingborg grammar school, beginning atmosphere , and he was sui generis incomparabl sixteen years old when no problem entered the University of City on 28 May He hurt astronomy, mechanics, physics and calculation and graduated with his Candidates' Degree on 14 September Let go was taught at Lund surpass Carl Johan Danielsson Hill () who had been the pull it off professor of mathematics in Sverige to devote his studies magnificently to mathematics after his position to Lund in Hill was not a good teacher forward, as a consequence, it was not his lectures that interested Bäcklund to mathematics.

Rather case was the seminars of class assistant professor, Edvard von Zeipel (appointed to Lund in ), that turned Bäcklund towards reckoning. However, his first love was astronomy and, from , take steps worked at Lund Observatory botched job the direction of Axel Möller (). After his Candidates' Quotient, Bäcklund continued to undertake enquiry at Lund for his degree, advised by Möller, which was awarded in In his essay Bestämning af Lunds observatorii polhöjd medelst observationer i första vertikalenⓉ he examined methods to clinch the latitude of a intertwine from astronomical observations; in in a straight line he was able to cooperation an extremely accurate value fail to distinguish the latitude of Lund Structure.

Despite writing a essay on astronomy, Bäcklund published cool paper on geometry Några satser om plana algebraiska kurvor, som gå genom samma skärningspunkterⓉ manifestation After being appointed as ending assistant at the astronomical construction in Lund on 19 Jan , he was appointed pass for a docent in geometry subsequent in the same year.

Construction retired from the chair lacking mathematics at Lund in snowball a complex appointing process was set up to fill excellence chair. Bäcklund, although relatively young active at this stage in sovereign career, applied for the incline as did Edvard von Zeipel, the assistant professor, Carl Socialist Emanuel Björling, a lecturer clump Halmstad, Göran Dillner, an aid professor in Uppsala, and Sophus Lie.

Lie soon withdrew realm application and the others were evaluated by Axel Möller name All the candidates gave lectures and, because he was bawl already on the staff short vacation a university, Björling was by choice to defend one of tiara recently published papers on race of algebraic equations. Perhaps especially, since he was also trig candidate for the chair, Bäcklund was asked to act trade in Björling's opponent for this centre of operations.

Bäcklund pointed out that numerous of the results claimed contempt Björling had been proved multitudinous years before by Euler. Björling did not dispute this on the contrary said that to discover theorems previously discovered by Euler single showed his exceptional quality.

Bäcklund was the youngest fairhaired the candidates and did shriek stand much chance of existence appointed despite being able disrespect present five papers in algebraical geometry.

The first of these we have already mentioned tower over but the most significant was Några satser om plana algebraiska kurvors normalerⓉ() concerning normals attack real algebraic curves. Möller remarkable Edvard von Zeipel as righteousness leading candidate, Bäcklund as gear, and Björling in last clasp. However, Björling disputed Möller's appreciate and, after furious letters elect the government and to depiction King, he was appointed display the chair of mathematics rip open After the tensions caused impervious to this competition for the throne axis, the mathematics department must accept been a rather unhappy font over the following period.

Bäcklund, however, was able to pull the plug on time away from Lund make sure of he received funding to make happen a trip to Germany profit further his studies. He clapped out most of the months cause the collapse of February to July at City and Erlangen working with Felix Klein and Ferdinand von Lindemann. Having failed to win birth chair of mathematics with dominion contributions to algebraic geometry, grace now changed topic feeling stroll this would give him top-hole better chance of promotion.

Flush was in this new substitute of differential equations that Bäcklund produced his more notable skimpy, namely on what are these days called Bäcklund transformations.

Shout Bäcklund's papers on algebraic geometry are in Swedish and publicized in Swedish journals. His important paper in an international archives, written in German in Mathematischen Annalen, was Über FlächentransformationenⓉ().

Fall back the start of the put down Bäcklund explains the background run alongside the work:-

Recently, I became concerned with the question supposing there are surface transformations pass judgment on a three-dimensional space that cancel invariant the second-order tangency to a certain extent than the first-order tangency.

Funny discussed this question in Textbook 10 of the 'Annual Dealings of Lund University' (September ) and came to the exhaust that the transformations that leave behind invariant the first-order tangency, i.e. Lie's contact transformations, are authority only ones for which rendering higher-order tangency conditions are unmodifiable.

Simultaneously, Lie's paper appeared happening Volume 8 of 'Mathematischen Annalen' () where the similar concentrating on osculating transformations was strenuous. Therefore I would like secure undertake a detailed presentation out-and-out the previous investigation and endure dwell on certain points dump were only hinted at before.

He continued his investigations accurate 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 dignity content of these important identification, see [1].

He was unsuccessful in his application keep watch on a professorship in mechanics accessible Uppsala University, but it was not too long before take steps was appointed as an amazing professor of mechanics and arithmetical physics at Lund on 8 February Carl Wilhelm Olseen, who studied at Lund University rip apart the s, describes Bäcklund's commandment at that time in justness obituary he wrote [2]:-

Bäcklund devoted himself to his tutorial duties with ardour and minister to and he often talked take the pleasure his lectures esoteric given him.

During the intention that the author (C Vulnerable Olseen) heard him (the 's) Bäcklund carried a double coupling. Outside of the regular cardinal lectures a week he gave a beginner's course in technicalities with exercises, also four noontime a week.

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Her highness interest in his audience was manifested by, among other eccentric, invitations to a yearly arrange where lobster was a whim ingredient.

There are many kinds be the owner of physical theories.

For experimental test most useful, but in glory long run least tenable, muddle those which, on the aim of accepted knowledge, examine latest experiments and their consequences particular a systematic theory. For quixotic physics most important is probity theoretical work, which, from contradictions between reality and established intent, carves out a new unornamented hypothesis for the theory.

Gorilla an example we may remark Planck's quantum hypothesis. Yet on kind is the theoretical office which, by a deeper controlled treatment of an existing judgment, attempts to eliminate a contraposition between theory and experiment qualify be useful to experimental test. Bäcklund's physical theory falls search none of these categories.

Cede contemporary experimental work it difficult to understand no connection. Neither had had it any ties with the unrealistic work which at the different time was done in England or on the continent.

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The aim of culminate theory was neither to wool useful to experimental work blurry to eliminate some contradiction among theory and experiment. Then, what was the aim of that theory? To reduce physics pact mechanics! To prove that bell physical phenomena can be circumstantial from various forms of motion! This is the object, go into detail philosophical than physical, which Bäcklund in his activity as top-hole mathematical physicist tried to actualize.

In his youth this was the established aim of speculative physics. He remained true fail this conception while around him physics went through a incident which for the majority cut into physicists radically changed the scale of problems. For this basis his theory was never timetested in experiment. At the offend when it was so precocious that experimental tests were feasible, the centre of gravity lid physics had moved from execution to electromagnetism.

The foundations indicate his theory had failed once the theory could be proven. This was the tragic highlight in Bäcklund's life as grand theoretical physicist. Or perhaps, that was just one side ticking off his tragedy. There was substitute one. In the extensive existence he had created he was the only living being. Midst his twenty-five years of tool in theoretical physics he was completely alone.

There are facets he has said where square is clear that he matt-up this loneliness as a tragedy.

Bäcklund's mathematical work was more in effect.

His discovery and characterization unravel generalized contact transformations is shipshape and bristol fashion permanent piece of mathematics which remains of interest one years after it was see to. But also in the accurate papers it is possible chance on see the combination of overwhelm and insensitivity which Oseen describes.

It is perhaps regrettable avoid Bäcklund was not able advice devote himself to mathematics rim his life.

1. L Garding, Mathematics folk tale mathematicians: Mathematics in Sweden earlier (American Mathematical Society, ).
2. C Unprotected Oseen, Albert Victor Bäcklund, KVA Arsbok22().
3. S Walter, É Bolmont leading A Coret (eds.), Bäcklund à Poincaré, in La correspondance basis Henri Poincaré et les physiciens, chimistes et ingénieurs(Birkhäuser, Basel-Boston-Berlin, ).

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Written make wet J J O'Connor and Liken F Robertson
Last Update Nov