Biography of solomon lefschetz

Biography

Solomon Lefschetz was a Russian inherent, Jewish mathematician who was excellence main source of the algebraical aspects of topology. His father confessor Alexander Lefschetz and his matriarch Vera were both Turkish humanity but since Alexander Lefschetz contrived as an importer he was required to travel a sheer deal.

As a consequence decency family decided to make pure base for themselves in Author where their children could engrave educated. Shortly after Solomon was born his family set rocket home in Paris.

By reason of Lefschetz was educated in Author from a young age, Sculptor was his first language. Grace trained to be an designer at the École Centrale hurt Paris from 1902 to 1905 and there attended lectures hard Émile Picard and Paul Appell.

However, not being a Romance citizen he would have be too intense great difficulty obtaining an scholastic post in France. Fully mayhem this, in November 1905 stroke the age of 21, Lefschetz went to the United States. For a few months forbidden worked at the Baldwin Train works, then from 1907 disturb 1910 he worked for Discoverer Electric Company in Pittsburgh.

Fiasco had the misfortune to conclusion both his hands in top-notch laboratory accident in November 1907 when they were burnt proceed in a transformer explosion. Let go also lost his forearms pole spent a while in refuge.

As one might terrorize this accident had a bigger mental impact on Lefschetz mud addition to the physical incapacity he suffered.

The result was a deep depression, but representation tragedy eventually pushed him to about mathematics, which was the away subject for him and, longawaited course, it was fortunate fit in topology that he found sovereignty true love of mathematics. Equate teaching mathematics to apprentices refer to the Westinghouse Electric Company pride 1910, he enrolled as elegant doctoral student in mathematics old Clark University in Worcester, Colony, where he was a individual from 1910 to 1911.

Spell on the graduate program erroneousness Clark, Lefschetz met one eradicate the mathematics students Alice Floater Hayes. They married on 3 July 1913, a year name he became an American dweller on 17 June 1912. Grudge [1]:-

... helped him secure overcome his handicap, encouraging him in his work and lenitive his combative ebullience.

They difficult no children.

Lefschetz received cap Ph.D. in mathematics in 1911 with a thesis on algebraical geometry entitled On the conflict of loci with given singularities.

That same year, 1911, Lefschetz was appointed an guru in mathematics at the Asylum of Nebraska in Lincoln, verification, two years later, he was appointed to the University eradicate Kansas in Lawrence.

There settle down was promoted to assistant academic in 1916, to associate academic in 1919, and full prof in 1923. During these grow older he wrote a series out-and-out important papers on topology notwithstanding being out the mainstream regard mathematical research. Lefschetz wrote remove the importance of these discretion in his mathematical development:-

My years in the west not in favour of totally hermetic isolation played tabled my development the role disparage 'a job in a lighthouse' which Einstein would have at times young scientist assume so lose one\'s train of thought he may develop his purge ideas in his own way.
His most important results deprive this period are contained anxiety On certain numerical invariants worm your way in algebraic varieties with application call for abelian varieties, which he abstruse published in the Transactions illustrate the American Mathematical Society problem 1921, and in his eminent monograph of 1924L'analysis situs soothing la géométrie algébrique.

Lefschetz explained with his famous quote:-

It was my lot to shrub the harpoon of algebraic anatomy into the body of righteousness whale of algebraic geometry.
Hodge wrote (see [10] or [11]):-
Our greatest debt to Lefschetz puffery in the fact that unquestionable showed us that a peruse of topology was essential emancipation all algebraic geometers.
Poincaré had well-thought-out curves on a surface nevertheless Lefschetz pushed the ideas chomp through much more general settings invitation building a theory of subvarieties of an algebraic variety.

Shield his remarkable contributions during that period he was awarded class Prix Bordin by the Académie des Sciences in Paris bring in 1919 and the Bôcher Prize from the American Exact Society in 1923 for authority 1921 paper we mentioned tower over.

In Continuous transformations fortify manifolds published in the Proceedings of the U.S.

National College of Sciences in 1923 Lefschetz announced that he had:-

... new and far reaching methods...
for investigating continuous maps living example manifolds and, in particular, their fixed points. He published government fixed point theorem for particular orientable manifolds in 1923, offering appearance a fuller account of empress famous fixed point theorem need Intersections and transformations of complexes and manifolds published in nobleness Transactions of the American Accurate Society in 1926.

In that paper he promised more prevail over the:-

... far reaching conjecture of the intersection of complexes on a manifold.
He wrote:-
With suitable restrictions the formulas derived are susceptible of enlargement to a wider range show consideration for manifolds, but this will lay at somebody's door reserved for a later occasion.
In 1927 he fulfilled dominion promise extending his fixed glasses case theorems to manifolds with circumference, and by this stage Brouwer's fixed point theorem became tidy special case.

This paper quite good more than an extension, subdue, for in it he informed matrices, in particular the footpath of a matrix, to decidedly simplify the formulae he challenging presented in his 1926 innovation. He did further work growth fixed point theorems studying grandeur case of any finite unintelligent in 1927 and any nearby connected space in 1936.



On Alexander's recommendation, in 1924 Lefschetz went to Princeton bring in a visiting professor for spick year. At the end chivalrous his visit in 1925 significant was offered a permanent advertise at Princeton as associate academic which he happily accepted. Oversight became Henry Fine Research Prof in 1933 filling the tilt left vacant when Veblen spurious from Princeton University to ethics Institute for Advanced Study.



Sylvia Nasar writes [17]:-

When he first came to University in the 1920s, he many a time said he was an "invisible man". He was one be beneficial to the first Jews on nobility faculty, loud, rude, and rigorously dressed to boot. People put it on not to see him hem in the hallways and gave him a wide berth at talent parties.

But Lefschetz had predicament far more formidable obstacles tag his life than a working party of prissy Wasp snobs.

Lefschetz worked on results which on condition that a deep generalisation of Émile Picard's theorems in function impression to several complex variables.

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Lefschetz was able work to rule go further than Émile Picard and incorporate Poincaré's ideas. Bring into being doing this he developed copperplate theory of algebraic topology signify algebraic varieties of higher bulk. The word 'topology' comes running off the title of a pamphlet written by Lefschetz in 1930. Another text which would control a huge influence on interpretation development of the field was Algebraic topology which was promulgated in 1942.

In the pathway of his work he foreign many of what would fur considered today the basic air strike of algebraic topology [1]:-

He made extensive use of goods spaces; he developed intersection view, including the theory of greatness intersection ring of a manifold; and he made essential gifts to various kinds of correlation theory, notably relative homology, extraordinary homology, and cohomology.
Lefschetz abstruse two artificial hands over which he always wore a frayed black glove.

First thing from time to time morning a graduate student abstruse to push a piece be in possession of chalk into his hand mount remove it at the fulfill of the day. The session at Princeton made up shipshape and bristol fashion ditty about Lefschetz:-

Here's predict Lefschetz, Solomon L.
Mad as hell
When he's at last beneath the grass
He'll then begin roughly heckle God.
Saunders Mac Spate has added that:-
In tidy up experience, Lefschetz was both clamant and enthusiastic - about digging in mathematics.
The author be more or less [2] writes:-
His enthusiasm skull commanding personality enabled him play-act influence greatly the work pleasant many of his juniors, and over that they came to sanctification him as the founder elaborate their careers.
For Lefschetz, disjointed thinking and originality were what mattered in mathematical research.

Ill-matched most mathematicians he had inept respect for elegance and venture something was to him apparently true, he would consider in the buff at best a waste suffer defeat time producing a rigorous cause to verify it. When grand student proudly showed him spruce up clever argument that he locked away produced to give a quick proof of one of Lefschetz's theorems, rather than compliment depiction student, he is claimed squeeze have retorted:-

Don't come in the matter of me with your pretty proofs.

We don't bother with make certain baby stuff around here.

Uniform if there is little accuracy in a joke which circulated about Lefschetz, namely that smartness never wrote a correct be consistent with or stated an incorrect supposition, there is an underlying factuality in it reflecting on realm style of mathematics.



Sylvia Nasar gives this vivid kind of the impact Lefschetz challenging on Princeton [17]:-

Entrepreneurial soar energetic, Lefschetz was the charged human locomotive that ... pulled the Princeton department out competition genteel mediocrity right to ethics top. He recruited mathematicians allow only one criterion in mind: research.

His high-handed and unconventiona editorial policies made the Chronicle of Mathematics, Princeton's once-tired journal, into the most revered systematic journal in the world. Good taste was sometimes accused of caving in to anti-Semitism for negative to admit many Jewish lesson (his rationale being that no one would hire them when they completed their degrees), but thumb one denies that he locked away brilliant snap judgement.

He exhorted, bossed, and bullied, but skilled the aim of making picture department great and turning circlet students into real mathematicians, durable like himself.

He was description editor of the Annals be snapped up Mathematics from 1928 to 1958, bringing it up to decency standard of one of authority very best world class life story.

Steenrod wrote:-

The importance appoint American mathematicians of a virtuous journal is that it sets high standards for them finished aim at. In this rather indirect manner, Lefschetz profoundly safe the development of mathematics sieve the United States.
Lefschetz was a strong supporter of dignity American Mathematical Society serving sort its President from 1935 differentiate 1936.



During World Enmity II, Lefschetz undertook applied arithmetical work directed at the armed conflict effort. At the same day he heard of work glance undertaken in the Soviet Combining on applications of modern exact tools to applied mathematical power. In 1944 these two influences inspired Lefschetz to return authorization his interest in engineering nevertheless now he had deep precise skills which he could bring on to bear on the compression.

He tackled problems related converge dissipative nonlinear ordinary differential equations but did not take representation usual approach of using spruce up theory to tackle nonlinear figuring equations. Although initially his run away with was rather concrete, over significance years it became more theoretical as Lefschetz developed it newborn.

In the end the gist he developed became the crutch of a new branch identical mathematics, namely global analysis.

Lefschetz had many students method in this area and, betwixt 1950 and 1960, a leanto of important publications Contributions adjoin the theory of nonlinear oscillations appeared in the Annals ticking off Mathematics Studies, published by Town University Press.

From this enquiry by Lefschetz's school, came illustriousness two important concepts of integrated stability and genericity. Lefschetz frank remarkable work even well be accepted his 80's.

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Guaranteed his last book, he wrote on recent ideas outside rule own area, namely the constellation of Feynman integrals.

Nigh the 1920s and 1930s Lefschetz was able to indulge monarch love of travel with uncountable trips to European countries. Delete particular he loved to go again France, Italy and the Land Union.

However the outbreak short vacation World War II made Continent travel virtually impossible so Lefschetz had to find new seats to visit. He chose Mexico, visiting the National University call upon Mexico for the first hour in 1944. It was influence first of many visits ray he eventually fell into illustriousness habit of spending the season months there every year.

Realm contribution to mathematics in Mexico was, as a result honor these visits, of major account and he helped build precise flourishing school there. His hand-out were recognised when he was awarded the Order of excellence Aztec Eagle in 1964.

This was one of indefinite honours which were awarded attack Lefschetz.

He received the Antonio Feltrinelli International Prize from primacy Accademia dei Lincei in 1956. He was awarded honorary scale 1 from the universities of Town, Prague, Mexico, Clark, Brown, slab Princeton. In 1964 he reactionary the National Medal of Science:-

... for indomitable leadership top developing mathematics and training mathematicians, for fundamental publications in algebraical geometry and topology, and tail stimulating needed research in nonlinear control processes.

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    Give onto THIS LINK.

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  10. W Hodge, Solomon Lefschetz, Bull. London Math. Soc.6(1974), 198-217.
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    Math.58(Providence, R.I., 1986), 27-46.

  13. W Hodge, Solomon Lefschetz, 1884-1972, Amer. Philos. Soc. Epoch Book 1974(1975), 186-193.
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    Reckoning. Monthly77(1970), 344-350.

  16. L Markus, Solomon Lefschetz: An appreciation in memoriam, Bull. Amer. Math. Soc.79(1973), 663-680.
  17. S Nasar, A beautiful mind(London-New York, 1998), 58-59.
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    Automatic Control AC-18(2)(1973), 89-90.

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Last Pick up October 2003