Abstract
Abstract: ThisisashorttributetoAleksandrA.Borovkovontheoccasionofhis80thbirthday.Keywords: probability,statistics,queuingtheory,limittheorems March6,2011isthe80thbirthdayofAcademicianAleksandrAlekseevichBorovkov.Anyjubileeforthepersoncelebratingisarathersadoccasion,butareasontolookback,evaluatehisaccomplishments,recallwhathewentthrough,andponderaboutthefuture. Fortheothersajubileeofadistinguishedscientistisnotonlyanopportunitytothankthecolleagueforwhathedidforeachofus,butalsoareasonforthinkingaboutscienceandthepeoplewhokeepandcreateknowledge,bearingresponsibilityforitbeforethefuturegenerations.BorovkovwasborninMoscow. HisfatherAlekse˘iAndreevichwasanoutstandingaircraftdesigner.HecontributedtothedevelopmentofretractableundercarriagefortheI–16fighterthatwentintomassproduction. Jointly with A. F. Florov he designed four modifications of the UTI training fighters andworkedonthefirstSovietjetfighterintheexperimentaldesignbureauofI.F.Bolkhovitinov. Aviationhistory notes an original project of a plane with pushing propeller and ramjet boosters, known in theWestastheBorovkov–FlorovD.Sincechildhood,Borovkovdreamedofrepeatingthepathofhisfatherandgoingintoaircraftdesign.Theearlydeathofhisfatherinaplanecrashin1945interferedwiththisintention. Asecondobstaclefor the realization of the youthful dream was the assignment to a special group of the Mechanics andMathematicsFacultyatMoscowStateUniversityandthesubsequentdraftintoasecretdecipheringunitoftheSovietArmy. ItwastherethatBorovkovbecameinvolvedinprobabilityandstatisticswhichsincethenhavebecomehisprincipaloccupation.Dismissed from the Army, Borovkov entered into graduate education in the Steklov MathematicalInstitute. His scientific advisor was A. N. Kolmogorov. In 1959 Borovkov defended his thesis for thedegree of a candidate of sciences, and Kolmogorov recommended him to S. L. Sobolev for heading thelaboratory of probability and statistics at the Institute of Mathematics of the Siberian Branch of theUSSR Academy of Sciences which had been founded near Novosibirsk those years. For half a centuryalreadythecreativecontributionofBorovkovhasbeenstemmingfromSiberia.Mathematicsisthestudyofthemostgeneralformsofobjectivethinking,providingstandardsandtools for other branches of science. Mathematics became the logic of thought. We have to understandthatlogiccanbedifferent. Thespecialplaceinmodernscienceisoccupiedbystochasticreasoning.Certainty does not belong to people. The world around us is so complicated and diverse thatwe cannot ignore the deficiency and randomness of our knowledge and observations. The man livesin the world of chance. To see the patterns behind our own ignorance is the task of probability andstatistics. Luckily,theignoranceisversatileandhomogeneous: themankindencountersaplentitudeoftheindependentrandomvariablesthatarebyandlargeidenticallydistributedduetotheuniversalgapsinourknowledge. Ahumanweakness—ignorance—turnsintothepoweroflimittheoremsandthelawoflargenumbers.Modernstochasticsisoftenpositionedasabranchofmeasuretheory. Thisissomewhatimprecise.Measuretheorygoesbacktogeometrywhichgrewoutofthelegalproceduresrequiringcompletedefinite-nessandunambiguityinapplication. Aristotle’slogicfollowedgeometryandreflecteditsmethodology.Probabilityhasitsrootsnotinjurisprudence,butintheproceduresofsoothsayingandfortunetelling,whichmeanspredictingthefuturefromrandomormysticalexperiments.
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