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Who were the world's greatest mathematicians, and why?
Srinivasa Ramanujan (1887-1920) hailed as an all-time great mathematician, like Euler, Gauss or Jacobi, for his natural genius, has left behind 4000 original theorems, despite his lack of formal education and a short life-span. In his formative years, after having failed in his F.A. (First examination in Arts) class at College, he ran from pillar to post in search of a benefactor. It is during this period, 1903-1914, he kept a record of the final results of his original research work in the form of entries in two large-sized Note Books. These were the ones which he showed to Dewan Bahadur Ramachandra Rao (Collector of Nellore), V. Ramaswamy Iyer (Founder of Indian Mathematical Society), R. Narayana Iyer (Treasurer of IMS and Manager, Madras Port Trust), and to several others to convince them of his abilities as a Mathematician. The orchestrated efforts of his admirers, culminated in the encouragement he received from Prof. G.H. Hardy of Trinity College, Cambridge, whose warm response to the historic letter of Ramanujan which contained about 100 theorems, resulted in inducing the Madras University, to its lasting credit, to rise to the occasion thrice - in offering him the first research scholarship of the University in May 1913 ; then in offering him a scholarship of 250 pounds a year for five years with 100 pounds for passage by ship and for initial outfit to go to England in 1914 ; and finally, by granting Ramanujan 250 pounds a year as an allowance for 5 years commencing from April 1919 soon after his triumphant return from Cambridge ``with a scientific standing and reputation such as no Indian has enjoyed before''.Ramanujan was awarded in 1916 the B.A. Degree by research of the Cambridge University. He was elected a Fellow of the Royal Society of London in Feb. 1918 being a ``Research student in Mathematics Distinguished as a pure mathematician particularly for his investigations in elliptic functions and the theory of numbers'' and he was elected to a Trinity College Fellowship, in Oct. 1918 (- a prize fellowship worth 250 pounds a year for six years with no duties or condition, which he was not destined to avail of). The ``Collected Papers of Ramanujan'' was edited by Profs. G.H.Hardy, P.V. Seshu Aiyar and B.M. Wilson and first published by Cambridge University Press in 1927 (later by Chelsea, 1962 ; and by Narosa, 1987), seven years after his death. His `Lost' Notebook found in the estate of Prof. G.N. Watson in the spring of 1976 by Prof. George Andrews of Pennsylvania State University, and its facsimile edition was brought out by Narosa Publishing House in 1987, on the occasion of Ramanujan's birth centenary. His bust was commissioned by Professors R. Askey, S. Chandrasekhar, G.E. Andrews, Bruce C. Berndt (`the gang of four'!) and `more than one hundred mathematicians and scientists who contributed money for the bust' sculpted by Paul Granlund in 1984 and another was commissioned for the Ramanujan Institute of the University of Madras, by Mr. Masilamani in 1994. His original Note Books have been edited in a series of five volumes by Bruce C. Berndt (``Ramanujan Note Books'', Springer, Parts I to V, 1985 onwards), who devoted his attention to each and every one of the three to four thousand theorems. Robert Kanigel recently wrote a delightfully readable biography entitled : ``The Man who knew Infinity : a life of the Genius Ramanujan'' (Scribners 1991; Rupa & Co. 1993). Truly, the life of Ramanujan in the words of C.P. Snow: ``is an admirable story and one which showers credit on nearly everyone''.During his five year stay in Cambridge, which unfortunately overlapped with the first World War years, he published 21 papers, five of which were in collaboration with Prof. G.H. Hardy and these as well as his earlier publications before he set sail to England are all contained in the ``Collected Papers of Srinivasa Ramanujan'', referred earlier. It is important to note that though Ramanujan took his ``Note Books'' with him he had no time to delve deep into them. The 600 formulae he jotted down on loose sheets of paper during the one year he was in India, after his meritorious stay at Cambridge, are the contents of the `Lost' Note Book found by Andrews in 1976. He was ailing throughout that one year after his return from England (March 1919 - April 26, 1920). The last and only letter he wrote to Hardy, from India, after his return, in Jan. 1920, four months before his demise, contained no news about his declining health but only information about his latest work : ``I discovered very interesting functions recently which I call `Mock' theta-functions. Unlike the `False' theta-functions (studied partially by Prof. Rogers in his interesting paper) they enter into mathematics as beautifully as ordinary theta-functions. I am sending you with this letter some examples ... ''. The following observation of Richard Askey is noteworthy: ``Try to imagine the quality of Ramanujan's mind, one which drove him to work unceasingly while deathly ill, and one great enough to grow deeper while his body became weaker. I stand in awe of his accomplishments; understanding is beyond me. We would admire any mathematician whose life's work was half of what Ramanujan found in the last year of his life while he was dying''.
What is the general consensus of historians (not theologians) on Jesus' history? Is the message of the Bible true?
History is limited in what it can tell us, but what it can say is important. It can tell us what the people involved thought about themselves—who they believed they were and what they believed about what they were doing—but it cannot tell us if their message is “true.” Evaluating the message remains a personal decision.Because of this fact of personal inference, there is no 100% consensus on anything concerning Jesus or the Bible. There is, however, a majority view amongst the best and most qualified scholars in the field.There are dissenters, there have been dissenters throughout history, and there will always be dissenters. Dissent does not automatically imply disrespect for the historian’s scholarship either. Good scholars can and do disagree. But scholarship in this field of study is currently going through a kind of revolution. The majority of scholars used to be “liberal” with many of their views based on the assumptions of historical criticism and/or form criticism, and the pendulum is swinging in the other direction right now.That’s because of the impact of history on theology.Previous critical assumptions based on the application of evolution to the biblical texts—(the assumption they had evolved and changed over time)—have been seriously undermined by the discovery of the Dead Sea Scrolls. The Dead Sea Scrolls, at 1000 years older than the Masoretic text of the Old Testament, show virtually no evolution: the assumption was wrong. That throws all the conclusions made based on those assumptions into the can—so to speak. They will all need to be re-evaluated.History is now reverberating through theology accordingly.Another assumption of previous critical methods was that all poor people of the first century were illiterate. But archaeology has turned up evidence that the average citizen of the first century was not as illiterate as previously thought. Plus, there is second source information that Matthew—as a tax collector—was literate, that he first wrote his gospel in Hebrew/Aramaic quite early (the 40’s), and that it was used by Mark to write his own as well as being translated into Greek at a later date. Mark spoke both languages because his father was Greek and his mother was Hebrew.History is impacting theology again since this is the reverse of what was said for decades.What is the general consensus of historians on Jesus history? Gary Habermas is probably the premier authority on that; he developed a new method of historical evaluation called the minimum facts approach based entirely on the idea of consensus views.Having specialized for several decades in critical studies of the resurrection of Jesus, I recently decided to update my Bibliography. What began rather modestly evolved into a five year study of well over 2000 sources on this topic, published from 1975 to the present in German, French, and English. I was most interested in scholarly trends, ... One area of concentration was the common historical content recognized by virtually all researchers.Habermas established that there are four core facts — by means of critical historical methodology — that are accepted by the vast majority of critical scholars whatever their school of thought. These core facts are:The death of Jesus due to crucifixion;the subsequent experiences that the disciples were convinced were literal appearances of the risen Jesus;the corresponding transformation of the disciples;Paul’s conversion appearance that he also believed was an appearance of the then risen Jesus.There are other historical facts that most, if not all, critical scholars recognize. Including the four core facts, there are a total of 12:Jesus died by crucifixion; 2) was buried; 3) his death caused the disciples to despair, lose hope, and believe his life had ended. 4) Although not as widely accepted, many scholars hold that the tomb in which Jesus was buried was discovered to be empty—means unknown—just a few days later. 5) Critical scholars agree the disciples had experiences which THEY believed were the literal appearances of the risen Jesus. 6) Because of these experiences the disciples were transformed from doubters to proclaimers, from fearful to bold. 7)The resurrection message was the center of preaching in the early church; 8)especially in Jerusalem where he had died and was buried. 9) As a result, the church was born and grew; 10) with Sunday as the primary day of worship. 11) James who had been a skeptic was converted when he believed he saw the resurrected Jesus. 12) A few years later Paul was converted when he, likewise, believed he had an experience of the risen Jesus.With the exception of the empty tomb, the vast majority of critical scholars who deal with this subject agree these are the minimum of known historical facts.Habermas goes on to discuss the empty tomb.I found that approximately 75% of the surveyed scholars accept one or more arguments for the historicity of the empty tomb. The remaining 25% accept one or more arguments against the early church's knowledge of an empty tomb.The survey revealed almost two dozen reasons supporting Jesus’ empty tomb. Historian Michael Grant surprisingly states that "the historian . . . cannot justifiably deny the empty tomb" because normally applied historical criteria indicate that, "the evidence is firm and plausible enough to necessitate the conclusion that the tomb was indeed found empty." ( Michael Grant, Jesus: An Historian’s Review of the Gospels (N.Y.: Collier, 1992), p.176.)These facts cannot be waved away by referring to “discrepancies” in the New Testament texts or its general “unreliability.” These facts place Jesus in history and the events surrounding him and his life and death as events in history as well.http://garyhabermas.com/books/EvidenceBook/GaryHabermas_Evidence-for-the-historical-Jesus-Release_1point1.pdfExperiences of the Risen JesusThe Apostles believed.The substantially unanimous verdict of contemporary critical scholars is that Jesus' disciples genuinely believed that Jesus was alive, resurrected from the dead. Reginald Fuller refers to the disciples’ belief in Jesus' resurrection as "one of the indisputable facts of history." Upon what was their claim based? Fuller continues that it is clear that the disciples had real experiences, characterized as appearances or visions of the risen Jesus. Whether these are explained naturally or supernaturally, this experience "is a fact upon which both believer and unbeliever may agree." (Fuller, The Foundations of New Testament Christology (New York: Scribner's, 1965), p.142.)Their belief transformed them.Virtually no critical scholar questions that the disciples’ convictions regarding the risen Jesus caused their radical transformation, even being willing to die for their beliefs. Their change does not evidence the resurrection appearances per se, but it is a clear indication that the disciples at least thought that they had experienced the risen Jesus. Alternatives must account for this belief. (For critical agreement in various elements here, see Willi Marxsen, Jesus and Easter (Nashville: Abingdon, 1990), 66; J. Dore, "Croire en la Resurrection de Jesus-Christ," etudes, Vol. 356 (1982), 536-537; Funk, Honest to Jesus, especially 270; Wedderburn, pp.46-47; Hengel, 65; J.K. Elliott, "The First Easter," History Today, Vol. 29 (1979), pp.210, 215, 218; Wolfhart Pannenberg, Jesus--God and Man, second ed., trans. Lewis L. Wilkins and Duane A. Priebe (Philadelphia: Westminster, 1977), p.96; Michael Grant, Saint Peter: A Biography (N.Y.: Scribner, 1994), pp. 89, 96; Sanders, 11, 276-280; Hugh Jackson, "The Resurrection Belief of the Earliest Church: A Response to the Failure of Prophecy," The Journal of Religion, Vol. 55 (1975), pp.419-422; Elaine Pagels, The Gnostic Gospels (NY: Random House, 1979), p.8. )Paul is a witness to something that radically transformed him.Contemporary critical scholars agree that the apostle Paul is the primary witness to the early resurrection experiences. A former opponent (1 Cor. 15:9; Gal. 1:13-14; Phil. 3:4-7), Paul states that the risen Jesus appeared personally to him (1 Cor. 9:1; 15:8; Gal. 1:16). The scholarly consensus here is attested by atheist Michael Martin, who avers: "However, we have only one contemporary eyewitness account of a postresurrection appearance of Jesus, namely Paul’s." (Michael Martin, The Case Against Christianity (Philadelphia: Temple University, 1991), p.81. Walter Kaspar, Jesus the Christ, new ed., trans. V. Green (Mahweh: Paulist, 1976), p.125.)The creed in 1 Corinthians is evidence of early Christian belief.In addition to Paul's own experience, few conclusions are more widely recognized than that, in 1 Corinthians 15:3ff., Paul records an ancient oral tradition(s). This pre-Pauline report summarizes the early Gospel content, that Christ died for human sin, was buried, rose from the dead, and then appeared to many witnesses, both individuals and groups. Critical scholars agree that Paul received the material well before this book was written. (Reginald Fuller, The Formation of the Resurrection Narratives (New York: Macmillan, 1980), 10. Of the vast number of scholars who agree, some examples include John Kloppenborg, "An Analysis of the Pre-Pauline Formula in 1 Cor 15:3b-5 in Light of Some Recent Literature," Catholic Biblical Quarterly, Vol. 40 (1978), especially 351, 360; Jerome Murphy-O'Connor, "Tradition and Redaction in 1 Cor 15:3-7," Catholic Biblical Quarterly, Vol. 43 (1981), 582-589; John Meier, A Marginal Jew: Rethinking the Historical Jesus (New York: Doubleday, 2001), Vol. 2:139; Sanders, The Historical Figure of Jesus, 277; Pinchas Lapide, The Resurrection of Jesus: A Jewish Perspective (Minneapolis: Augsberg, 1983), 97-99.)This creed is the oldest known evidence.Critical scholars generally agree that this pre-Pauline creed(s) may be the earliest in the New Testament. (Joachim Jeremias, "Easter: The Earliest Tradition and the Earliest Interpretation," New Testament Theology, trans. John Bowden (N.Y.: Scribner's, 1971), p.306.) Even skeptical scholars frequently agree. Gerd Ludemann maintains that "the elements in the tradition are to be dated to the first two years after the crucifixion of Jesus. . . . not later than three years. . . . the formation of the appearance traditions mentioned in I Cor.15.3-8 falls into the time between 30 and 33 CE. . . ." (Gerd Ludemann, The Resurrection of Jesus, trans. John Bowden (Minneapolis: Fortress, 1994), p.38). Similarly, Michael Goulder thinks that it "goes back at least to what Paul was taught when he was converted, a couple of years after the crucifixion." (Michael Goulder, "The Baseless Fabric of a Vision," in Gavin D’Costa, editor, Resurrection Reconsidered (Oxford: Oneworld, 1996), 48.) Thomas Sheehan agrees that this tradition "probably goes back to at least 32-34 C.E., that is, to within two to four years of the crucifixion." Others clearly consent. ((Thomas Sheehan, The First Coming: How the Kingdom of God became Christianity (New York: Random House, 1986), 118; cf. 110-111.)JamesThe majority of recent scholars, including many rather skeptical ones, agree that James was converted from unbelief by what he believed was Jesus' personal appearance. Critical scholars usually recognize that James, the brother of Jesus, was a skeptical unbeliever prior to Jesus' crucifixion (Mk. 3:21-35; Jn. 7:5). Not long afterwards, James is a leader of the Jerusalem church, where Paul finds him during his two visits (Gal. 1:18-19; 2:1-10; cf. Acts 15:13-21). In-between, the pre-Pauline statement in 1 Corinthians 15:7 states that the risen Jesus appeared to James. Fuller concludes that even if the New Testament had not referenced the resurrection appearance to James, "we should have to invent" one in order to account for his conversion and his promotion to his lofty position in the Jerusalem church. (Fuller, The Formation of the Resurrection Narratives, p.37; Ludemann, The Resurrection of Jesus, 109; Helmut Koester, Introduction to the New Testament (Philadelphia: Fortress, 1982), Vol. 2:84; Robert Funk, Honest to Jesus (San Francisco: Harper Collins, 1996), p.33; Wedderburn, 116; John Shelby Spong, The Easter Moment (San Francisco: Harper and Row, 1987), p.68; Peter Stuhlmacher, "The Resurrection of Jesus and the Resurrection of the Dead," trans. Jonathan M. Whitlock, Ex Auditu, Vol. 9 (1993), p.49; E.P. Sanders, "But Did it Happen?" The Spectator, Vol. 276 (1996), p.17.)… [Because] many researchers accept the maxim that a viable natural hypothesis is to be accepted before a supernatural one, postulating and checking alternative scenarios by the known data will probably continue. This process makes sense.On the other hand, if alternative theses continually fail amid dissatisfaction with agnostic reluctance, the reasons favoring the disciples' experiences might indicate that the most likely scenario is that the disciples actually did see the risen Jesus.In general, the more thoroughly one option fails, the more likely the others become. And the more strongly an option is established, the more the others diminish. Even without a final solution here, however, there is still value in honing our instruments and narrowing our options.That is what history can do for us: narrow our options. But the individual responses about “truth” remain completely personal.These are not exact quotes from Gary Habermas but they are his thoughts and research and conclusions, and they seem irrefutable.What is the general consensus of historians (not theologians) on Jesus' history?That Jesus was a historical person who died and whose —possible actual—reappearance afterwards was so shockingly life altering it radically changed everyone who came in contact with what they fully believed was a risen Messiah.Coming up with naturalistic explanations of that has kept many an agnostic and atheist apologist busy for many centuries now.
Was Marcus Aurelius as good a man as it is said?
The Statue of Marcus Aurelius (detail) in the Musei Capitolini in Rome:We have a severe problem learning about this emperor:The major sources for the life and rule of Marcus Aurelius are patchy and frequently unreliable. The most important group of sources, the biographies contained in the Historia Augusta, claim to be written by a group of authors at the turn of the 4th century, but are in fact written by a single author (referred to here as "the biographer") from the later 4th century (c. 395).[4]The source mentioned above is, frankly, largely horse manure.His predecessor is Antoninus Pius and to give an example of what I think ‘history’ has done, I regard him as the historical basis for Pope Pius I. In other words, much later, people remade ‘history’ to fit their religious - and thus, also political - point of view. This is why I term it a “textual tradition” and how an archaeological point of view has the potential to be far superior.The predecessor of Antonius Pius is Hadrian, who I described as the worst emperor ever and I likened him to Hitler:John Bartram's answer to Who was the worst Roman emperor?Hadrian and the cult of AntinousHadrian the ChrestianTo me, therefore, I have to ask myself: does Marcus Aurelius follow in the footsteps in his predecessors?Bust of Marcus Aurelius in the Musée Saint-Raymond, Toulouse, France:He married his eleven-year-old daughter, Annia Lucilla, to her uncle:.Soon after the emperors' accession, Marcus' eleven-year-old daughter, Annia Lucilla, was betrothed to Lucius (in spite of the fact that he was, formally, her uncle).[156]I also see a likeness in this with Herod I the Great and his relatives marrying not just each other, but uncles marrying young nieces. By itself, perhaps this can be dismissed as just something unpleasant, or a bit odd, but I see it as part of a wider, theological perspective:Incest as a colonial Hellenistic markerLucius Catilius Severus Julianus Claudius Reginus was Roman consul twice, in the years 110 CE (as consul suffectus) and 120 CE (as consul ordinarius).[1] In 120 CE his co-consul was Antoninus Pius.[2] Catilius served as provincial governor in Asia and Africa multiple times[3] and also was prefect of Rome.[1]I therefore see him as a link between Hadrian and Antoninus Pius on one hand, and Marcus Aurelius on the other. More than as a theoretical link, but as tutor to Marcus Aurelius, I see his job as ensuring the next emperor had the same outlook (which I interpret as Chrestian).As Julius Caesar is said to have planned to war with Parthia, perhaps too much should not be read into the war conducted by Marcus Aurelius. It began with that uncle who married his daughter incestuously - Lucius Catilius Severus - as the leading general and it didn’t go well, at all.Again, as imperial Rome always butted horns with the Iranian east and thus fought in Mesopotamia, one can just dismiss this as continuing empire building. I see, however, something more.As the First Jewish-Roman War erupted, thanks to Saul and his Herodian compatriots, Jewish refugees fled eastwards."Paul as Herodian"Essay by Dr. Andrew P. Gould, Ohio State U. Distinguished Professor of Mathematical and Physical SciencesThe armed wing of The Poor (of the Dead Sea scrolls and Qumran) were already ensconced there and Jewish merchants had settled eastwards since released from slavery by Cyrus the Great. I think hunting them down had been the objective of Trajan and Hadrian in the Second Jewish-Roman War and now, Marcus Aurelius continued the strategic plan.Lucius spent most of the campaign in Antioch, though he wintered at Laodicea and summered at Daphne, a resort just outside Antioch.[209] Critics declaimed Lucius' luxurious lifestyle.[210] He had taken to gambling, they said; he would "dice the whole night through".[211] He enjoyed the company of actors.[212][notes 17]Libo died early in the war; perhaps Lucius had murdered him.[214]Debauchery is a hallmark of the Chrestian elite, as we see earlier with, for example, Flavius Clemens; he married his niece Flavia Domitilla (saint), daughter of his sister; Suetonius: “ Flavius was a man of most contemptible laziness”.Chrestianity in the First CenturyMarcus Aurelius took Armenia, then the little kingdom of Osroene with its capital, Edessa. Later, we see Caracalla focus on Erbil, capital of Adiabene, and personally desecrate the royal tombs there. Though historians generally struggle to rationalise any of this, I see a pattern:These emperors are after more than killing the observant, messianic Jews of first-century Judaea, and their refugees, but also eradicating their famous supporters: Helen and Izas/Izates (as described in detail by Josephus). His children won renown resisting the Roman army in the first war. Modern scholarship tends to identify this “Izas” as king Abgar V in Edessa. Helen’s tomb looks to me to have become the basis of the tomb of “Jesus”.MMT as Jamesian Letter to "The Great King of the Peoples Beyond the Euphrates", The Journal of Higher Criticism vol. 11, no.1, Spring 2005.In short, like Hadrian, this emperor seems to following the cult which I term - after the title of its divine man - Chrestian:Above: CIL VI 24944 with Antonia Minor, her husband Drusus and the Pompeii banker Jucundus as Chrestian. Dated to early first-century.As Chrest is one form of Greek Good, calling him a Good Emperor is perhaps appropriate in an ironic way.
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