Wielkie tęsknoty ludzkości (mistyka – matematyka – magia)

The second volume of the three-part series of Professor Krzysztof Maurin’s works – an eminent mathematician, the founder of the Polish school of mathematical physics, a philosopher and a thinker – contains texts copied from the author’s notes. The chapters devoted to mathematics on the one hand express the view about the organic relation between mathematics and humanities, and on the other, show that mathematics has the language of symbols which allow to encompass a much wider area of thought.

Vladimir Igorevich Arnold. 12 June 1937—3 June 2010

Vladimir Arnold was a pre-eminent mathematician of the second half of the twentieth and early twenty-first century. Kolmogorov–Arnold–Moser (KAM) theory, Arnold diffusion, Arnold tongues in bifurcation theory, Liouville–Arnold theorem in completely integrable systems, Arnold conjectures in symplectic topology—this is a very incomplete list of notions and results named after him. Arnold was a charismatic leader of a mathematical school, a prolific writer, a flamboyant speaker and a tremendously erudite person. Our biographical sketch describes his extraordinary personality and his major contributions to mathematics.

Ciência, misticismo e educação: uma análise russelliana da pretensa neutralidade da matemática frente à religião

ResumoO propósito deste artigo consiste na elucidação dos elementos da obra de Bertrand Russell (1872-1970), eminente matemático e filósofo, que tornem possíveis os debates acerca da pretensa neutralidade da matemática diante dos misticismos que sempre estiveram presentes na história da humanidade, mas que, devido aos equívocos que impregnaram sua perspectiva, consideramos, muitas vezes, genericamente obscurantistas e perniciosos. Para isto, tornou-se necessário evidenciar as abordagens à ciência, aos misticismos e à educação na obra russelliana. Pretende-se, portanto, destacando a possibilidade de compreender a matemática como credo, demonstrar que posturas decorrem da tradicional educação matemática que podem favorecer posturas de intolerância religiosa e sugerir, também com Russell, a introdução de uma postura de enfrentamento.Palavras-chave: Matemática; Bertrand Russell; Misticismo; FilosofiaScience, mysticism and education: a russellian analysis of the supposed neutrality of mathematics towards religionAbstractThe purpose of this article is to elucidate the elements of the work of Bertrand Russell (1872-1970), eminent mathematician and philosopher, which make possible the debates about the alleged neutrality of mathematics towards the mysticism that has always been present in human history, but due to misconceptions that pervade their perspective, we consider often generically obscurantist and pernicious. For this, it was necessary to highlight the approaches to science to mysticism and education in Russell's work. It is intended, therefore, highlighting the possibility of understanding mathematics as creed, show that attitudes stem from traditional mathematics education that can foster religious intolerance poses and suggest, also with Russell, the introduction of a confronting posture.Keywords: Mathematics; Bertrand Russell; Mysticism; Philosophy

Classical Text in Translation

The paper presented here was written as early as sometime between 1939 and 1944 by the eminent mathematician Aleksandr Yakovlevich Khinchin, who is well known for his contributions to the theory of probability, statistical physics, theory of numbers, and theory of functions. For reasons unknown to me, it remained unpublished, although I remember that Khinchin had submitted it to the periodical Uspekhi matematicheskikh nauk. After he died, while I was putting in order the scientific and literary heritage of Khinchin, I remembered this work and began looking for it. Regrettably, I was unable to find any copies of a final version and the editorial office of Uspekhi did not have any record of the article. So I decided to make use of a copy that had been retyped in 1946 by my students, E. L. Rvacheva and D. G. Meyzler, even though it had some lacunae. I am convinced that even in this state, Khinchin's work is of considerable interest.

The English and the Dutchman's Log

In his detailed and valuable account of the history of the Log (this Journal, 9, 70) Commander Waters is surely at fault as regards the part he ascribes to the Gresham Professor, Gunter. This eminent mathematician delighted in designing instruments with engraved scales, and at first issued the customary Description and Use in Latin, a sufficient indication that he wrote only for fellow scholars. Importuned probably by the instrument-makers, he later published English versions of the tracts (in 1623), and among the numerous ‘uses’ included a couple of chapters on those for navigational purposes.

Whitehead's Philosophy: The World as Process

This paper will endeavour to present an outline of the Organic Philosophy associated with the name of Whitehead. Whitehead resembles Spinoza and Leibniz in that he is a philosopher who has tried to construct a world-outlook that will do justice to science and to the other aspects of life and knowledge. Moreover, just as in his day Leibniz was an eminent mathematician and scientist, so Whitehead in our day enjoys the same distinction. But Whitehead's philosophy differs both from that of Spinoza and from that of Leibniz. Spinoza based his philosophy upon the monistic substance, of which the actual events in the world are the inferior modes. Whitehead bases his philosophy upon the actual events themselves and derives the solidarity of the world as a whole from their mutual interplay. Thus the organic philosophy is pluralistic in contrast with Spinoza's monism. In comparing Whitehead's philosophy with that of Leibniz, we find that they agree in both being pluralistic, but they differ in the emphasis placed upon the notion of mentality. Leibniz's monads are best conceived as generalizations of the notion of mentality, and the conception of physical bodies only enters into his philosophy subordinately and derivatively. Whitehead, however, in his philosophy of organism endeavours to hold the balance between the physical and mental more evenly, and thus does justice to both aspects of reality.

The Vignoles snuff-box

Among the gifts received by the Society is that of a Snuff-box once the property of Charles Blacker Vignoles, F.R.S., which was presented to the Society on 16 July 1942 by Mr E. B. Vignoles M.I.E.E., and Lieutenant-Colonel W. A. Vignoles, D.S.O., M.I.E.E, his grandsons. The circumstances of Vignoles’s life and of the manner in which he acquired this Snuff-box are of such interest as to be worthy of record. Charles Blacker Vignoles, only child of Captain Charles Henry Vignoles of the 43rd Regiment and his wife Camilla, daughter of Dr Charles Hutton, F.R.S., the eminent mathematician, was born in Ireland on 31 May 1793. The regiment was sent to Guadeloupe early in 1794, whither Camilla and her son accompanied them ; and here both parents died in June of that year, within two days of one another, in the tragic circumstances related by Monsieur Courtois, their kindly host, in the letter to Dr Hutton quoted below. Charles was left an infant prisoner in the hands of M. Courtois. Before leaving the island the child was given a commission in the British army and was placed on half'pay, being too young to serve. He was, in fact, barely eighteen months old.

Isaac Barrow

Isaac Barrow has been described as “an eminent mathematician and classical scholar, and one of the greatest of the great Anglican divines and preachers of the Caroline period.”* His father was a linen draper in London—a man of royalist sympathies who followed the English court to Paris during the period of the Commonwealth and Protectorate (1649-1660). For a time, Barrow was a pupil at Charterhouse in London. His career there may be judged from his father's statement that “if it should please the good Lord to take one of his children, he could best spare Isaac.” It is not surprising that his son was sent to another school, the one chosen being Felstead in Essex.

Some Remarks on ‘Probability’

Since games of chance have always exercised a fascination for people of all countries and at all times it is not to be wondered at that the theory of probability was first evolved from the dice-table. Possibly the earliest problem was to find the different probabilities of the various throws which can be made with three dice: this occurs in a document published in the fifteenth century, and the problem was taken up again by Cardan about a hundred years later. The first serious investigation into the laws of chance was, however, due to Pascal, who may be considered as the founder of the science. Pascal's attention was first drawn to the subject by a gambler who put to him problems relating to the game of ‘hasard.’ One particular problem seemed to Pascal of the utmost importance and led to a series of discussions between Pascal and Fermat, another equally eminent mathematician. The problem was the ‘Problem of Points’ and may be stated thus: Two players want each a given number of points to win a game; if they separate without finishing the game, how should the stakes be divided? Many variations of this were considered, even those where the players were not of equal skill, and although the problems would not be difficult of solution in light of modern knowledge, there was considerable divergence of opinion as to the correct methods to be applied.