Probability is a mathematical discipline whose aims are akin to those,

for example, of geometry of analytical mechanics.

In each field we must carefully distinguish three aspects of the theory:

(a) the formal logical content,

(b) the intuitive background,

(c) the applications.

The character, and the charm, of the whole structure cannot be appreciated without

(a) the formal logical content,

(b) the intuitive background,

(c) the applications.

The character, and the charm, of the whole structure cannot be appreciated without

considering all three aspects in their proper relation.

*William Feller, An Introduction to Probability Theory and its Applications*

The 188th day of the year; 188 is the largest known even number that can be expressed as the sum of two (distinct) primes in exactly five ways. *Prime Curios

*Students might seek smaller numbers that can be so expressed.*.

EVENTS

1339 There was an annular-total eclipse, with the total part of the track finding its way between the Orkney and Shetland Islands without touching either. At this location the track of totality was only 1 km wide, with a duration of 1 second! Presuming that you could position a boat to an accuracy of 1 km, totality must have been a ring of Baily's Beads. *NSEC 1668, Sir Isaac Newton received his M.A. from Trinity College in Cambridge.*TIS

1742 Goldbach's conjecture was sent in a letter to Leonhard Euler on 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 10

^{14}- but still remains unproved. *TIS

1747 Johann Sebastian Bach dedicated his Musikalisches Opfer (Musical Oﬀering) to Frederick the Great. For a discussion of the mathematical signiﬁcance of this cerebral music, see Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. *VFR

1777 Johan Bernoulli, then astronomer Royal, Berlin, is paid a sum of 84 pounds for the Sexcentenary tables. "To Mr. John Hyacinth Magellan....for the use of Mr. Bournoulli .. as a reward for his care and trouble in constructing a manuscript Book of Tables for facilita."

Two years later they would pay 28.35 pounds to Dr. Charles Hutton for translating the preface of the tables.

1823 William Rowan Hamilton passed into Trinity College, Dublin. He was easily ﬁrst out of the 100 candidates. *VFR

1847 Lassel discovered a satellite of Neptune. *VFR (this date does not concur with other dates on these discoveries) In 1846 Lassell discovered Triton, the largest moon of Neptune, just 17 days after the discovery of Neptune itself by German astronomer Johann Gottfried Galle. In 1848 he independently co-discovered Hyperion, a moon of Saturn. In 1851 he discovered Ariel and Umbriel, two new moons of Uranus.*Wik

1855, a letter from Michael Faraday in The Times newspaper, London, described the polluted state of the River Thames he had observed on a boat trip: "The whole of the river was an opaque pale brown fluid. In order to test the degree of opacity, I ... dropped [pieces of card] into the water at every pier the boat came to; before they had sunk an inch below the surface they were indistinguishable, though the sun shone brightly at the time." His words, he said, were no exaggeration, they were "the simple truth." He asserted, "If there be sufficient authority to remove a putrescent pond from the neighborhood of a few simple dwellings, surely the river which flows for so many miles through London ought not to be allowed to become a fermenting sewer." *TIS I wrote a few years ago about the return of the seahorse to the muddy waters of the Thames.

1960 Press conference announces discovery of laser to the world. "VoilÁ. that Was It! The Laser was Born!" *Hughes Research Lab Web page.

BIRTHS

1638 Francois or Francois Bertrand Barrême Barrême,(7 July 1638, Tarascon, France - 1703, Paris France) is considered one of the founders of accounting . After having engaged in trading in Italy , he moved to Paris where he gave lessons in bookkeeping and became a protégé of Colbert . Expert for the accounts of the Accounting Chamber of Paris and King's ordinary arithmetician, he is the author of books of mathematical conversions. His books were so common that today his name is used for what was once in English called a "ready reckoner", a table of numbers used to facilitate simple calculations, esp one for applying rates of discount, interest, charging, etc, to different sums . *Wik 1746 Giuseppe Piazzi (July 7, 1746 - July 22, 1826) an Italian mathematician and astronomer. He discovered the asteroid Ceres and established an observatory at Palermo, now the Osservatorio Astronomico di Palermo – Giuseppe S. Vaiana. (for more detail see the source article) *Today in Astronomy

*Wik |

1816 Rudolf Wolf Swiss (7 July 1816 – 6 December 1893) astronomer and astronomical historian. Wolf's main contribution was the discovery of the 11 year sunspot cycle and he was the codiscoverer of its connection with geomagnetic activity on Earth. In 1849 he devised a system now known as Wolf's sunspot numbers. This system is still in use for studying solar activity by counting sunspots and sunspot groups. In mathematics, Wolf wrote on prime number theory and geometry, then later on probability and statistics - a long paper discussed Buffon's needle experiment. He estimated by Monte Carlo methods.*TIS

1888 Archibald Goldie (7 July 1888 in Glenisla, Angus, Scotland - 24 Jan 1964 in London, England) studied at the universities of St Andrews and Cambridge. He served in the Meteorological Service of the British Army in World War I and continued to work in various branches of the Meteorological Office.*SAU

1906 Birthdate of the probabilist William Feller (July 7, 1906 – January 14, 1970). He once said that multiplication, especially before breakfast, is seldom commutative. He died in 1970. *VFR

Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators".*Wik

DEATHS

1900 Eduard Wiltheiss (12 June 1855 Worms, Germany – 7 July 1900 Halle) was a German mathematician who made major contributions to the theory of abelian functions *VFR1927 Magnus Gustaf Mittag-Leffler died (16 March 1846 – 7 July 1927) . Swedish mathematician who founded the international mathematical journal Acta Mathematica and whose contributions to mathematical research helped advance the Scandinavian school of mathematics. Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem.*TIS

1930 Sir Arthur Conan Doyle (22 May 1859 – 7 July 1930) Scottish novelist, physician, spiritualist. His fictional detective, Sherlock Holmes, emulates the scientist, diligently searching through data and to make sense of it. "It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts." *TIS

1942 William Henry Young (London, 20 October 1863 - Lausanne, 7 July 1942) discovered Lebesgue integration, independently but 2 years after Lebesgue. He studied Fourier series and orthogonal series in general.*SAU

1975 William Hodge (17 June 1903 – 7 July 1975) studied at Edinburgh and Cambridge Universities. After some time at Bristol and in the USA he returned to Cambridge and became Lowndean Professor of Astronomy and Geometry. His main interests were in Algebraic Geometry and Differential Geometry. He became an honorary member of the EMS in 1954. He was knighted in 1959. *SAU His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and pertaining more generally to Kähler manifolds—has been a major influence on subsequent work in geometry. *Wik

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell