Depth beyond depth was revealed to me - the Byss and Abyss.

I saw - as one might see the transit of Venus or even the Lord Mayor's Show

- a quantity passing through infinity and changing its sign from plus to minus.

I saw exactly why it happened and why the tergiversation

was inevitable but it was after dinner

and I let it go.

The 124th day of the year;124 =σ( 1! * 2! * 4!) *Prime Curios (The **sigma function** of a positive integer *n* is the sum of the positive divisors of *n)*

124 is also an Odious number: a number with an odd number of 1's in its binary expansion.(just recently, it occurred to me that it would be more appropriate if an Odious number, had an odd number of "0's")

124 in base two is expressed as 1111100.

124 in base five is a repdigit, 444, which means it's one less than 5^3 (students new to studying bases should observe that a repdigit of (n-1) which is k units long in base n, will always be (n^k)-1. [like 99 in base 10 is 10^2-1]

and ±1 ± 2 ± 3 ± 4 ± 5 ± 6 ± 7 ± 8 ± 9 ± 10 ± 11 ± 12 = 0 has 124 solutions (collect the whole set) *Math Year-Round @MathYearRound

And for Algebra students, 124 is divisible by four so it is the difference of two squares of numbers that differ by 2, and since 124 / 4 = 31, the numbers must straddle 31, 32² - 30² = 124.

Several More math facts for this date at https://mathdaypballew.blogspot.com/

The Letters were written to the wealthy Augsburg Magistrate Mark Welser (1558-1614), a well-known patron of the new sciences, in responses to Christoph Scheiner's own Letters on Sunspots, published through Wesler in 1612.

Galileo and Scheiner were later to quarrel bitterly over priority of discovery of sunspots; in fact the first recorded sunspot observation is on 8 December 1610 by the Englishman Thomas Harriott (1560-1621), and the first publication by Johann Fabricius.

The title page of Galileo's letters, published by Wesler, is shown below. The lynx depicted on the Title page indicates Galileo's membership in the Lincean academy (Accademia dei Lincei, for the "sharp-eyed")

* |

**Groupe d\'astrophysique de l\'Université de Montréal**

1675 Charles II orders Royal Greenwich Observatory be built to solve Longitude problem. * Nat. Maritime Museum@NMMGreenwich

**1694**David Gregory and Newton disagree on "kissing numbers" during Gregory's visit to Newton in Cambridge. Newton asserted that 12 was the maximum number of spheres that could be placed touching around a central sphere. Gregory held out that a 13th was possible. Kepler had shown a completely rigid arrangement of 12 spheres around one in his Six-cornered Snow. His method is called a hexagonal packing. But Newton and Gregory both knew that placing the surrounding 12 spheres at the vertices of an icosahedron around the central sphere, there was enough space to move the balls around, In fact, any two balls could be moved around and interchanged while all twelve balls were still in contact with the central one. The maximum "kissing number" is known for the first four dimensions, but beyond that only the eighth (240) and twenty-fourth(196,560) are exactly known. *Plus Math, *Wik (Newton was right, but it wasn't proven until 1953.) If you want to take up the challenge, in the fifth dimension the "kissing number" is known to be 40 <= k <=44.

**1756**A letter from John Elliot, a young naval officer, to his father.

"There is no News here worth troubling you with, only the discovery of the longitude by a Hanovarien, it is perform’d by an Observation of the Moon & any fix’d Star by knowing there distance at a given place & observing there diff[erence]e at Sea given the difference of time[. T]he obs[ervatio]n is simple & easey but the Calculation is extreamly perplexd. I had this from a Man that is making the Instrument."

The Hanovarien mentioned is Tobias Mayer. *Richard Dunn, Board of Longitude Project, Royal Museums Greenwich

**1780**The American Academy of Arts and Sciences, the ﬁrst national arts and sciences society in the U.S., was founded on this date in Boston “to cultivate every art and science which may tend to advance the interest, dignity, honor and happiness of a free, independent and virtuous people.” James Bowdoin was the ﬁrst president. *VFR [The original incorporaters were later joined by Benjamin Franklin, George Washington, Thomas Jefferson, Charles Bulfinch, Alexander Hamilton, and John Quincy]*TIS

**1925**The ACLU found John Scopes by running a newspaper ad seeking a teacher willing to test the law about teaching human evolution in the classrooms of Tennessee. From the May 4, 1925, edition of the

*Chattanooga Times*:

**1933**, the discovery of radio waves from the centre of the Milky Way galaxy was described by Karl Jansky in a paper he read to the International Radio Union in Washington. The galactic radio waves were very low intensity, short wavelength (14.6 m, frequency about 20 MHz) and required sensitive apparatus for their detection. Their intensity varied regularly with the time of day, and with the seasons. They came from an unchanging direction in space, independent of terrestrial sources. He had conducted his research on static hiss at the radio research department of Bell Telephone Labs, Holmdel, N.J. The New York Times carried a front page report the next day.*TIS

First Radio Telescope |

**1935**Albert Einstein, in a letter to the New York Times, writes, "In the judgement of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began". *Dwight E. Neuenschwander, Emmy Noether's Wonderful Theorem

*Wik |

**1989,**the space probe Magellan was carried in the cargo bay by the STS-30 Space Shuttle Atlantis mission launched from Kennedy Space Center in Florida. The space probe was named after the 16th-century Portuguese explorer Ferdinand Magellan. This was the first planetary spacecraft to be released from a shuttle in Earth orbit. It arrived at its planned polar orbit around Venus on 10 Aug 1990, which it circled once every 3-hr 15-min. As the planet rotated slowly beneath it, Magellan collected radar images of the surface in strips about 17-28 km (10-17 mi) wide and radioed back the information. Its mission included taking other measurements. On 11 Oct 1994, it was directed towards the surface, collecting data until it burned up in the atmosphere.*TIS

1995 Commodore Bought By German Company:

German electronics company Escom AG paid $10 million for the rights to the name, patents and intellectual property of Commodore Electronics Ltd. A pioneer in the personal computer industry, Commodore halted production in 1994 and declared bankruptcy. Escom AG planned to resume production of Commodore personal computers, including its most recent model, the Amiga. The company later sold its Amiga rights. *CHM

*Wik |

**2000**A rare conjunction occurs on the New Moon including all seven of the traditional celestial bodies known from ancient times up until 1781 with the discovery of Uranus. The May 2000 conjunction consisted of: the Sun and Moon, Mercury, Venus, Mars, Jupiter, and Saturn. *Wik

2011 Star Wars Day, as told to me by a student..."May the Fourth be with you."

**1733 Jean-Charles Borda**, (4 May 1733; died 20 Feb 1799 at age 65.) a major ﬁgure in the French navy who participated in several scientific voyages and the American revolution. Besides his contributions to navigational instruments he did important work on ﬂuid mechanics, even showing that Newton’s theory of ﬂuid resistance was untenable. He is best known for the voting system he created in 1770.*VFR [He was one of the main driving forces in the introduction of the decimal system. Borda made good use of calculus and experiment to unify areas of physics. For his surveying, he also developed a series of trigonometric tables. In 1782, while in command of a flotilla of six French ships, he was captured by the British. Borda's health declined after his release. He is one of 72 scientists commemorated by plaques on the Eiffel tower.]*TIS

**1821 Pafnuty Lvovich Chebyshev**(May 16 [O.S. May 4] 1821 – December 8 [O.S. November 26] 1894)Russian mathematician who founded the St. Petersburg mathematical school (sometimes called the Chebyshev school), who is remembered primarily for his work on the theory of prime numbers, including the determination of the number of primes not exceeding a given number. He wrote about many subjects, including the theory of congruences in 1849, probability theory, quadratic forms, orthogonal functions, the theory of integrals, the construction of maps, and the calculation of geometric volumes. Chebyshev was also interested in mechanics and studied the problems involved in converting rotary motion into rectilinear motion by mechanical coupling. The Chebyshev parallel motion is three linked bars approximating rectilinear motion. *Wik [I remember a poem about the Chebyshev's theorem first conjectured by Bertrand but proved by Chebyshev.... Chebyshev said it, so I'll say it again, there's always a prime, between N and 2N {there are many variants} PB]

**1845William Kingdon Clifford**(4 May 1845 – 3 March 1879 ) He played an important role in introducing the ideas of Riemann and other writers on non-Euclidean geometry to English mathematicians. “Clifford was a ﬁrst-class gymnast, whose repertory apparently included hanging by his toes from the crossbar of a weather cock on a church tower, a feat beﬁtting a High Churchman, as he then was.” *VFR

English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honor, with interesting applications in contemporary mathematical physics and geometry. He was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression "mind-stuff". *Wikipedia {He enjoyed children and wrote children's stories including "The Little People."} "An atom must be at least as complex as a grand piano. "

Though Clifford never constructed a full theory of spacetime and relativity, there are some remarkable observations he made in print that foreshadowed these modern concepts: In his book Elements of Dynamic (1878), he introduced "quasi-harmonic motion in a hyperbola". He wrote an expression for a parametrized unit hyperbola, which other authors later used as a model for relativistic velocity. Elsewhere he states,

The geometry of rotors and motors ... forms the basis of the whole modern theory of the relative rest (Static) and the relative motion (Kinematic and Kinetic) of invariable systems.

This passage makes reference to biquaternions, though Clifford made these into split-biquaternions as his independent development. The book continues with a chapter "On the bending of space", the substance of general relativity. Clifford also discussed his views in On the Space-Theory of Matter in 1876.

1862 Alice Liddell (4 May 1852 – 16 November 1934), subject of the Alice in wonderland stories. 4 May is also probably the date on which the mad hatter's tea party took place. Charles Wells suggested to me that perhaps that was the date on which young Alice and Charles Dodgson went for a row with her dad and Dodgson first told the tale. There are, Charles points out, two references to the date being the fourth (the white rabbit for instance has a watch that tells the date, not the time and asks Alice the date) and two referring to the month of May . It turns out that that boat ride was on July 4 of 1862. There is however evidence in the book that Dodgson intended to make the story on Alice's date of birth. In that year, for example, the date of her birth there was exactly two days difference between solar and lunar time. Thus the Hatter's response to the date, "Two days wrong" perhaps. Anyway, a novel idea (bad pun) Charles, and thanks for the comment.

**1876 Heinrich Jung**(4 May 1876 in Essen, Germany - 1953 in Halle, Germany) was a German mathematician who worked on algebraic functions. *SAU

**1926 David Allan Bromley**(4 May 1926; 10 Feb 2005 at age 78) was a Canadian-American physicist who was considered the “father of modern heavy ion science” for his pioneering experiments on both the structure and dynamics of atomic nuclei. He was a leader in developing particle accelerators detection systems and computer-based data acquisition and analysis systems. While at Atomic Energy of Canada (1955-60) he installed the first tandem Van Der Graaff accelerator. He was founder and director (1963-89) of the A.W. Wright Nuclear Structure Laboratory at Yale University, which has produced more experimental nuclear physicists than any other facility. During this time he became active on numerous national and international science policy boards. From 1980-89, he was a member of the White House Science Council.*TIS

**1615 Adriaan van Roomen**(29 September 1561 – 4 May 1615) One of Roomen's most impressive results was finding π to 16 decimal places. He did this in 1593 using 230 sided polygons. Roomen's interest in π was almost certainly as a result of his friendship with Ludolph van Ceulen.*SAU [van Roomen posed a problem to solve a 45th degree polynomial set equal to a complex square root with another square root inside it (here). Viete solved the equation establishing the use of trigonometry as a tool in algebraic solutions. ] {van Roomen also found a new solution to the classic Problem of Apollonius but it was not a "classic" construction in that it could not be done with only a straightedge and compass. Gergone (see below) found a proof that was constructable with the classic tools.}

**1677 Isaac Barrow**(Oct 1630, 4 May 1677) died of an overdose of drugs probably opium. Neil Middlemiss pointed out that the original source of this information may be Aubrey's "Brief Lives" wherein he claims, "his pill (an opiate)...he took it excessively at Mr. Wilson's...and 'twas the cause of his death."

Barrow had taken opiates with fasting previously in Constantinople when suffering from fever. Over dosing on opiates may have been somewhat common in the period, a tweet from

**HookesLondon**casually mentions another in 1672:" Colwall at Garways. Mr Chamberlain told of Lady Viners death kild by opium."

Isaac Barrow was an English Christian theologian, and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's, and Newton went on to develop calculus in a modern form. In 1662 he was made professor of geometry at Gresham College, and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge. During his tenure of this chair he published two mathematical works of great learning and elegance, the first on geometry and the second on optics. In 1669 he resigned his professorship in favor of Isaac Newton . *Wik

I just learned from a tweet from @mathshistory that Barrow was the "first to recognize that integration and differentiation are inverse operations" He is buried in the Chapel at Trinity College.

**1859 Joseph Diaz Gergonne**(19 June 1771 Nancy, France—4 May 1859 Montpellier, France)... Finding problems getting his mathematics papers published, Gergonne established his own mathematics journal, the first part appearing in 1810. The Journal was officially called the Annales de mathématiques pures et appliquées but became known as Annales de Gergonne . Gergonne's mathematical interests were in geometry so it is not surprising that it was this topic which figured most prominently in his journal. In fact many famous mathematicians published in the twenty-one volumes of the Annales de Gergonne which appeared during a period of twenty-two years. In addition to Gergonne himself (who published around 200 articles), Poncelet, Servois, Bobillier, Steiner, Plücker, Chasles, Brianchon, Dupin, Lamé, Galois and many others had papers appear in the Journal. Gergonne provided an elegant solution to the Problem of Apollonius in 1816. This problem is to find a circle which touches three given circles. Gergonne introduced the word polar and the principle of duality in projective geometry was one of his main contributions. *SAU

**1936 Alfred Cardew Dixon**(22 May 1865 in Northallerton, Yorkshire, England - 4 May 1936 in Northwood, Middlesex, England) Alfred Dixon graduated from London and Cambridge and then had professorial appointments in Galway and Belfast. He worked on ordinary and partial differential equations. *SAU

**1961 Herbert Westren Turnbul**(31 Aug 1885, l4 May 1961 at age 75). English mathematician who made extensive and notable contributions to the study of algebraic invariants and concomitants of quadratics. Turnbull was also interested in the history of mathematics, writing The Mathematical Discoveries of Newton (1945), and began work on the Correspondence of Isaac Newton. *TIS

**1974 Otton Marcin Nikodym**(13 Aug 1887 in Zablotow, Galicia, Austria-Hungary (now Ukraine) - 4 May 1974 in Utica,New York, USA) On 2 April 1919, the Polish Mathematical Society was founded by sixteen mathematicians - among them Otton Nikodym. In 1924, under strong pressure from Sierpinski, Nikodym agreed to take his doctoral examination at Warsaw University. It seems he did not care much for the title or publication - his response to Sierpinski's persuasion was, "Am I going to be any wiser because of that?"

Nikodym's name is mostly known in measure theory (e. g. the Radon-Nikodym theorem and derivative, the Nikodym convergence theorem, the Nikodym-Grothendieck boundedness theorem), in functional analysis (the Radon-Nikodym property of a Banach space, the Frechet-Nikodym metric space, a Nikodym set), projections onto convex sets with applications to Dirichlet problem, generalized solutions of differential equations, descriptive set theory and the foundations of quantum mechanics. *SAU

**2001 Anne Anastas**i (19 Dec 1908, 4 May 2001 at age 92) American psychologist known as the "test guru," for her pioneering development of psychometrics, the measurement and understanding of psychological traits. Her seminal work, Psychological Testing (1954), remains a classic text in the subject. In it, she drew attention to the ways in which trait development is influenced by education and heredity. She explored how variables in the measurement of those traits include differences in training, culture, and language. In 1972, she became the first woman to be elected president of the American Psychological Association in half a century. For her accomplishments, she was awarded the National Medal of Science in 1987.*TIS

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

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