Thursday 16 May 2024

On This Day in Math - May 16


To isolate mathematics from the practical demands of the sciences
is to invite the sterility of a cow shut away from the bulls.

Pafnuty Chebyshev
Quoted in G Simmons, Calculus Gems (New York 1992)

The 136th day of the year; 136 is the sum of the cubes of the digits of the sum of the cubes of its digits. (13 + 33 + 63 = 244 and 23 + 43 + 43 = 136) *Tanya Khovanova, Number Gossip (Only one other number pair share this relation. Can you find them?)

The sum of all prime factors of 136 is equal to the reversal of \( \pi(136)\). \( \pi(n)\) is the number of primes less than n (so \( \pi(136)=32 \) and the sum of the prime factors of 136 is 2+2+2+17 =23)

136 is the sum of the first 16 numbers, the numbers in a four by four magic square. It is the magic square associated with the planet Jupiter,and appears in the Albrecht Durer woodcut, "Melancholia I," on the wall behind the suffering "thinker." Some suggest it was there to represent the association of Jupitar (Jovia) and joviality to balance the mood of the work.

As the sum of the first 16 integers, it is a triangular number, but it also the sum of three triangular numbers.  It is the last year day with this quality.

In binary 136 is written as the concatenation of two binary "Eights".  (10001000).  In base 9 is a palindrome (161) and in Hexdecimal it is a repdigit (88).  

Lots of numbers are expressible as the sum of two squares, but 136 is the smallest that can be expressed  where neither of the two are squares of a prime. (136 = 10^2 + 6^2) *Prime Curios

136 is the number of walks of length 9 between two adjacent vertices in the cycle graph C_8 (A,B,C,D,E,F,G,H)
See More Number facts at Math Day of the Year Facts


1571 Johannes Kepler was conceived at 4:37 a.m. on his parents’ wedding night, according to his computations for his own horoscope. His actual date of birth is more certain, Dec 17th of the same year. He was born in Weil der Stadt, about 20 km west of Stuttgart, There is a museum in the Marketplatz that claims to be his birthplace, but the building seems to only date to about 1648.

1667 " the course of attempting to conceive of the physical laws that would explain how the Moon revolved around the Earth, Newton happened to be sitting near the apple tree in the garden at Woolsthorpe when he saw an apple drop to the ground. At that moment, he realized that the same central pull of the Earth applied to both objects. *Brody & Brody, The Science Class You Wish You Had
On April 15, 1726, writer William Stukeley held a conversation with Isaac Newton in Kensington during which Newton recalled “when formerly, the notion of gravitation came into his mind.” Later, Stukeley writing in his Memoirs of Sir Isaac Newton's Life, recorded that Newton said, “It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth's centre.” *TIS The story was also related to John Conduitt who was Newton's assistant at the Royal mint, and the husband of Newton's niece. The idea that the apple hit Newton on the head seems to date from the early 20th Century. A copy of the page of Stukeley's manuscript where he tells this story is available on-line at the Royal Society.

1678  Hooke records in his diary that he has been performing experiments on mercury barometers at the Great Fire memorial on Fish St.  "It descended at the top by about 1/3 of an inch." *Lisa Jardine, Ingenious Pursuits pg 78

1695 Leibniz, in a letter to Johann Bernoulli, tells of his discovery of the multinomial theorem, “a wonderful rule for the coefficients of powers not only of the binomial x + y, but also of the trinomial x + y + z, in fact, of any polynomial.” [Smith, Source Book, p. 229]*VFR
This allows us to find terms of the expansion of, say, (x+y+z)6 and show that the term with x3y2z will have a coefficient of

1713 John Machin was appointed as Professor of Astronomy at Gresham College, London. He succeed Dr Torriano and went on to hold the chair until his death 38 years later. *SAU  He is best known for developing a quickly converging series for pi in 1706 and using it to compute pi to 100 decimal places.  To compute π to 100 decimal places, he combined his formula with the Taylor series expansion for the inverse tangent. (Brook Taylor was Machin's contemporary in Cambridge University.) Machin's formula remained the primary tool of pi-hunters for centuries (well into the computer era).

1800 Gauss records in his diary “On about these days (May 16) we most elegantly resolved the problem of the chronology of the Easter Feast.” [Gray, Expositiones Mathematicae, 2(1984), 97–130] *VFR

1876, root beer was invented by Charles Elmer Hires.  it is the longest continuously made soft drink in the United States.   I'll drink to that!

1910 Halley's comet was big news during its visible period in New York City. Beginning with the Saturday edition of May 14 and continuing on through the Sunday edition of May 22, the comet was given top billing in the New York Times. This was the period when the comet was at the height of its brilliance and activity and the coverage clearly reflected this.
May 16: European and American astronomers agree Earth will not suffer from passing through comet’s tail. *Joseph M. Laufer, Halley's Comet Society - USA

1931 Einstein visited Oxford University to give the Rhodes Lectures, and receive a degree. During his talks, one of his blackboards was preserved and is now stored in the Museum of the History of Science in Oxford. The calculations are related to what is now called the Friedman-Einstein model of the universe.

The numerical estimates of cosmic parameters in Einstein’s 1931 paper – and on the blackboard – contain a systematic error. Analysis of the 1931 paper shows that, given the contemporaneous Hubble constant of 500 km s−1Mpc−1, Einstein's estimates of cosmic density, radius and timespan should have been ρ ~ 10−28 g/cm3, P ~ 108 light-years and t ~ 109 years respectively. One line on the blackboard, not included in the published paper, makes the nature of Einstein's error clear. In the fourth line on the blackboard, Einstein obtains a value of 10−53 cm−2 for the quantity D2, defined in the top line of the blackboard as D = (1/c). (1/P).(dP/dt), i.e., the Hubble constant divided by the speed of light. Simple calculation shows that the contemporaneous value of the Hubble constant in fact implied a value of D2 ~ 10−55 cm−2 (or 10−51 m−2) for this quantity. It appears that Einstein stumbled in converting megaparsecs to cm, giving a density of matter that was too high by a factor of a hundred, a cosmic radius that was too low by a factor of ten, and a timespan for the expansion that was too high by a factor of ten. These errors were corrected in a later review of relativistic cosmology written by Einstein in 1945. *Wik

1940 Dr. H. J. Spinden reported the decipherment of Mayan relics in Mexico indicate a civilization 1250 years in advance of Europe in astronomy and mathematics.

1960 "VoilÁ. that Was It! The Laser was Born!" words Hughes Research Laboratories' physicist Dr. Theodore Maiman used in recounting the historic moment he and fellow researchers Drs. Irnee D'Haenens and Charles Asawa's synthetic ruby laser produced light pulses that steadily increased in brightness as the simple, yet revolutionary, device was powered up. "The output trace started to shoot up in peak intensity and the initial decay time rapidly decreased," he recalled. *Hughes Research Lab Web page.

2005 President George W Bush announced that Lenore Blum was one of the recipients of the 2004 Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring. The citation reads:-

"Lenore Blum of Carnegie Mellon University helped pioneer the Expanding Your Horizons program at Mills College in 1973. The program - designed to introduce young female students to women in science and related careers - has since gone national through the Math/Science Network. Blum's leadership has also been instrumental in transforming the culture of computing at Carnegie Mellon to embrace diversity as critical for the field and future of our nation and by creating a model mentorship organization, Women@SCS, for women students in computer science."

2014  Google celebrates the anniversary of the birth of Maria Gaetana Agnesi (below) .


1718 Maria Gaetana Agnesi (May 16, 1718 – January 9, 1799)  Her Istituzioni analitiche of 1748 was an important calculus text. Her name is most often associated with the cubic curve called the Witch of Agnesi, which gets its name by mistranslation. Her sister Maria Teresa was a noted composer.*VFR
For stat's students, I point out that the “witch” is also the same curve as Gossett’s t-distribution with only one degree of freedom. Find more on the history of the name “witch”. After the death of her father in 1752, Agnesi entirely devoted herself and spent her money to do charitable work. She died in total poverty in the poorhouse of which she had been the director. The MAA Digital Library has images of several pages from Istituzioni analitiche, including her illustration of the construction of "The Witch".  There is also a image of page 381 on which she clearly writes la versiera.

1804  Elizabeth Palmer Peabody, (May 16, 1804 – January 3, 1894) the educator who opened the first English-language kindergarten in the United States. Long before most educators, Peabody embraced the premise that children's play has intrinsic developmental and educational value. *Library of Congress 

1821 Pafnuty Lvovich Chebyshev (16  May 1821 (4 May OS) - 8 Dec 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. *TIS
(I always loved the little jingle by Nathan Fine, "Chebyshev said, and I say it again. There is always a prime between n and 2n.")
For an amusing article on how to spell Tschebyscheff, see The Thread (Birkhauser Boston) by Philip J. Davis, or an article with the same title in the Two-Year College Mathematics Journal, 14(1983), 98–104. *VFR

1925 Nancy Grace Roman (May 16, 1925..Nashville, Tennessee, U.S.-December 25, 2018 (aged 93)) was an American astronomer and one of the first female executives at NASA. She is known to many as the "Mother of Hubble" for her role in planning the Hubble Space Telescope. Throughout her career, Roman was also an active public speaker and educator, and an advocate for women in the sciences.
When Roman was eleven years old, she showed interest in astronomy by forming an astronomy club among her classmates in Nevada. She and her classmates got together once a week and learned about constellations from books. Although discouraged by those around her, Roman knew by the time she was in high school that she wanted to pursue her passion for astronomy. She attended Western High School in Baltimore where she participated in an accelerated program and was graduated in three years. *Wik

1934 Roy P(atrick) Kerr (16 May 1934 - )is a New Zealander mathematician who solved (1963) Einstein's field equations of general relativity to describe rotating black holes, thus providing a major contribution to the field of astrophysics. He deduced a unique two-parameter family of solutions which describes the space-time around black holes in July 1963. The two parameters are the mass of the black hole and the angular momentum of the black hole. (The static solution, with zero angular momentum, was discovered by Karl Schwarzschild in Dec 1915.) Rotating black holes are often called Kerr Black Holes. He showed that there is a vortex-like region outside the event horizon, called the ergo-region, that drags space and time around with the rotating black hole.*TIS  In 2023(?) Kerr argued that Penrose and Hawking were wrong in their description of singularities, and says "Singularities don't exist."

1950  Johannes Georg Bednorz ( born 16 May 1950, ) is a German physicist who, together with K. Alex Müller, discovered high-temperature superconductivity in ceramics, for which they shared the 1987 Nobel Prize in Physics.

In 1982, after obtaining his PhD, he joined the IBM lab. There, he joined Müller's ongoing research on superconductivity. In 1983, Bednorz and Müller began a systematic study of the electrical properties of ceramics formed from transition metal oxides, and in 1986 they succeeded in inducing superconductivity in a lanthanum barium copper oxide (LaBaCuO, also known as LBCO). The oxide's critical temperature (Tc) was 35 K, a full 12 K higher than the previous record. This discovery stimulated a great deal of additional research in high-temperature superconductivity on cuprate materials with structures similar to LBCO, soon leading to the discovery of compounds such as BSCCO (Tc 107K) and YBCO (Tc 92K).


1830 Baron Jean-Baptiste-Joseph Fourier (21 Mar 1768; 16 May 1830 at age 62) French mathematician, Egyptologist and administrator who exerted strong influence on mathematical physics through his Théorie analytique de la chaleur (1822; The Analytical Theory of Heat). He introduced an infinite mathematical series to aid in solving conduction equations. This analysis technique allows the function of any variable to be expanded into a series of sines of multiples of the variable, which is now known as the Fourier series. His equations spawned many new areas of study in mathematics and physics, including the branch of optics named for him, have subsequently been applied other natural phenomena such as tides, weather and sunspots.*TIS His work on heat was termed by Maxwell, “a great mathematical poem.” He traveled to Egypt with Napoleon and became convinced that desert heat was ideal for good health. Consequently, he wore many layers of garments and lived in rooms of unbearably high heat. This hastened his death, by heart disease, so that he died, thoroughly cooked. [Eves, History of Mathematics, 362] *VFR

He introduced an infinite mathematical series to aid in solving conduction equations. This analysis technique allows the function of any variable to be expanded into a series of sines of multiples of the variable, which is now known as the Fourier series. His equations spawned many new areas of study in mathematics and physics, including the branch of optics named for him, have subsequently been applied other natural phenomena such as tides, weather and sunspots.*TIS Fourier was buried in the Pere Lachaise Cemetery in Paris in a tomb decorated with an Egyptian motif.

1935 Hector Munro Macdonald (19 Jan 1865 in Edinburgh, Scotland - 16 May 1935 in Aberdeen, Scotland) Macdonald graduated from Aberdeen and Cambridge Universities. He stayed on at Cambridge and won the Adams prize. He returned to Aberdeen as Professor. He did important work on electromagnetic waves. *SAU

1943 Roberto Marcolongo (August 28, 1862 in Rome – May 16, 1943 in Rome) was an Italian mathematician , known for his research in vector calculus and theoretical physics .

He graduated in 1886, and later he was an assistant of Valentino Cerruti in Rome. In 1895 he became professor of rational mechanics at the University of Messina . In 1908 he moved to the University of Naples , where he remained until retirement in 1935.

He worked on vector calculus together with Cesare Burali-Forti , which was then known as "Italian notation". In 1906 he wrote an early work which used the four-dimensional formalism to account for relativistic invariance under Lorentz transformations .

In 1921 he published to Messina one of the first treaties on the special relativity and general, where he used the absolute differential calculus without coordinates, developed with Burali-Forti, as opposed to the absolute differential calculus with coordinates of Tullio Levi-Civita and Gregorio Ricci-Curbastro .

He was a member of the Accademia dei Lincei and other Italian academies.

1983 Edouard Zeckendorf (2 May 1901 in Liège, Belgium - 16 May 1983 in Liège, Belgium)

Eduourd Zeckendorf was an amateur mathematician whose name is given to the property that every positive integer can be represented uniquely as the sum of non-consecutive Fibonacci numbers, the sequence defined by
F1 = F2 = 1 and Fn = Fn-1 + Fn-2 for n greater than 2.
This is called Zeckendorf's theorem, and the subsequence of Fibonacci numbers which add up to a given integer is called its Zeckendorf representation. (Because F1F2, we need to exclude F1 from the representation to give uniqueness.) For example,
71 = 55 + 13 + 3,
1111 = 987 + 89 + 34 + 1.
Zeckendorf qualified as a medical doctor, became an officer in the Belgium army in 1925 and subsequently also qualified as a dentist. Following the surrender of the Belgium army in May 1940 Zeckendorf was interned as a prisoner of war until 1945. He subsequently published several mathematical papers, nearly all of them in the Bulletin de la Société Royale des Sciences de Liège, mainly on elementary number theory.


1995 Raymond Arthur Lyttleton(May 7, 1911 – May 16, 1995) English mathematician and theoretical astronomer who researched stellar evolution and composition. In 1939, with Fred Hoyle, he demonstrated the large scale existance of interstellar hydrogen, refuting the existing belief of that space was devoid of interstellar gas. Together, in the early 1940's, they applied nuclear physics to explain how energy is generated by stars. In his own mongoraph (1953) Lyttleton described stability of rotating liquid masses, which he extended later to explain that the Earth had a liquid core resulting from a phase change associated with a combination of intense pressure and temperature. With Hermann Bondi, in 1959, he proposed the electrostatic theory of the expanding universe. He authored various astronomy books. *TIS

2013  Heinrich Rohrer (6 June 1933 – 16 May 2013) was a Swiss physicist who shared half of the 1986 Nobel Prize in Physics with Gerd Binnig for the design of the scanning tunneling microscope (STM). The other half of the Prize was awarded to Ernst Ruska. Ruska's electron microscope of the 1930s was unable to show surface structure at the atomic level. Rohrer and Binnig began work in 1978 on a scanning tunneling microscope in which a fine probe passes within a few angstroms of the surface of the sample. A positive voltage on the probe enables electrons to move from the sample to the probe by the tunnel effect, and the detected current can used to keep the probe at a constant distance from the surface. As the probe moves in parallel lines, a 3D image of the surface can be constructed.

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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