## Saturday 27 May 2023

### On This Day in Math - May 27

The mathematics are distinguished by

a particular privilege, that is,

in the course of ages, they may always advance

and can never recede.

~Edward Gibbon, Decline and Fall of the Roman Empire

The 147th day of the year; if you iterate the process of summing the cubes of the digits of a number starting with 147, you eventually start repeating 153. This seems to be true for all multiples of three.

from Das Ambigramm, 147 = 4+5+6..... + 16 + 17 = 18+19+...+ 23+24.

147 is the sum of two Fibonacci numbers, F(12) + F(4 )= 144 + 3 = 147

And 147 = 14^2 - 7^2

If there are no fouls, the maximum score on a snooker break is 147.

And Derek Orr@Derektionary pointed out that "147 is the smallest number formed by a column of numbers on a phone button pad"

147 in binary has an equal number of zeros and ones.

The binary form of 147 (10010011) contains all the two-digit binary numbers (00, 01, 10 and 11).

More math facts for every day of the year here.

EVENTS

669 BC "If the Sun at its rising is like a crescent and wears a crown like the Moon: the king wll capture his enemy's land; evil will leave the land, and (the land) will experience good . . . " Refers to a solar eclipse of 27 May 669 BC. BY Rasil the older, Babylonian scribe to the king. *NSEC

1638  In a letter to Fr Marin Mersenne, Descartes claimed to have a general rule to find  number n with a sum of its factors S(n) given only the ratio of n:S(n) = p/q.  He showed that n:S(n) = 4/9 is solved for n= 360 .  Fermat responded to Mersenne that 2016 has the same property.. (for students, S(6) would = 1+2+3+6 = 12
1n 1557 Robert Recorde had observed that the aliquot parts of the number 120, add up to 240.  Eventually these multiply perfect numbers would become labled $P_3$ (since the sum of all its divisors, including the number itself, would sum to three times the original number).  Mersenne would write to Descartes in 1631, asking if a second such $P_3$ could be found.  After a seven year wait, Descartes responded in Sept. of 1637 with $P_3 = 673 = 2^5*3*7$. Mersenne would respond that Fermat had a method of finding many such numbers, and had also found 673.  The third $P_3 =523776 = 2^9 * 3 * 11 * 31$ was presented in a letter to Mersenne by Andre Jumeau, the Prior of St. Croix..  In his letter he challenged Descartes to find the fourth.
In his reply on this date, Descartes said that Fermat's rule would provide no other solutions than 120 and 673 .  He then proceeds to give the fourth, $P_3 = 1476304896 = 2^{13} * 3 * 11 * 43 * 127$ .

Soon after Descartes gave six $P_4$  :

$P_4$(1)  =  30240; $P_4$(2)  =32760 ; $P_4$(3) =23569920; $P_4$(4)  =  142990848; $P_4$(5)>  =  66433720320; $P_4$(6)  =403031236608 .
(*History of the theory of numbers  By Leonard Eugene Dickson)

1641 Descartes writes to Fr Mersenne again, which was not unusual. The letter wasn't really about math, but about changing his mind about some old disagreements with other philosophers. But then the story got interesting. After Mersenne’s death in 1648, the letter became the property of the French mathematician Gilles de Roberval. When he died in 1675, the French Academy of the Sciences watched over the document for more than a century, until it was stolen by count Guglielmo Libri (1803-1869), a notorious kleptomaniac.

An American collector, Charles Roberts (1846-1902), purchased the letter at an auction in the UK. After his death, he bequeathed his collection to his fellow Quakers at Haverford College.

The previously unknown letter was found by Erik-Jan Bos, a Dutch Historian, through Google. “I regularly browse online. A month ago, I was on one of my little forays when I stumbled upon something I hadn’t seen before.” The document Bos found was a summary of autographs (handwritten, signed texts) that mentioned the letter. The collection the summary referred to is the property of a Quaker-run college in Haverford, Pennsylvania. “They didn’t know this letter had never been published before,” Bos said. The newly discovered letter is only the third by Descartes found in the last 25 years.

When the college learned the letter had been stolen it decided to return it to it former owners. It has since transferred the letter to the French Institute, of which the Academy of the Sciences is a part. *Guardian, *Haverford College

1762 Benjamin Franklin writes to Sir John Pringle, who would become president of the Royal Society in 1772 and physician to King George III in 1774 with a map first naming the "Gulph Stream."

Boston customs officials observed a two-weeks’ difference in the arrival times of ships sailing east to west from England to New York versus England to Rhode Island. He consulted a cousin, Nantucket mariner Timothy Folger, about the problem. Folger was certain that the Gulf Stream was the culprit, for Rhode Island captains were aware of the current through their whaling activities, whereas those of the English packet boats were not. Franklin asked Folger to add the location and dimensions of this current to an available chart so that he could communicate the information to the English sea captains.
Published in England circa 1768, the map was mostly ignored by the stubborn English navigators. Though few copies of this English version seem to have survived (Library of Congress has one), Franklin also had the chart printed in France around 1785, and he published it again with his article “Sundry Maritime Observations” in the Transactions of the American Philosophical Society in 1786. However, it took a long time before the British followed Franklin’s advice on how to avoid fighting this current.

*princeton.edu

1832 In a letter to Legendre, Jacobi stated that the solutions to x2-ay2=1 can be expressed in terms of the sine and cosine of

1849 On this day in 1849, Pafnuty Chebyshev defended his doctoral number theory dissertation The Theory of Congruences at St Petersburg University. This work received a prize from the Academy of Sciences. *MacTutor

1919 Astronomical party arrives at  São Tomé and Príncipe, officially the Democratic Republic of São Tomé and Príncipe, is a Portuguese-speaking island nation in the Gulf of Guinea, off the western equatorial coast of Central Africa.  Príncipe was the site where astronomical observations of the total solar eclipse of 29 May 1919 confirmed Einstein's prediction of the curvature of light.  The expedition was sponsored by the Royal Society and led by Sir Arthur Stanley Eddington.

Eddington sent one team to Sobral in Brazil, and went himself went to the African island of Príncipe. Stars in the Hyades cluster were behind the sun during the eclipse, and were appeared to shift from their true positions by 1.75 arcseconds. This gravitational deflection of light by the sun's mass provided the first experimental verification of Albert Einstein's theory of general relativity.

1937 Golden Gate bridge opened.*VFR In 1937, the Golden Gate Bridge, San Francisco was first opened to the public as a Pedestrian Day. By 6 am, 18,000 people were waiting for the toll gates to open. Many crossed in unique ways, hoping to be prize-winners as the first to establish a record, whether by walking backwards or on stilts, tap-dancing, roller-skating or playing instruments. It was a sprinter, Donald Bryan, from San Francisco Junior College, who became the first person to cross the entire span. At 10 am, Chief engineer Joseph Strauss gave no speech, but instead read a poem he had written for the event. By the end of the day, about 200,000 people had joined the celebration. The bridge was ceremonially opened to traffic the next day.*TIS

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2020  Today’s Doodle, illustrated by Chile-based guest artist Pablo Luebert, celebrates the 95th birthday of a luminary ambassador of the southern night sky: Chilean astrophysicist, author, and professor Adelina Gutiérrez Alonso. Light-years ahead of her time, she was the first Chilean to earn a doctorate in astrophysics, a pioneer not only in her field, but also for women scientists around the world.

Born in the Chilean capital of Santiago on this day in 1925, Carmen Adelina Gutiérrez Alonso was determined from a young age to become a science researcher and teacher. Her scientific career formally took off in 1949, when she joined the faculty at the University of Chile, home of the historic National Astronomical Observatory. In her early years, Adelina crunched data from distant stars, including that collected by her colleague Hugo Moreno León; the two eventually married and formed a fruitful partnership that resulted in a wealth of scientific publications.

But for Adelina, the sky wasn’t the limit. To further her exploration into the mysteries of the cosmos, she moved to the United States in the late 1950s. She graduated from the University of Indiana in 1964 with her unprecedented doctorate in astrophysics, and upon her return home, she helped to establish and lead the country’s first Bachelor of Astronomy program at her alma mater, the University of Chile.

In honor of her stellar scientific contributions, Adelina Gutiérrez Alonso became the first woman and astronomer inducted into the Chilean Academy of Sciences in 1967.

2021 Ray From Nowhere

On May 27, 2021, an ultrahigh-energy cosmic ray (UHECR) hit Earth’s atmosphere over Utah, sparking showers of subatomic secondary particles that rained down on ground-based detectors. The event measured an estimated 244 exa-electron volts (EeV) in energy, meaning this cosmic ray packed a wallop akin to a well-pitched baseball. Dubbed “Amaterasu” (the goddess of the sun in Japanese mythology) by its discoverers, this single UHECR was the most energetic particle seen on Earth in three decades.

Why this is interesting: Attempts to reconstruct Amaterasu’s path to Earth traced back to the Local Void, a barren expanse of intergalactic space bordering the Milky Way that lacks stars, galaxies and most anything else that could be the ray’s obvious astrophysical source. So where did it really come from? Researchers have no shortage of ideas. But for now no one can even say for sure whether this UHECR was a lightweight proton or something much heavier, like the nucleus of an iron atom—and the distinction matters for plotting Amaterasu’s precise cosmic trajectory, and thus its mysterious origins.

What the experts say: Perhaps Amaterasu’s source “just happens to be a galaxy where a star went fairly close to its supermassive black hole,” says Glennys Farrar, professor of physics at New York University. “I think that’s the most plausible explanation.”  *SciAm Today in Science

BIRTHS

1332 Ibn Khaldūn or Ibn Khaldoun (full name, Arabic: أبو زيد عبد الرحمن بن محمد بن خلدون الحضرمي‎, Abū Zayd ‘Abdu r-Raḥmān bin Muḥammad bin Khaldūn Al-Ḥaḍrami, May 27, 1332 AD/732 AH – March 19, 1406 AD/808 AH) was a Muslim historiographer and historian who is often viewed as one of the fathers of modern historiography,sociology and economics.
He is best known for his Muqaddimah (known as Prolegomenon in English), which was discovered, evaluated and fully appreciated first by 19th century European scholarship, although it has also had considerable influence on 17th-century Ottoman historians like Ḥajjī Khalīfa and Mustafa Naima who relied on his theories to analyze the growth and decline of the Ottoman Empire. Later in the 19th century, Western scholars recognized him as one of the greatest philosophers to come out of the Muslim world. *Wik

1660 Francis Hauksbee the elder (baptized on 27 May 1660 in Colchester–buried in St Dunstan's-in-the-West, London on 29 April 1713.), also known as Francis Hawksbee, was an 18th-century English scientist best known for his work on electricity and electrostatic repulsion.
Initially apprenticed in 1678 to his elder brother as a draper, Hauksbee became Isaac Newton’s lab assistant. In 1703 he was appointed curator, instrument maker and experimentalist of the Royal Society by Newton, who had recently become president of the society and wished to resurrect the Royal Society’s weekly demonstrations.
Until 1705, most of these experiments were air pump experiments of a mundane nature, but Hauksbee then turned to investigating the luminosity of mercury which was known to emit a glow under barometric vacuum conditions.
By 1705, Hauksbee had discovered that if he placed a small amount of mercury in the glass of his modified version of Otto von Guericke's generator, evacuated the air from it to create a mild vacuum and rubbed the ball in order to build up a charge, a glow was visible if he placed his hand on the outside of the ball. This glow was bright enough to read by. It seemed to be similar to St. Elmo's Fire. This effect later became the basis of the gas-discharge lamp, which led to neon lighting and mercury vapor lamps. In 1706 he produced an 'Influence machine' to generate this effect. He was elected a Fellow of the Royal Society the same year.

Hauksbee continued to experiment with electricity, making numerous observations and developing machines to generate and demonstrate various electrical phenomena. In 1709 he published Physico-Mechanical Experiments on Various Subjects which summarized much of his scientific work.
In 1708, Hauksbee independently discovered Charles' law of gases, which states that, for a given mass of gas at a constant pressure, the volume of the gas is proportional to its temperature.
The Royal Society Hauksbee Awards, awarded in 2010, were given by the Royal Society to the “unsung heroes of science, technology, engineering and mathematics.” *Wik

1862 John Edward Campbell (27 May 1862, Lisburn, Ireland – 1 October 1924, Oxford, Oxfordshire, England) is remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras. *SAU His 1903 book, Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups, popularized the ideas of Sophus Lie among British mathematicians.

He was elected a Fellow of the Royal Society in 1905, and served as President of the London Mathematical Society from 1918 to 1920. *Wik & *Renaissance Mathematicus

1967 Sir John Douglas Cockcroft (27 May 1897, 18 Sep 1967) British physicist, who shared (with Ernest T.S. Walton of Ireland) the 1951 Nobel Prize for Physics for pioneering the use of particle accelerators to study the atomic nucleus. Together, in 1929, they built an accelerator, the Cockcroft-Walton generator, that generated large numbers of particles at lower energies - the first atom-smasher. In 1932, they used it to disintegrate lithium atoms by bombarding them with protons, the first artificial nuclear reaction not utilizing radioactive substances. They conducted further research on the splitting of other atoms and established the importance of accelerators as a tool for nuclear research. Their accelerator design became one of the most useful in the world's laboratories. *TIS He was the first Master of Churchill College and is buried at the Parish of the Ascension Burial Ground in Cambridge, together with his wife Elizabeth and son John, known as Timothy, who had died at the age of two in 1929.*Wik

1907 Herbert Karl Johannes Seifert (May 27, 1907, Bernstadt – October 1, 1996, Heidelberg) was a German mathematician known for his work in topology. Seifert did other important work related to knot invariants. In 1934 he published results, using surfaces today called Seifert surfaces, which he used to calculate homological knot invariants. Another topic which Seifert worked on was the homeomorphism problem for 3-dimensional closed manifolds. *SAU

a Seifert surface is an orientable surface whose boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most easily calculated using a Seifert surface.

 *Wik

1925 Carmen Adelina Gutiérrez Alonso (aka Adelina Gutiérrez, May 27, 1925 – April 11, 2015) was a Chilean scientist, academic and professor of astrophysics. She was the first Chilean to obtain a doctoral degree in astrophysics and the first woman to become a member of the Chilean Academy of Sciences.

Gutiérrez began working as a science teacher at the Liceo Dario Salas and the Faculty of Physical and Mathematical Sciences (FCFM) of the University of Chile. From June 1, 1949, Gutiérrez worked at National Astronomical Observatory of Chile. At that observatory, her work was initially restricted to analyzing astronomical data obtained by other scientists. While working there, Gutiérrez developed an interest in the photoelectric photometry of austral stars, a subject which she addressed in numerous publications. During the time that she was working at the National Astronomical Observatory, Gutiérrez also became a full faculty member in Faculty of Physical and Mathematical Sciences of the University of Chile.

In the late 1950s, Gutiérrez traveled to the United States to study for a PhD in astrophysics, which has obtained in June 1964, becoming the first Chilean to obtain such a degree. In 1965, after having returned to Chile, Gutiérrez, Hugo Moreno León and Claudio Anguita founded a bachelor's degree course in astronomy at the University of Chile. Gutiérrez was responsible for overseeing the course. In 1976, Gutiérrez also founded a master's degree course in astronomy at the University of Chile.

In 1967, Gutiérrez began working with Hugo Moreno León in the newly opened Cerro Tololo Observatory. That same year she was named a full member of the Chilean Academy of Sciences Institute. She was the first woman and the first astronomer to join that select group of scientists.

DEATHS

1896 Aleksandr Grigorievich Stoletov (August 10, 1839 – May 27, 1896) was a Russian physicist, founder of electrical engineering, and professor in Moscow University. He was the brother of general Nikolai Stoletov. By the end of the 20th century his disciples had headed the chairs of Physics in five out of seven major universities in Russia.
His major contributions include pioneer work in the field of ferromagnetism and discovery of the laws and principles of the outer photoelectric effect.*Wik

1928 Arthur Moritz Schönflies (April 17, 1853 – May 27, 1928) worked first on geometry and kinematics but became best known for his work on set theory and crystallography. He classified the 230 space groups in 1891 He studied under Kummer and Weierstrass, and was influenced by Felix Klein.
The Schoenflies problem is to prove that an (n − 1)-sphere in Euclidean n-space bounds a topological ball, however embedded. This question is much more subtle than initially appears. *Wik *SAU

1960  Milton B. Porter  Professor at Univ of Texas, he was the dissertation adviser for Goldie Horton, the first woman to get a PhD in Mathematics at Univ of Texas.  Eighteen years later he married her.  He died in Austin Texas.

1962 FELIX ADALBERT BEHREND (23 April 1911 in Charlottenburg, Berlin, Germany -27 May 1962 in Richmond, Victoria, Australia) Felix Behrend's sympathies within pure mathematics were wide, and his creativeness ranged over theory of numbers, algebraic equations, topology, and foundations of analysis. A problem that caught his fancy early and that still occupied him shortly before his death was that of finite models in Euclidean 3-space of the real projective plane. He remained productive for much of the two years of his final illness, and left many unfinished notes in which his work on foundations of analysis is continued. (From his obituary by B H Neumann)

1964 Colin Brian Haselgrove  (26 September 1926 – 27 May 1964) In 1958 Haselgrove published his most famous number theory result in A disproof of a conjecture of Pólya. The conjecture of Pólya claims that for every x greater than 1 there are at least as many numbers less than or equal to x having an odd number of prime factors as there are numbers with an even number of prime factors. R S Lehman and W G Spohn had verified the conjecture for all numbers x up to 800,000 but Haselgrove found a counterexample using methods based on those developed by Ingham with the help of computations carried out on the EDSAC 1 computer at Cambridge. He also verified the calculations using Manchester University's Mark I computer before publishing the results. In the same paper Haselgrove announced that he had also disproved a number theory conjecture of Turán. *SAU

2012 Friedrich Ernst Peter Hirzebruch (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as "the most important mathematician in the Germany of the postwar period.
Amongst many other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded him the Order of the Sacred Treasure in 1996. He also won an Einstein Medal in 1999, and received the Cantor medal in 2004.*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