Thursday, 28 May 2026

From Surds, to Ab-Surds

 




I still use the word surd for irrational square roots, and I know there is a undercurrent in modern math education to remove what is considered "difficult"  language in the classroom.  I leave that to those still fighting in the classroom to decide, but as a historian, the term is too rich in content not to use it, and teach itHence the title of From Surds, to Ab-Surds


When I first saw the image above I thought, Oh, that's neat. I mean I know it doesn't normally work, but then I also like the crazy wrong cancellations that work, such as


If you restrict yourself to two digit numbers, there are two more of these.  For folks who want to search them out, I will give the four at the bottom of the post.  
And in case you wondered, there are three digit examples also, and onward.  Here are a couple to get you started

\( \frac{106}{625}\),  ... \( \frac{116}{464}\),  ... and for variety \( \frac{98}{392}\),  ... 

 I know you were wondering, and yes,  it goes on... 
\( \frac{1019}{5095}\),  ... 

  I know there are lots more, so if you expand on this list, send me a note.  

As I sat and tried to think of other similar "wrong" examples that work with surds, I realized it might make a really good first or second year algebra challenge.  There is nothing very difficult about the algebra itself, so it allows the problem to be setting up the algebraic structure of the arithmetic problem.  


My early thoughts quickly generated enough to recognize a pattern to generate as many as I would want, *** 
 \( \sqrt {3 \frac{3}{8}} = 3 \sqrt{ \frac{3}{8}} \) 

*** or one in higher values.  For example:


 \( \sqrt {49 \frac{49}{2400}} = 49 \sqrt{ \frac{49}{2400}} \) 

  And in general it will always work in this form::

    \( \sqrt {n \frac{n}{n^2-1}} = n \sqrt{ \frac{n}{n^2-1}} \) 

Are there other patterns that would produce fractional oddities like these?  (Send them to me.)


I was reminded by Subramanian R that there is an easy extension of these to higher powers and roots .  For instance, the first problem can be adjusted to cube roots by using 2^3 -1 in the denominator.. 

 \(\sqrt[3](2 \frac{2}{7}) = 2 \sqrt[3](\frac{2}{7}) \)

 \(\sqrt[4](2 \frac{2}{15}) = 2 \sqrt[4](\frac{2}{15}) \)

And in general, \(\sqrt[r](k\frac{k}{k^r-1})= k\sqrt[r](\frac{k}{k^r-1})\)


********************************
The four two-digit false cancellations are 
\(\frac{16}{64}\)
\(\frac{19}{95}\)
\(\frac{26}{65}\)
\(\frac{49}{98}\)

On This Day in Math - May 28

  



Twice two makes four seems to me
simply a piece of insolence. 
Twice two makes four is a pert coxcomb who stands
with arms akimbo barring your path and spitting.
I admit that twice two makes four is an excellent thing,
but if we are to give everything its due,
twice two makes five is sometimes
a very charming thing too.  
~Fyodor Mikhailovich Dostoevsky


The 148th day of the year;  148 is a Palindrome in base 6(404) and base 36 (44).

 \(e^{\pi\sqrt{148}}\)   is an integer..... almost, 39660184000219160.00096667...

148 is also a Loeschian number, a number of the form a2 + ab + b2. These numbers and the triples (a,b,L) formed by points in space are used, among other places in locations of spheres under hexagonal packing.   
Voodooguru informed me that the Loeschian numbers are named after August Lösch,
 according to https://en.wikipedia.org/wiki/Loeschian_number. He was an economist:

"Overall, Lösch made a plenitude of significant findings in the world of economics, but his main contributions were to regional economics, specifically, pioneering the location theory, spatial equilibrium analysis and hierarchical spatial systems displaying a hexagonal pattern."
The Loeschian numbers are the norms of the Eisenstein integers that form a triangular lattice on the complex plane.  

If you let x and y be both be greater than 1, then x + xy + y will never equal 148.  And that means that the product of the first 148 integers is not divisible by the sum of the first 148 integers.

A Vampire number is a number whose digits can be regrouped into two smaller numbers that multiply to make the original (1260 = 21*60).  There are 148 vampire numbers with six digits.   (***How many with four digits?)  


More math facts for every day of the year here



EVENTS

585 BC Thales predicted the total eclipse of the sun that took place on this date. See Herschel, Outline of Astronomy (1902), pp. 833 and 839. [Eves, Circles, 33◦] *VFR  WW Rouse Ball says it is uncertain whether the date is the 585 date, or Sep 30, 609 BC.  Heath, and most others, seem to settle on the 585 BC date.


1555  On this day in 1555, John Dee   was arrested and charged with "calculating"  because he had cast horoscopes of Queen Mary and Princess Elizabeth. The charges were raised to treason against Mary. At this time mathematics in England was considered to be equivalent to the possession of magical powers. Aubrey writes that the authorities had:-

... burned mathematical books for conjuring books.

Although he was guilty of the charges brought against him, Dee was released in August after being held for three months.  *MacTutor  


Dee appeared in the Star Chamber and exonerated himself, but was turned over to the Catholic bishop Edmund Bonner for religious examination. His strong, lifelong penchant for secrecy may have worsened matters. The episode was the most dramatic in a series of attacks and slanders that dogged Dee throughout his life. Clearing his name yet again, he soon became a close associate of Bonner

John Dee memorial plaque installed in 2013 inside the church of St Mary the Virgin, Mortlake
*Wik



1607  Kepler used his newly devised camera obscura, which he named, to observe the solar disk and saw a sunspot, which he mistook for a transit of Mercury, to the amazement of later astronomers who all agreed that of all people, Kepler really should have known better. The first recorded mention of what was surely sunspots.  

   One year after the introduction of the telescope astronomers identified spots on the Sun. Fabricius was the first to print a book on sunspots at the end of 1611, but this book had little diffusion. Fabricius rightly thought that the spots belonged to the Sun. The Jesuit C. Scheiner independently observed sunspots on the Sun and he announced his discovery at the end of 1611 in three letters under the pseudonym Apelles. Scheiner failed to observe the returning of the spots and hence did not recognize the solar rotation. Therefore he preferred to see the spots as caused by little bodies orbiting the Sun. Based on Scheiner’s observations, Kepler concluded that the spots were on the solar surface like dross floating on melted metal. 

Scheiner drawings


1684   Robert Hooke delivered some of his most perceptive and far sighted views of the geology of what he called this "terraqueous globe"  in lectures beginning on May 28 and published posthumously.  In these lectures he shared ideas novel to his contemporaries, including "the organic origin, and significance of fossils; cyclicity of the processes of sedimentation,  erosion, consolidation, uplift, and denudation; various processes of petrifacation; subterraneous eruptions  and earthquakes; biologic evolution; the oblate spheroid shape of the Earth; Polar wandering, and universal gravitation. "  *Ellen Tan Drake; Hooke's Ideas of the Terraqueous  Globe and a Theory of Evolution




1765 The Longitude Board at Greenwich awards Leonhard Euler an amount of 300 Pounds, "Reward for Theorems furnished by him to assist Professor Mayer in the Construction of Lunar Tables upon the Principles of Gravitation laid down by Sir Isaac Newton."
Tobias Mayer had died in 1762, but his widow received an amount of 3000 Pounds for his work in the same meeting for his construction of the tables, which she signed over to the Committee. *Derek Howse, Britain's Board of Longitude:The Finances, 1714-1828


1783, Benjamin Franklin receives a letter at his hotel in Paris from Wolfgang von Kempelen, creator of the Turk chess playing automaton, inviting him to see and play his automaton as well as inspect the half-finished talking machine.
Franklin accepted the challenge, played the Turk a few days later at the Café de la Regence and lost. Although Franklin was a lover of chess, he does not mention this event in any of his recorded correspondence, perhaps, some explain, because he was known to be a very poor loser. *Tom Standage, The Turk, 2002 Walker Publishing

The Turk was in fact a mechanical illusion that allowed a human chess master hiding inside to operate the machine. With a skilled operator, the Turk won most of the games played during its demonstrations around Europe and the Americas for nearly 84 years, playing and defeating many challengers including statesmen such as Napoleon Bonaparte and Benjamin Franklin. The device was later purchased in 1804 and exhibited by Johann Nepomuk Mälzel. *Wik


*Bibliophilia ‏@Libroantiguo

1890  The Harvard Observatory distributed the “Henry Draper Memorial far and wide, including publication in Nature and other scientific journals. The report found one of its most appreciative audiences in England, at the home of astronomer and military engineer Colonel John Herschel. As a grandson of William Herschel (discoverer of the planet Uranus) and a son of Sir John Herschel (thrice president of the Royal Astronomical Society), the colonel had seen his share of important leaps in celestial knowledge. 

“I have just rec’d your last H. D. Mem. report,” he wrote to Pickering on May 28, 1890. “It is very like a pudding all plums—but I will ask you to convey to Miss Maury ( Antonia Maury  was an American astronomer who was the first to detect and calculate the orbit of a spectroscopic binary. She published an important early catalog of stellar spectra using her own system of stellar classification, which was later adopted by the International Astronomical Union) congratulations on having connected her name with one of the most notable advances in physical astronomy ever made.” Like the colonel’s much celebrated great-aunt, Caroline Herschel, Miss Maury had entered a field of discovery dominated by men, yet she stood among the first astronomers to detect an entirely new group of objects through the upstart method of spectral photography. Its future—and hers—seemed full of promise.”  *The Glass Universe: How the Ladies of the Harvard Observatory Took the Measure of the Stars by Dava Sobel



1897, Jell-o was introduced, 52 years after Peter Cooper (inventor of the Tom Thumb engine) held the first U.S. patent for a gelatine dessert. Pearl B. Wait, a carpenter and cough medicine manufacturer from LeRoy, N.Y., produced varieties in strawberry, raspberry, orange and lemon fruit flavours, named Jell-O by his wife, May Davis Wait. Sales were poor; Wait sold the Jell-O business for 450 dollars to his neighbor, Orator F.Woodward, who had founded the Genesee Pure Food Co. two years earlier. Success came slowly, but with Woodward's creative sales and sampling strategies, Jell-O began to catch on. In 1902, when he launched his first advertising campaign in Ladies' Home Journal, sales eventually reached 250,000 dollars*TIS

Most early Jell-O advertising featured women in starched white aprons, Jell-O packaging or the Jell-O Girl, Elizabeth King. King was photographed playing with Jell-O boxes until she grew too old for the ads. *mid-century menu 


Don't forget, "There's always room for Jello."




1936  Alan Turing submitted his paper ‘On Computable Numbers’,  in 1936.  His idea was not turned into a reality for more than ten years – when he would make a vital contribution to the Allied victory in the Second World War. *History Today

One Historian said his paper had no relation to his work at Bletchley Park.




In 1937, the Golden Gate Bridge, San Francisco was ceremonially opened to vehicles by President Franklin Delano Roosevelt who pressed a telegraph key in the White House. Within the first hour after the toll gates opened, 1,800 cars crossed the bridge. By day's end, 32,300 vehicles and 19,350 pedestrians had paid to pass over the bridge. A firework display that night celebrated the opening of the bridge. The previous day, a Pedestrian Day had been held which first opened the bridge for public use. The building and design of the bridge had been supervised by chief engineer Joseph B. Strauss. Construction had started on 5 Jan 1933. It was the first bridge to span the mouth of a major U.S. ocean harbour.*TIS

"Gentlemen, Start your engines!"



1959 Committee formed which developed COBOL. COBOL is one of the oldest programming languages. Its name is an acronym for COmmon Business-Oriented Language, defining its primary domain in business, finance, and administrative systems for companies and governments.
The COBOL specification was created by a committee of researchers from private industry, universities, and government during the second half of 1959. The specifications were to a great extent inspired by the FLOW-MATIC language invented by Grace Hopper - commonly referred to as "the mother of the COBOL language." The IBM COMTRAN language invented by Bob Bemer was also drawn upon, but the FACT language specification from Honeywell was not distributed to committee members until late in the process and had relatively little impact. FLOW-MATIC's status as the only language of the bunch to have actually been implemented made it particularly attractive to the committee.*Wik




1971, the U.S.S.R. Mars 3 was launched. It arrived at Mars on December 2, 1971. The lander was released from the Mars 3 orbiter and became the first spacecraft to land successfully on Mars. It failed after relaying 20 seconds of video data to the orbiter. The Mars 3 orbiter returned data until Aug 1972, sending measurements of surface temperature and atmospheric composition. The first USSR Mars probe was launched 10 Oct 1960, but it failed to reach earth orbit. The next four USSR probes, including Mars 1, also failed. The USA Mariner 3 Mars Flyby attempt in 1964 failed when its solar panels did not open. USA's Mariners 4, 6, and 7 successfully returned Mars photos. Also in 1971, the USSR Mars 2 lander crashed.*TIS




1981 The New Scientist (pp 506-507) describes a mathematical theory of how coloration develops in animals. Zebras have stripes rather that spots because coloring is determined at an early stage of the development of the fetus. [Mathematics Magazine 54 (1981), p 215.] *VFR


In 1998, NASA released a picture of what California astronomer Susan Terebey said may be the first extrasolar planet ever seen, dubbed TMR-1C. Digitized pictures taken by the Hubbell Space Telescope seemed to show an image of a planet apparently flung from a pair of young stars in the constellation Taurus, 450 light years from Earth. Located at one end of a bright trail that led from the newborn stars, the faint object appeared as if it was their offspring, a planet a few times as massive as Jupiter that had been expelled from its birthplace. However, by the following year, scrutiny of its spectrum suggested to other astronomers that it could be merely a background star. Telescopic tracking for several years should resolve the answer.*TIS


2013 David L. Donoho has been awarded the 2013 Shaw Prize in Mathematical Sciences for his profound contributions to modern mathematical statistics and in particular the development of optimal algorithms for statistical estimation in the presence of noise and of efficient techniques for sparse representation and recovery in large data-sets.
The Anne T and Robert M Bass Professor of the Humanities and Sciences, and Professor of Statistics at Stanford University, Dr. Donoho is well known for his role in developing new mathematical and statistical tools to deal with problems ranging from large data-sets in high dimensions to contamination with noise. *SIAM





BIRTHS

1676 Jacopo Riccati (28 May 1676 – 15 April 1754) was an Italian mathematician who wrote on philosophy, physics and differential equations. He is chiefly known for the Riccati differential equation. *SAU   The general Riccati diferential equation is of the form dy/dx = A+ By + Cy2 where A, B, and C represent functions of x..(there are actually several types of diff equations known by this term..)  He had two sons who also contributed to mathematics.  Vincenzo was a professor in Bologna, and Giordano published works in Geometry and on Newton's works.  Jacopo (and both sons) died in Treviso.


1710 Johann(II) Bernoulli (28 May 1710 in Basel, Switzerland - 17 July 1790 in Basel, Switzerland)
was a member of the Swiss mathematical family. He worked mainly on heat and light. He was one of three sons of Johann Bernoulli. In fact he was the most successful of the three. He originally studied law and in 1727 he obtained the degree of doctor of jurisprudence. He worked on mathematics both with his father and as an independent worker. He had the remarkable distinction of winning the Prize of the Paris Academy on no less than four separate occasions. On the strength of this he was appointed to his father's chair in Basel when Johann Bernoulli died. *Wik




1850 Wooster Woodruff Beman (May 28, 1850 - January 1, 1922). He attended school in Valparaiso, Ind., and entered the University of Michigan in 1866, receiving his B.A. degree in 1870. After teaching for a year at Kalamazoo College as instructor in Greek and mathematics, he returned to the University of Michigan as an instructor while also working for his master's degree, which he received in 1873. In 1874, he became assistant professor, in 1882 associate professor, and in 1887 full professor.
In addition to his teaching, Beman wrote books and articles on the history and teaching of elementary mathematics. Among his works are "Nature and Meaning of Numbers" (from the German), and "Continuity and Irrational Numbers." He was the joint author, with D. E. Smith, of "Plane and Solid Geometry," "Higher Arithmetic," "New Plane and Solid Geometry," "Elements of Algebra," "Academic Algebra," translations of "Famous Problems of Elementary Geometry," and "A Brief History of Mathematics." *Michigan Historical Collections. They also were editors of T. Sundara Row's Geometric Exercises in Paper Folding:



1872  Marian Smoluchowski ( 28 May 1872 – 5 September 1917) was a Polish physicist who worked in the territories of the Austro-Hungarian Empire. He was a pioneer of statistical physics and made significant contributions to the theory of Brownian motion and stochastic processes. He is known for the Smoluchowski equation, Einstein–Smoluchowski relation and Feynman–Smoluchowski ratchet. *Wik



1888 Jim Thorpe (May 28, 1888 – March 28, 1953) World-class athlete He was born in a one-room cabin near Prague in Indian Territory, now Oklahoma. Thorpe's versatile talents earned him the distinction of being chosen, in 1950, the greatest football player and the greatest American athlete of the first half of the twentieth century by American sports writers and broadcasters. Thorpe won the gold medal in both the decathlon and pentathlon events at the Stockholm Olympics, but was stripped of his medals when a reporter revealed he had played semi-professional baseball. It was not until after his death that Thorpe's amateur status was restored, and his name reentered in the Olympic record book. (Library of Congress web page)
So why is this on a math page…Well it seems that Jim Thorpe may have indirectly influenced the naming of the # key on the telephone. One of several stories for how it is named is this one: In the 1960's when Bell Telephone added two new buttons for push button telephones, they used the * symbol and the # symbol. Although most people call the * an asterisk, the telephone folks decided to use "star". The other symbol, #, has been called lots of different names such as crosshatch, and now the common term on twitter seems to be "hashtag".  Others have  referred to it as tic-tac-toe, the pound sign, and the number sign (leave it to the telephone company to put the number sign on one of the two keys without a number); but the term now "officially" used by the American telephone industry for the symbol is octothorpe although it is more often called the pound key in conversations with the public.
It seems that the name was made up more or less spontaneously by Bell Engineer Don MacPherson while meeting with their first potential customer. The octo part was chosen because of the eight points at the ends of the line segments, and the thorpe was in honor of Jim Thorpe, the great Native American athlete. Why honor Thorpe? At the time MacPherson was working with a group that was trying to restore Thorpe's Olympic medals, which had been taken from him when it was found he had played semi-professional baseball prior to his track victories in the Olympics in Sweden. [It's not math, but I love the story that when the King of Sweden gave him the gold medal, the king said, "You are surely the greatest athlete on the earth". The modest Thorpe smiled and replied, "Thanks, King."]
There are a host of other names for the # symbol, and many of them can be found at this page from Wikipedia which includes several different stories about the creation of "octothorpe" or "octothorn" and also has this rather interesting clip:
"The pronunciation of # as `pound' is common in the US but a bad idea. The British Commonwealth has its own, rather more apposite, use of `pound sign. On British keyboards the UK pound currency symbol once frequenlty replaced #, with # being elsewhere on the keyboard. The US usage derives from an old-fashioned commercial practice of using a # suffix to tag pound weights on bills of lading. The character is usually pronounced `hash' outside the US. There are more culture wars over the correct name of this character than any other, which has led to the “ha-ha” only serious suggestion that it be pronounced `shibboleth' (see Judges 12:6 in the Old Testament)." (pballew Etymology page)

The Cincinnati Reds bought Jim Thorpe from the New YorkGiants in 1917



1895 Rudolph Minkowski ( May 28, 1895 – January 4, 1976)  was a German-American astronomer. He  studied spectra, distributions, and motions of planetary nebulae and more than doubled the number known. He investigated novae and supernovae and their remnants, especially the the physics and expansion of the Crab Nebula (a pulsar remnant). With Walter Baade, Minkowski divided supernovae into Types I and II on the basis of spectral characteristics and they identified optical counterparts of many of the early radio sources, including Cygnus A, Virgo A (M87), Perseus A (NGC 1275), and Centaurus A (NGC 5128). Just before retirement he found what was for years the largest known redshift in a galaxy. He was awarded the Bruce Medal in 1961 for distinguished services to astronomy.*TIS




1908 Egbert Rudolf van Kampen (28 May 1908 – 11 February 1942) was a Dutch mathematician., In 1908 he left Europe and traveled to the United States to take up the position which he had been offered at Johns Hopkins University in Baltimore, Maryland. There he met Oscar Zariski who had taught at Johns Hopkins University as a Johnston Scholar from 1927 until 1929 when he had joined the Faculty. Zariski had been working on the fundamental group of the complement of an algebraic curve, and he had found generators and relations for the fundamental group but was unable to show that he had found sufficient relations to give a presentation for the group. Van Kampen solved the problem, showing that Zariski's relations were sufficient, and the result is now known as the Zariski–van Kampen theorem. This led van Kampen to formulate and prove what is nowadays known as the Seifert–van Kampen theorem. *Wik



1911 Alfred Otto Carl Nier (May 28, 1911 – May 16, 1994) was an American physicist who pioneered the development of mass spectrometry.   He refined the mass spectrometric process to distinguish isotopes. In 1934, with Lyman T. Aldrich he applied the decay of potassium-40 to argon-40 to measure the age of geological materials. He discovered (1936-38) a number of new isotopes of such low abundance they had not been previously detected, including S36, Ca46, Ca48, and Os186. Nier showed how the ratio of radioactive isotopes of uranium and its decay products was a second method to estimate the age of rocks. During WW-II, with others, he showed (1940) that the rarer uranium-235 undergoes fission, not common U-238. Thereafter, Nier was active in the separaton of these two isotopes, important in developing atomic bombs. *TIS




1912 Paul-Émile Lecoq de Boisbaudran, also called François Lecoq de Boisbaudran (18 April 1838 – 28 May 1912), was a French chemist known for his discoveries of the chemical elements gallium, samarium and dysprosium.  He  improved spectroscopic methods which had recently been developed by Kirchhoff. In 1859, he set out to scan minerals for unknown spectral lines. Fifteen years of persistence paid off when he discovered the elements gallium (1875), samarium (1880), and dysprosium (1886). He ranks with Robert Bunsen, Gustav Kirchhoff and William Crookes as one of the founders of the science of spectroscopy. Guided by the general arrangement of spectral lines for elements in the same family, he believed the element he called gallium (in honour of France) was the eka-aluminium predicted by Mendeleev between aluminium and indium. Since it is liquid between about 30 - 1700 deg C, a gallium in quartz thermometer can measure high temperatures.*TIS



1912 Ruby Violet Payne-Scott, (28 May 1912 – 25 May 1981) was an Australian pioneer in radiophysics and radio astronomy, and was the first female radio astronomer.
One of the more outstanding physicists that Australia has ever produced and one of the first people in the world to consider the possibility of radio astronomy, and thereby responsible for what is now a fundamental part of the modern lexicon of science, she was often the only woman in her classes at the University of Sydney.
Her career arguably reached its zenith while working for the Australian government's Commonwealth Scientific and Industrial Research Organisation (then called CSIR, now known as CSIRO) at Dover Heights, Hornsby and especially Potts Hill in Sydney. Some of her fundamental contributions to solar radio astronomy came at the end of this period. She is the discoverer of Type I and Type III bursts and participated in the recognition of Type II and IV bursts.
She played a major role in the first-ever radio astronomical interferometer observation from 26 January 1946, when the sea-cliff interferometer was used to determine the position and angular size of a solar burst. This observation occurred at either Dover Heights (ex Army shore defence radar) or at Beacon Hill, near Collaroy on Sydney's north shore (ex Royal Australian Air Force surveillance radar establishment - however this radar did not become active until early 1950).
During World War II, she was engaged in top secret work investigating radar. She was the expert on the detection of aircraft using PPI (Plan Position Indicator) displays. She was also at the time a member of the Communist Party and an early advocate for women's rights. The Australian Security Intelligence Organisation (ASIO) was interested in Payne-Scott and had a substantial file on her activities, with some distortions.
*Wik

*Wik



1912 Hans Zassenhaus, algebraist. (28 May 1912–21 November 1991) was a German mathematician, known for work in many parts of abstract algebra, and as a pioneer of computer algebra.
He was born in Koblenz–Moselweiss, and became a student and then assistant of Emil Artin. He was subsequently a professor at McGill University, the University of Notre Dame, and Ohio State University, and was one of the founding editors of the Journal of Number Theory. He died in Columbus, Ohio. *Wik




1930 Frank Donald Drake ( May 28, 1930 -  Sep. 2, 2022) is an American astronomer who formulated the Drake Equation (1961) to estimate the number of technological civilizations that may exist in our galaxy. In 1960, Drake led the first search, the two-month Project Ozma to listen for patterns in radio waves with a complex, ordered pattern that might be assumed to represent messages from some extraterrestrial intelligence. Carl Sagan and Drake designed the plaques on Pioneer 10 and Pioneer 11 for the purpose of greeting and informing any extraterrestrial life that might find the vessels after they left the solar system. *TIS

The equation was formulated in 1961 by Frank Drake, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at the first scientific meeting on the search for extraterrestrial intelligence (SETI)


N = the number of civilizations in the Milky Way galaxy with which communication might be possible (i.e. which are on the current past light cone);  was the product of these seven terms.


R∗ = the average rate of star formation in our Galaxy

fp = the fraction of those stars that have planets

ne = the average number of planets that can potentially support life per star that has planets

fl = the fraction of planets that could support life that actually develop life at some point

fi = the fraction of planets with life that actually go on to develop intelligent life (civilizations)

fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time for which such civilizations release detectable signals into space

Inserting the minimum estimates for each value produced a value of 20 civilizations in the Milky Way.


Allen Telescope for SETI



1930 Keith William Morton (born 28 May 1930, Ipswich, Suffolk, England) is a British mathematician working on partial differential equations, and their numerical analysis.

Morton graduated with a B.A. in 1952 and began working in the Theoretical Physics Division of the Atomic Energy Research Establishment at Harwell (which was in Berkshire at the time but, following boundary changes in 1974, is now in Oxfordshire). There he worked on Monte Carlo methods for nuclear criticality and published a number of papers in collaboration with John Michael Hammersley who was Principal Scientific Officer at the Atomic Energy Research Establishment at Harwell at the time. These joint papers are: Transposed branching processes (1954); Poor man's Monte Carlo (1954); The estimation of location and scale parameters from grouped data (1954); and A new Monte Carlo technique: antithetic variates (1956). Poor man's Monte Carlo, which includes a paper and a discussion, was published by the Royal Statistical Society and reviewed by Alston Householder who writes:-

This paper and the subsequent discussion relate chiefly to the art of applying Monte Carlo, and no brief summary can do justice to either. The basic thesis can be inferred from the title, that one does not necessarily need high speed machines to use Monte Carlo effectively. The authors first point out that only the name and not the method is new (the discussion brings out that King Solomon was an early practitioner) and then discuss three problems: the critical size of a nuclear reactor, the test of a quantum hypothesis, and self-avoiding walks.

Alston Householder also reviewed the 1956 paper mentioned above and writes:-

... the paper represents a major contribution to the study of Monte Carlo Methods.  *SAU




 

DEATHS



1883 Ernst Arnold Kohlschütter (July 6, 1883 – May 28, 1969) a German astronomer and astrophysicist from Halle.
In 1908 he was awarded his Ph.D. from the University of Göttingen.
In 1911 he began working at the Mount Wilson Observatory, studying the spectra of the Sun and stars. In collaboration with Walter Sidney Adams, and in 1914 they discovered that the absolute luminosity of a star was proportional to the relative intensity of the lines in the spectrum. This allowed astronomers to determine the distance of stars, including main sequence and giants, using the spectroscope.
He became the director of the Bonn observatory in 1925. Therein he was dedicated to astrometric studies.
The crater Kohlschütter on the Moon is named in his honor. *Today in Astronomy



1980 Rolf Herman Nevanlinna ( 22 October 1895 – 28 May 1980) was a Finnish mathematician who made significant contributions to complex analysis.

When Nevanlinna earned his doctorate in 1919, there were no university posts available so he became a school teacher. His brother, Frithiof, had received his doctorate in 1918 but likewise was unable to take up a post at a university, and instead began working as a mathematician for an insurance company. Frithiof recruited Rolf to the company, and Nevanlinna worked for the company and as a school teacher until he was appointed a Docent of Mathematics at the University of Helsinki in 1922. During this time, he had been contacted by Edmund Landau and requested to move to Germany to work at the University of Göttingen, but did not accept.

After his appointment as Docent of Mathematics, he gave up his insurance job but did not resign his position as school teacher until he received a newly created full professorship at the university in 1926. Despite this heavy workload, it was between the years of 1922–25 that he developed what would become to be known as Nevanlinna theory.

From 1947 Nevanlinna had a chair in the University of Zurich, which he held on a half-time basis after receiving in 1948 a permanent position as one of the 12 salaried Academicians in the newly created Academy of Finland.

Rolf Nevanlinna's most important mathematical achievement is the value distribution theory of meromorphic functions. The roots of the theory go back to the result of Émile Picard in 1879, showing that a non-constant complex-valued function which is analytic in the entire complex plane assumes all complex values save at most one. In the early 1920s Rolf Nevanlinna, partly in collaboration with his brother Frithiof, extended the theory to cover meromorphic functions, i.e. functions analytic in the plane except for isolated points in which the Laurent series of the function has a finite number of terms with a negative power of the variable. Nevanlinna's value distribution theory or Nevanlinna theory is crystallised in its two Main Theorems. Qualitatively, the first one states that if a value is assumed less frequently than average, then the function comes close to that value more often than average. The Second Main Theorem, more difficult than the first one, states roughly that there are relatively few values which the function assumes less often than average.




 1982 Carlo Miranda (15 August 1912 – 28 May 1982) was an Italian mathematician, working on mathematical analysis, theory of elliptic partial differential equations and complex analysis: he is known for giving the first proof of the Poincaré–Miranda theorem for Miranda's theorem in complex analysis, and for writing an influential monograph in the theory of elliptic partial differential equations.

Tthe Poincaré–Miranda theorem is a generalization of intermediate value theorem, from a single function in a single dimension, to n functions in n dimensions. The theorem is named after Henri Poincaré — who conjectured it in 1883 — and Carlo Miranda — who in 1940 showed that it is equivalent to the Brouwer fixed-point theorem. *Wik




 1997 Ronald Vernon Book (April 1937 – May 28, 1997 in Santa Barbara, California) worked in theoretical computer science. He published more than 150 papers in scientific journals.




2000 Donald Watts Davies, CBE FRS (7 June 1924 – 28 May 2000) was a Welsh computer scientist who was employed at the UK National Physical Laboratory (NPL).

In 1965 he conceived of packet switching, which is today the dominant basis for data communications in computer networks worldwide. Davies proposed a commercial national data network in the United Kingdom and designed and built the local-area NPL network to demonstrate the technology. Many of the wide-area packet-switched networks built in the 1970s were similar "in nearly all respects" to his original 1965 design. The ARPANET project credited Davies for his influence, which was key to the development of the Internet.

Davies' work was independent of the work of Paul Baran in the United States who had a similar idea in the early 1960s, and who also provided input to the ARPANET project, after his work was highlighted by Davies' team.



2003 Ilya Prigogine (25 Jan 1917; 28 May 2003) Russian-born Belgian physical chemist who received the Nobel Prize for Chemistry in 1977 for contributions to nonequilibrium thermodynamics, or how life could continue indefinitely in apparent defiance of the classical laws of physics. The main theme of Prigogine's work was the search for a better understanding of the role of time in the physical sciences and in biology. He attempted to reconcile a tendency in nature for disorder to increase (for statues to crumble or ice cubes to melt, as described in the second law of thermodynamics) with so-called "self-organisation", a countervailing tendency to create order from disorder (as seen in, for example, the formation of the complex proteins in a living creature from a mixture of simple molecules). *TIS



***  There are 7 four-digit vampire numbers, 1260, 1395, 1435, 1530, 1827, 2187, 6880,***



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

Wednesday, 27 May 2026

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, also known as a maximum or a "one-four-seven".  It's achieved by potting (sinking) all 15 reds, then 15 blacks for a total of 120 points, followed by all six colors for an additional 27 points. A 147 is a highly significant achievement in snooker, comparable to a nine-dart finish in darts or a hole-in-one in golf. 


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).

Strike Fighter Squadron 147 (VFA-147), also known as the "Argonauts," is a United States Navy strike fighter squadron based at MCAS Iwaukuni, Japan.  



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

Pafnuty Lvovich Chebyshev was a Russian mathematician and considered to be the founding father of Russian mathematics. Chebyshev is known for his fundamental contributions to the fields of probability, statistics, mechanics, and number theory.




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




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.

*Google




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

Amaterasu, born Amaterasu Omikami, is a Shinto deity in Japanese mythology whose name means ''The Great Divinity That Illuminates Heaven.'' Known as the Sun Goddess and ruler of the heavens, Amaterasu is also called Ohirume no Muchi no Kami, which means ''The Great Sun of the Kami.'' Kami are the gods of Shintoism, a Japanese indigenous religion that worships sacred spirits in nature and was the national religion of Japan until the end of World War II. Shinto translates as ''The Way of the Gods'' and comprises ancient beliefs that have survived unchanged for a millennium. Amaterasu Omikami is the Japanese Sun Goddess and has been worshiped for thousands of years. According to Japanese mythology, Amaterasu is an ancestor of the Imperial Family and the daughter of the deities Izanagi and Izanami. Amaterasu represents the transcendent, otherworldly spirit of the universe known as Kunitokotachi.





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



1909 William Webster Hansen (May 27, 1909 – May 23, 1949) was an American physicist and professor. He was one of the founders of the technology of microwave electronics.

He entered Stanford University at the age of 16, earning his B.A. in 1929 and his Ph.D. in 1933.

Hansen went on to become interested in the problem of accelerating electrons for X-ray experiments, using oscillating fields, rather than large static voltages. At the University of California, Berkeley, Ernest Lawrence and his assistant David H. Sloan, had worked on an accelerator driven by a resonant coil. Hansen proposed replacing the coil with a cavity resonator. In 1937, brothers Russel H. Varian and Sigurd F. Varian came to Stanford to work on the foundations of what was to become radar. Hansen exploited some of the Varian's work to develop the klystron and during the years 1937 to 1940, along with collaborators such as John R. Woodyard, founded the field of microwave electronics. In 1941, he moved his team to the Sperry Gyroscope Company where they spent the war years employing their expertise in radar applications and in other problems.

Returning to Stanford in 1945 as a full professor, he embarked on the construction of a series of linear accelerators based on klystron technology and of GeV performance. Along with the Varian brothers and Edward Ginzton, he co-founded Varian Associates in 1948. Sadly, he was never to see the completion of the klystron project. He died at age 39 in Palo Alto, California of berylliosis and fibrosis of the lungs, caused by inhaling the beryllium used in his research. In 1947, the Hansen Experimental Physics Laboratory (HEPL) was founded as a facility at Stanford University. The facility is designed to promote interdisciplinary enterprises across different branches of science and was named in his honor.



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.




1954  Lawrence Maxwell Krauss (born May 27, 1954) is a Canadian-American theoretical physicist and cosmologist who taught at Arizona State University (ASU), , Yale University, and Case Western Reserve University. He founded ASU's Origins Project in 2008 to investigate fundamental questions about the universe and served as the project's director. He was among the first physicists to propose the enigmatic dark energy that makes up most of the mass and energy in the universe. His area of study also includes relating elementary particles to the early universe, general relativity, and neutrino astrophysics. Krauss became the inaugural director of the Origins Project at Arizona State University in Aug 2008. This is a transdisciplinary initiative that nurtures research. Its mission is also to explore fundamental questions, ranging broadly from from the origins of the universe to life; and broaden public understanding of science issues. He has written a number of science books for the layman, including Fear of Physics (1993) and Quantum Man: Richard Feynman's Life in Science (2011). He is also active in popularizing science in print, radio and TV media.




1959  Donna Theo Strickland CC FRS FRSC HonFInstP (born 27 May 1959, ) is a Canadian optical physicist and pioneer in the field of pulsed lasers. She was awarded the Nobel Prize in Physics in 2018, together with Gérard Mourou, for the practical implementation of chirped pulse amplification. She is a professor at the University of Waterloo in Ontario, Canada.

She served as fellow, vice president, and president of Optica (formerly OSA), and is currently chair of its Presidential Advisory Committee. In 2018, she was listed as one of BBC's 100 Women.
From 1988 to 1991, Strickland was a research associate at the National Research Council of Canada, where she worked with Paul Corkum in the Ultrafast Phenomena Section, which had the distinction at that time of having produced the most powerful short-pulse laser in the world. She worked in the laser division of Lawrence Livermore National Laboratory from 1991 to 1992 and joined the technical staff of Princeton University's Advanced Technology Center for Photonics and Opto-electronic Materials in 1992. She joined the University of Waterloo in 1997 as an assistant professor. She became the first full-time female professor in physics at the University of Waterloo. Strickland is currently a professor, leading an ultrafast laser group that develops high-intensity laser systems for nonlinear optics investigations. She has described herself as a "laser jock" *Wik







DEATHS



1781 Giovanni Battista Beccaria FRS (3 October 1716 – 27 May 1781) was an Italian physicist. A fellow of the Royal Society, he published several papers on electrical subjects in the Phil. Trans.

 Hespread knowledge of Benjamin Franklin's discoveries with electricity, which he extended with his own research. He designed an electrical thermometer and investigated the relative powers of parallel plate condensers (capacitors). He formed explanations for meteorological and geophysical phenomena in terms of “natural electricity.” With his students, he experimentally probed the atmosphere with metal poles, kites and rockets. He published his work in five books.


*Linda Hall Org




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


1988 Ernst August Friedrich Ruska ( 25 December 1906 – 27 May 1988)[1] was a German physicist who won the Nobel Prize in Physics in 1986 for his work in electron optics, including the design of the first electron microscope. *Wik 

For “his fundamental work in electron optics and for the design of the first electron microscope” he was awarded a share of the Nobel Prize for Physics in 1986 (with Heinrich Rohrer and Gerd Binnig). In 1928, found that a magnetic coil could act as a lens to focus an electron beam. Adding a second lens he produced the first primitive (x17 power) electron microscope. By 1933, his refinements increased the magnification to x7000, exceeding what was possible with visible light. The first commercial model was marketed in 1939. Since then, electron microscopes rapidly found applications in biology, medicine and many other areas of science.*TIS




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