I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset.
~Harish-Chandra
The 289th day of the year; 289 is a Friedman number since (8 + 9)2 = 289 (A Friedman number is an integer which, in a given base, is the result of an expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷) and sometimes exponentiation.)Students might try to find the first few multi-digit Friedman numbers.
289 = 17^2, and it is too little known by students that for every prime p > 3 , 24 divides p^2-1. Since every prime is =1, 3, 5 or 7 Mod 8, their squares mod 8 are 1, 9 25, and 49 and all of those simplify to 1 mod 8. Also all primes are == 1 or 2 mod 3, and their squares are 1 or 4 (=1 mod 3) . so p^2 mod 24 = p^2 mod 3 times p^2 mod 8 is always one. Subtract 1 and P62 -1 is divisible by 8.
289 is the square of the sum of the first four primes, 289 = (2 + 3 + 5 + 7)2
There are only two square year days that are neither the sum, or the difference of two primes, 289 is the second.
There are only two square year days that are neither the sum, or the difference of two primes, 289 is the second.
289 is the largest 3-digit square with increasing digits.
289 is the hypotenuse of a primitive Pythagorean triple. Find the legs students!
1707 Roger Cotes elected first Plumian Professor of Astronomy and Experimental Philosophy at Cambridge at age 26. He is best known for his meticulous and creative editing of the second edition (1713) of Newton’s Principia. He was also an important developer of the integral calculus. *Ronald Gowing, Roger Cotes, Natural Philosopher, p. 14
He also found Euler's formula,
cosx + isinx = eix
before Euler, and expressed it in its logarithmic form.
1784 Jean-Pierre Blanchard, a French balloonist, was born July 4, 1753. The Golden Age of Ballooning began on Nov. 21, 1783, when Pilâtre de Rozier and François d'Arlandes soared aloft in a hot-air balloon made by the Montgolfier brothers. They launched from the Château de la Muette just outside Paris and floated for some 5 miles. Just over a week later, Jacques-Alexandre Charles and Nicolas Robert ascended to 3000 feet from the Tuileries in Paris, this time in a hydrogen balloon. Blanchard was caught up immediately in balloon frenzy, designed his own hydrogen balloon, complete with "oars" to swim through the air and an always-open parachute to slow descent should the gas bag spring a leak, and headed for the skies . He made his first ascent in a hydrogen balloon on Mar. 2, 1784, lifting off from the Champ de Mars. If there is a surviving contemporary image of that ascent, I have not seen it.
The difference between Blanchard and the Montgolfier brothers and Jacques Charles is that Blanchard was in it for the money. He was the first barnstorming balloonist who charged admission for his ascents and seems to have given the public (who showed up by the thousands) their money's worth, especially on the first ascent, when a military student demanded to come along and attacked Blanchard and the balloon with a sword when he was refused. The somewhat bloodied Blanchard proceeded with the flight anyway, which I am sure delighted the crowd.
Seeking larger paydays, Blanchard travelled with his balloon to England in August of 1784 and began to organize public ascents there. He made one ascent from Chelsea, for which (so it is recorded) 400,000 people showed up. He made the ascent with an English physician, who was added to the gondola to increase local interest. An engraving recorded the event, which took place on Oct. 16, 1784. Blanchard then ascended with another physician, John Jeffries (an ex-American, actually), on Nov. 30, 1784, and this time they wafted all the way from London to Kent.
This set the stage for Blanchard's goal all along, to balloon across the English Channel. Pilâtre de Rozier had the same idea; he was sitting on the other side of the channel with his hydrogen balloon, waiting for favorable winds to take him westward to Dover. Blanchard won the battle of the winds. He and Jeffries took off from Dover on Jan. 7, 1785. They almost ended up in the sea, as their bag of hydrogen was providing insufficient lift, and they threw nearly everything overboard, including most of their clothes, to maintain altitude. But the balloon for some reason recovered its buoyancy, and they made it to Calais and beyond, landing at Guines, to the great excitement of the local populace.
1797 Gauss records in his diary that he has discovered a new proof of the Pythagorean Theorem. See Gray, Expositiones Mathematicae, 2(1984), 97–130. *VFR I have had this here for several years, and no one seems to know the nature of his proof. Anyone???
1819 Thomas Young writes to Fresnel to thank him for a copy of his memoirs (sent to Young by Arago). "I return a thousand thanks, Monsieur, for the gift of your admirable memoir, which surely merits a very high rank amongst the papers which have contributed most to the progress of optics." *A history of physics in its elementary branches By Florian Cajori
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| Thomas Young |
1843 Hamilton discovered quaternions while walking along the Royal Canal in Dublin and immediately scratches the multiplication formulas on a bridge. Today a plaque on the bridge reads, "Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication i2 = j2 = k2 = ijk = −1 & cut it in a stone on this bridge." Since 1989, the Department of Mathematics of the National University of Ireland, Maynooth has organized a pilgrimage, where scientists (including the physicists Murray Gell-Mann in 2002, Steven Weinberg in 2005, and the mathematician Andrew Wiles in 2003) take a walk from Dunsink Observatory to the Royal Canal bridge where no trace of Hamilton's carving remains, unfortunately.
Here is how Hamilton described his memory of the discovery of the Quaternions to his son, "Every morning in the early part of the above-cited month, on my coming down to breakfast, your (then) little brother, William Edwin, and yourself, used to ask me, `Well, papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: `No, I can only add and subtract them. But on the 16th day of the same month (Oct) - which happened to be Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula which contains the Solution of the Problem, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on `Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following.'' *from Hamilton By Sir Robert Stawell Ball.
The plaque says:
Here as he walked by
on the 16th of October 1843
Sir William Rowan Hamilton
in a flash of genius discovered
the fundamental formula for
quaternion multiplication
i2 = j2 = k2 = i j k = −1
& cut it on a stone of this bridge
(Quatenion was a Latin term before Hamilton used it. Milton uses it in Paradise Lost to refer to the four elements of antiquity: air, earth, water, and fire. The last three are “the eldest birth of nature’s womb” because they are mentioned in Genesis before air is mentioned. *John Cook )
In 1982 the first image of the returning Halley's Comet was recorded with the 200-inch Hale telescope at Palomar Mountain. Caltech astronomers David Jewitt and G. Edward Danielson found the comet when it was still beyond the orbit of Saturn, more than 1.6 billion kilometers (960 million miles) from the Sun. *National Air and Space Museum
1988 Connect Four Solved first by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). Weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik
2016 The Hamilton walk takes place each year on this day. Students, professors, and math lovers in general will gather at the Dunsink Observatory around 3:30 pm and proceed to Broombridge in Cabra where he had his Eureka moment about Quaternions. (see 1843 in Events above) The annual event is part of Irish Math week.
The Hamilton Walk from Dunsink Observatory to Broom Bridge on the Royal Canal in Dublin takes place on 16 October each year. This is the anniversary of the day in 1843 when William Rowan Hamilton discovered the non-commutative algebraic system known as quaternions, while walking with his wife along the banks of the Royal Canal.(Tip to Mathematicians, take walks with your wife.)
It is famous for being the location where Sir William Rowan Hamilton first wrote down the fundamental formula for quaternions on 16 October 1843, which is to this day commemorated by a stone plaque on the northwest corner of the underside of the bridge. After being spoiled by the action of vandals and some visitors,[2] the plaque was moved to a different place, higher, under the railing of the bridge.
The text on the plaque reads:
Here as he walked by
on the 16th of October 1843
Sir William Rowan Hamilton
in a flash of genius discovered
the fundamental formula for
quaternion multiplication
& cut it on a stone of this bridge.
Smith was probably born at Lea near Gainsborough, the son of the rector of Gate Burton, Lincolnshire. He entered Trinity College, Cambridge, in 1708, and becoming minor fellow in 1714, major fellow in 1715 and senior fellow in 1739. From 1716 to 1760 he was Plumian Professor of Astronomy,and was chosen Master in 1742, in succession to Richard Bentley.
Besides editing two works by his cousin, Roger Cotes, who was his predecessor in the Plumian chair, he published A Compleat System of Opticks in 1738, (which was the principal textbook on Optics in the 18th Century) , and Harmonics, or the Philosophy of Musical Sounds in 1749.
Smith never married but lived with his unmarried sister Elzimar (1683–1758) in the lodge at Trinity College. Although he is often portrayed as a rather reclusive character, John Byrom's journal shows that in the 1720s and 1730s Smith could be quite sociable. Yet ill health, particularly gout, took its toll and severely inhibited his academic work and social activities. He died at the lodge on 2 February 1768, and on 8 February he was buried in Trinity College Chapel.
In his will Smith left £3500 South Sea stock to the University of Cambridge. The net income on the fund is annually divided equally between the Smith's Prize and the stipend of the Plumian Professor. *Wik
1879 Philip Edward Bertrand Jourdain (16 October 1879 – 1 October 1919) was a British logician and follower of Bertrand Russell. He corresponded with Georg Cantor and Gottlob Frege, and took a close interest in the paradoxes related to Russell's paradox, formulating the card paradox version of the liar paradox. He also worked on algebraic logic, and the history of science with Isaac Newton as a particular study. He was London editor for The Monist. *Wik
1882 Ernst Erich Jacobsthal (16 October 1882, Berlin – 6 February 1965, Überlingen) was a German mathematician, and brother to the archaeologist Paul Jacobsthal.
In 1906, he earned his PhD at the University of Berlin, where he was a student of Georg Frobenius, Hermann Schwarz and Issai Schur; his dissertation, Anwendung einer Formel aus der Theorie der quadratischen Reste (Application of a Formula from the Theory of Quadratic Remainders), provided a proof that prime numbers of the form 4n + 1 are the sum of two square numbers. *Wik
1930 John Charlton Polkinghorne KBE FRS (16 October 1930 – 9 March 2021) was an English theoretical physicist, theologian, writer, and Anglican priest. He was professor of Mathematical physics at the University of Cambridge from 1968 to 1979, when he resigned his chair to study for the priesthood, becoming an ordained Anglican priest in 1982. He served as the president of Queens' College, Cambridge from 1988 until 1996.*Wik
1937 William Sealy Gosset (13 June 1876 in Canterbury, England - 16 October 1937 in Beaconsfield, England) Gosset was the eldest son of Agnes Sealy Vidal and Colonel Frederic Gosset who came from Watlington in Oxfordshire. William was educated at Winchester, where his favourite hobby was shooting, then entered New College Oxford where he studied chemistry and mathematics. While there he studied under Airy. He obtained a First Class degree in both subjects, being awarded his mathematics degree in 1897 and his chemistry degree two years later.
Gosset obtained a post as a chemist with Arthur Guinness Son and Company in 1899. Working in the Guinness brewery in Dublin he did important work on statistics. In 1905 he contacted Karl Pearson and arranged to go to London to study at Pearson's laboratory, the Galton Eugenics Laboratory, at University College in session 1906-07. At this time he worked on the Poisson limit to the binomial and the sampling distribution of the mean, standard deviation, and correlation coefficient. He later published three important papers on the work he had undertaken during this year working in Pearson's laboratory.
Many people are familiar with the name "Student" but not with the name Gosset. In fact Gosset wrote under the name "Student" which explains why his name may be less well known than his important results in statistics. He invented the t-test to handle small samples for quality control in brewing. Gosset discovered the form of the t distribution by a combination of mathematical and empirical work with random numbers, an early application of the Monte-Carlo method.
McMullen says:-
To many in the statistical world "Student" was regarded as a statistical advisor to Guinness's brewery, to others he appeared to be a brewer devoting his spare time to statistics. ... though there is some truth in both these ideas they miss the central point, which was the intimate connection between his statistical research and the practical problems on which he was engaged. ... "Student" did a very large quantity of ordinary routine as well as his statistical work in the brewery, and all that in addition to consultative statistical work and to preparing his various published papers.
From 1922 he acquired a statistical assistant at the brewery, and he slowly built up a small statistics department which he ran until 1934.
Gosset certainly did not work in isolation. He corresponded with a large number of statisticians and he often visited his father in Watlington in England and on these occasions he would visit University College, London, and the Rothamsted Agricultural Experiment Station. He would discuss statistical problems with Fisher, Neyman and Pearson. *SAU
In probability and statistics, Student's t-distribution (or simply the t-distribution)
t_nu is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped.
However, t_nu has heavier tails and the amount of probability mass in the tails is controlled by the parameter nu . For nu = 1 the Student's t distribution
t_nu becomes the standard Cauchy distribution, whereas for nu→∞} it becomes the standard normal distribution
1983 Harish-Chandra (11 October 1923 – 16 October 1983) was an Indian mathematician, who did fundamental work in representation theory, especially Harmonic analysis on semisimple Lie groups.*Wik
1998 Jonathan Bruce Postel (6 Aug 1943, 16 Oct 1998) American computer scientist who played a pivotal role in creating and administering the Internet. In the late 1960s, Postel was a graduate student developing the ARPANET, a forerunner of the Internet for use by the U.S. Dept. of Defense. As director of the Internet Assigned Numbers Authority (IANA), which he formed, Postel was a creator of the Internet's address system. The Internet grew rapidly in the 1990s, and there was concern about its lack of regulation. Shortly before his death, Postel submitted a proposal to the U.S. government for an international nonprofit organization that would oversee the Internet and its assigned names and numbers. He died at age 55, from complications after heart surgery.*TIS
Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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