But just as much as it is easy to find the differential of a given quantity,
so it is difficult to find the integral of a given differential.
Moreover, sometimes we cannot say with certainty
whether the integral of a given quantity can be found or not.
~Bernoulli, Johann
The 208th Day of the Year
208 is the sum of the squares of the first five primes.
208 is the number of paths from (0,0) to (7,7) avoiding 3 or more consecutive east steps and 3 or more consecutive north steps.
208 is an abundant number, the proper divisors total 226(more than 208)
208 = 6^3 - 2^3
208 is the sum of a cube and a square, as were 204 and 206. 208 = 4^3 + 12^2
208 is an unprimeable number, changing any digit to something else will not make a prime.
208 = 2^4 x 13 and if you play the four-fours game, 208 = 4^4 - 4! - 4!
208 can be written as the sum of two squares in only one way, 12^2 + 8^2
208 = 53^2 - 51^2 = 17^2 - 9^2 = 28^2 - 24^2
(16*10^208-31)/3 is prime, and it has a 5 followed by 206 threes, finished of with 23. It is the largest year date in this sequence. Previous examples include 523, 5323, 53323, and 5333333333333323, for the exponents 1, 2, 3, 4 and 15
\(208 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2\), the sum of the first five prime squares, obviously the smallest number to be the sum of five distinct squares of primes.
208 is a junction number since it is the sum of n + SoD(n) for two (or more) numbers. One is 203 since 203 + 2 + 0 + 3 = 208, find the other(s?)
.
See more Math Facts for Every Year Day here
EVENTS
1630, On July 27 Giovanni Batista Baliani wrote a letter to Galileo Galilei about the explanation of an experiment he had made in which a siphon, led over a hill about twenty-one meters high, failed to work. Galileo responded with an explanation of the phenomena: he proposed that it was the power of a vacuum which held the water up, and at a certain height (in this case, thirty-four feet) the amount of water simply became too much and the force could not hold any more, like a cord that can only withstand so much weight hanging from it.
For hundreds of years, It had been known that water pumps could not lift water past a certain point. The distance water could not be pumped beyond was found to be around 34 feet. However, this height varied because it is based of the weight of the air, and was what Europeans like Galileo and Torricelli were trying to discover.
In 1640 Galileo and Torricelli conducted an experiment together with a suction pump at a well. They lowered the tube into the well and began to pump water as high as they could, but found that no matter their efforts the water could not pass more than about 34 feet about the water’s surface. Galileo concluded that, in fact, they were not pumping the water up the tube at all, but rather removing air from the pump creating a vacuum. This new thinking led one of Torricelli’s greatest inventions, the first barometer.
1794 What a difference a day makes! Jean Baptiste Joseph Fourier (1766?-1830) was a student at the École Normale, c1794. He was sentenced to the guillotine by Robespierre on July 28 of 1794, but Robespierre was overthrown the day before his scheduled execution (27 July, 1794) was due. Fourier went on to both political and scientific success. He was unanimously elected the first Secretary of the Institute of Egypt in 1798. He was Governor of Lower Egypt in 1798‑1801 or Commissioner at the Divan of Cairo . He led one of the expeditions of exploration which examined ancient monuments and he suggested the publication of the great report on Egypt. He was was a professor at the École Polytechnique up to 1806. Napoléon made him a baron and during Napoléon's return from Elba in 1815, he made Fourier a count and Prefect of the Rhone, based at Lyons, from 10 Mar to 1 May. In 1815, he was penniless in Paris and giving lessons for his living. The Prefect of Paris found out and made him director of the Bureau de la Statistique of the Préfecture of the Seine. He was elected to the Académie in 1816, but this was vetoed by the government, so he was elected again in 1817 and this was permitted. He was Prefect of the Department of Isère, whose capital is Grenoble, from 1802 to 1817 (1815??) He was Permanent Secretary of the Académie des Sciences in 1822-1830.
 |
| *TIS |
1829 By a remarkable coincidence, both Cauchy and Sturm sent papers to the Acad´emie des Sciences dealing with differential equations. Both of them used techniques which we recognize as matrix methods. Thus they are early contributors to linear algebra, a field which is usually dated to Cayley’s introduction of matrices in 1858. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, p. 1150]
In the 1830s, while teaching at the Collège Rollin in Paris, Sturm was developing his now-famous method for determining the number of real roots of an algebraic equation within a given interval. One evening, during a small mathematics salon hosted by Joseph Liouville, Sturm presented a clever trick involving sign changes in a sequence of polynomials. He claimed that the number of real roots could be precisely counted just by looking at the changes in sign from one term to the next.
Liouville was skeptical and challenged Sturm on the spot, believing that such a rule was too simple to be true for general equations. Sturm calmly worked through several examples, including a few with irrational and multiple roots. As he demonstrated the accuracy of his method, the room grew quiet. Finally, Liouville reportedly leaned back and said, “C’est trop élégant pour être faux” — It’s too elegant to be false.
This moment helped establish Sturm's reputation in Parisian mathematical circles and contributed to the eventual widespread adoption of his theorem — a foundational result in real algebra still taught today.
 |
| Charles Sturm |
1837 At a meeting of the Berlin Academy of Sciences, Dirichlet presented his first paper on analytic number theory. He proved the fundamental theorem that bears his name: Every arithmetical series an + b, n =0, 1, 2,... of integers where a and b are relatively prime, contains infinitely many primes. The result had long been conjectured. Legendre tried hard for a proof but could only establish special cases such as 4n + 1. *VFR
1861 The Athenaeum magazine carried a review of Charles Dodgson's pamphlet entitled The Formula of Plane Trigonometry in which he suggested new symbols for the six basic trig functions. The reviewer was not convinced.
1866 Cyrus W. Field finally succeeded, after two failures, in laying the first underwater telegraph cable 1,686 miles long across the Atlantic Ocean between North America and Europe. Massachusetts merchant and financier Cyrus W. Field first proposed laying a 2,000-mile copper cable along the ocean bottom from Newfoundland to Ireland in 1854, but the first three attempts ended in broken cables and failure. Field's persistence finally paid off in July 1866, when the Great Eastern, the largest ship then afloat, successfully laid the cable along the level, sandy bottom of the North Atlantic. *TIS
 |
*Thought.co
|
1905 A Karl Pearson letter appears in Nature asking for assistance on a problem"of considerable interest” about random walks (based on a question in a letter he had received from Sir Ronald Ross, who had discovered mosquitoes as the source of malaria spreading, without mentioning him by name), Two days later Lord Rayleigh wrote the periodical to inform them he had solved the problem and posted results in 1880 in Phil. Mag.. Pearson's response launched the common name for random walk used for many years, Drunkards Walk, "the most probable place to find a drunken man who is at all capable of keeping on his feet is somewhere near his starting point!” *Jordan Ellenberg , Shape
A favorite quote about dimensional random walks, "A drunk man will find his way home, but a drunk bird may get lost forever." usually attributed to Shizuo Kakutani
 |
| *Wik |
1936 Einstein writes to John Tate, editor of the Physical Review angrily withdrawing a paper that he had submitted for publication but had been rejected after peer review. Einstein and Rosen's paper claimed that gravitational waves did not exist. It was Einstein who introduced gravitational waves in his theory of general relativity in 1916, within a few months of finding the correct form of the field equations for it. However by 1936 he had changed his mind, and wrote to his friend, Max Born, "Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist,..."
Later he would submit the paper again, but then drastically revise the conclusions before publication. Einstein simply explained why “fundamental” changes in the paper were required because the “consequences” of the equations derived in the paper had previously been incorrectly inferred. The referee of the paper, it is now known, was relativist Howard Percy Robertson. He was on sabbatical at Caltech. When he returned to Princeton he struck up a friendship with Einstein’s then newly arrived assistant Infeld. Robertson then convinced Infield of the problems with the paper he had re-submitted, and after Infield talked to Einstein, the paper was revised. It seems that Einstein had never read the referee's comments.
*physicstoday
1948 Hungary issued a stamp commemorating the centenary of the birth of the physicist Baron Roland E˝otv˝os1 (1848–1919). [Scott #840]. *VFR They issued another in 1991
2007 Ralph Asher Alpher's belated recognition for his work on the "Big Bang" process. In 2005 Alpher was awarded the National Medal of Science. The citation for the award reads "For his unprecedented work in the areas of nucleosynthesis, for the prediction that universe expansion leaves behind background radiation, and for providing the model for the Big Bang theory." The medal was presented to his son Dr. Victor S. Alpher on July 27, 2007 by President George W. Bush, as his father could not travel to receive the award. *Wik
BIRTHS
1667 Johann Bernoulli (27 July 1667 – 1 January 1748; also known as Jean or John) was a Swiss mathematician who studied reflection and refraction of light, orthogonal trajectories of families of curves, quadrature of areas by series and the brachystochrone.*SAU
1733 Jeremiah Fenwicke Dixon (27 July 1733 – 22 January 1779) was an English surveyor and astronomer who is best known for his work with Charles Mason, from 1763 to 1767, in determining what was later called the Mason-Dixon line.
Dixon was born in Cockfield, near Bishop Auckland, County Durham, the fifth of seven children, to Sir George Fenwick Dixon 5th Bt. and Lady Mary Hunter. His father was a wealthy Quaker coal mine owner and aristocrat. His mother came from Newcastle, and was said to have been "the cleverest woman" to ever marry into the Dixon family. Dixon became interested in astronomy and mathematics during his education at Barnard Castle. Early in life he made acquaintances with the eminent intellectuals of Southern Durham: mathematician William Emerson, and astronomers John Bird and Thomas Wright. In all probability it was John Bird, who was an active Fellow of the Royal Society, who recommended Dixon as a suitable companion to accompany Mason.
Jeremiah Dixon served as assistant to Charles Mason in 1761 when the Royal Society selected Mason to observe the transit of Venus from Sumatra. However, their passage to Sumatra was delayed, and they landed instead at the Cape of Good Hope where the transit was observed on June 6, 1761. Dixon returned to the Cape once again with Nevil Maskelyne's clock to work on experiments with gravity.
Dixon and Mason signed an agreement in 1763 with the proprietors of Pennsylvania and Maryland, Thomas Penn and Frederick Calvert, sixth Baron Baltimore, to assist with resolving a boundary dispute between the two provinces. They arrived in Philadelphia in November 1763 and began work towards the end of the year. The survey was not complete until late 1766, following which they stayed on to measure a degree of Earth's meridian on the Delmarva Peninsula in Maryland, on behalf of the Royal Society. They also made a number of gravity measurements with the same instrument that Dixon had used with Maskelyne in 1761. Before returning to England in 1768, they were both admitted to the American Society for Promoting Useful Knowledge, in Philadelphia.
Dixon sailed to Norway in 1769 with William Bayly to observe another transit of Venus. The two split up, with Dixon at Hammerfest Island and Bayly at North Cape, in order to minimize the possibility of inclement weather obstructing their measurements. Following their return to England in July, Dixon resumed his work as a surveyor in Durham. He died unmarried in Cockfield on 22 January 1779, and was buried in an unmarked grave in the Quaker cemetery in Staindrop.
Although he was recognized as a Quaker, he was not a very good one, dressing in a long red coat and occasionally drinking to excess. *Wik
Dixon is (supposedly) the one standing
1801 Sir. George Biddell Airy (27 July 1801 – 2 January 1892) born in Alnwick, England. *VFR English astronomer who became the seventh Astronomer Royal (1836-92). In his life he studied interference fringes in optics, made a mathematical study of the rainbow and computed the density of the Earth by swinging a pendulum at the top and bottom of a deep mine, determined the mass of the planet Jupiter and its period rotation, calculated the orbits of comets and cataloged stars. He designed corrective lenses for astigmatism (1825), the first that worked. His motivation was his own astigmatism. Airy had a long-standing battle with Babbage. In 1854, the conflict continued between the two during the battle of the incompatible railway gauges in England. Airy championed the railway narrow gauge and Babbage for the wide gauge. *TIS
In his On the Algebra and Numerical Theory of Errors of Observation (1861), he joined the company of such mathematicians as Gauss, Legendre, and the American, Robert Adrain, in attempting to mathematically understand the behavior of error patterns in the process of taking observations. *MAA
1844 Ágoston Scholtz (27 July 1844 in Kotterbach, Zips district, Austro-Hungary (now Rudnany, Slovakia) - 6 May 1916 in Veszprém,) From 1871 he was a teacher of mathematics and natural philosophy at the Lutheranian Grammar School of Budapest which at that time had been upgraded to become a so called 'chief grammar school', namely one which offered eight years of teaching. This was precisely the school which later was attended by several famous mathematicians such as Johnny von Neumann and Eugene Wigner (or Jenó Pál Wigner as he was called at that time). Scholtz became the school director of the Lutheranian Grammar School in 1875. Unfortunately this excellent school was closed in 1952, and most of its equipment was lost. Due to the initiative and support of its former well-known students, among others Wigner, it was reopened in 1989 after being closed for thirty-seven years. Scholtz's field of research was projective geometry and theory of determinants. His results were recorded by Muir in his famous work The history of determinants *SAU
1848 Roland Baron von Eötvös (27 July 1848 – 8 April 1919) was a Hungarian physicist who studied at Heidelberg where he was taught by Kirchhoff, Helmholtz and Bunsen. Eötvös introduced the concept of molecular surface tension and published on capillarity (1876-86). For the rest of his life he concentrated on study of the Earth's gravitational field. He developed the Eötvös torsion balance, long unsurpassed in precision, which gave experimental proof that inertial mass and gravitational mass, to a high degree of accuracy, are equivalent - which later was a major principle of Albert Einstein.*TIS
1848 Friedrich Ernst Dorn (27 July 1848 – 16 December 1916) was a German physicist who was the first to discover that a radioactive substance, later named radon, is emitted from radium.Dorn was born in Guttstadt (Dobre Miasto), Province of Prussia (nowadays Warmia in Poland), and died in Halle, Province of Saxony.
He was educated at Königsberg and went on to teach at the university level. In 1885, at Halle University, Dorn took over the position of personal ordinarius professor for theoretical physics from Anton Oberbeck. Since Dorn was already an ordinarius professor, he was allowed to assume the title so as to not appear as having been demoted. In 1895, Dorn succeeded Hermann Knoblauch at Halle as the ordinarius professor for experimental physics and director of the physics institute. Dorn's previous duties were assumed by Carl Schmidt, who had been a Privatdozent and was called as an extraordinarius professor for theoretical physics.
In 1900, Dorn published a paper in which he described experiments that repeated and extended some earlier work on thorium by Ernest Rutherford. Dorn verified Rutherford's observation that a radioactive material was emitted by thorium, and discovered that a similar emission arose from the element radium. Additional work by Rutherford and Soddy showed that the same emission came from both thorium and radium, that it was a gas, and that it was actually a new element.
Dorn called the radioactive gaseous product from radium simply "emanation", but in 1904 Rutherford introduced the name "radium emanation" for the same material. Ramsay later suggested "niton", from the Latin word "nitens" meaning "shining". In 1923 the name was again changed, this time to radon by an international body of scientists.*Wik
1849 John Hopkinson (27 July 1849 – 27 August 1898) British physicist and electrical engineer who worked on the application of electricity and magnetism in devices like the dynamo and electromagnets. Hopkinson's law (the magnetic equivalent of Ohm's law) bears his name. In 1882, he patented his invention of the three-wire system (three phase) for electricity generation and distribution. He presented the principle the synchronous motors (1883), and designed electric generators with better efficiency. He also studied condensers and the phenomena of residual load. In his earlier career, he became (1872) engineering manager of Chance Brothers and Co., a glass manufacturer in Birmingham, where he studied lighthouse illumination, improving efficiency with flashing groups of lights.*TIS
1867 Derrick Norman Lehmer (27 July 1867, Somerset, Indiana, USA — 8 September 1938 in Berkeley, California, USA) was an American mathematician and number theorist.
In 1903, he presented a factorization of Jevons' number (8,616,460,799) at the San Francisco Section of the American Mathematical Society, December 19, 1903.
He published tables of prime numbers and prime factorizations, reaching 10,017,000 by 1909 (
In Number Theory and Its History, Ore calls this the "best factor table now (1948) available"). He developed a variety of mechanical and electro-mechanical factoring and computational devices, such as the Lehmer sieve, built with his son Derrick Henry Lehmer.
He is also known for a reversible algorithm that assigns a Lehmer code to every permutation of size n. *SAU
1870 Bertram Borden Boltwood (July 27, 1870 Amherst, Massachusetts - August 15, 1927, Hancock Point, Maine) was an American chemist and physicist whose work on the radioactive decay of uranium and thorium was important in the development of the theory of isotopes. Boltwood studied the "radioactive series" whereby radioactive elements sequentially decay into other isotopes or elements. Since lead was always present in such ores, he concluded (1905) that lead must be the stable end product from their radioactive decay. Each decay proceeds at a characteristic rate. In 1907, he proposed that the ratio of original radioactive material to its decay products measured how long the process had been taking place. Thus the ore in the earth's crust could be dated, and give the age of the earth as 2.2 billion years.*TIS
1871 Ernest Friedrich Ferdinand Zermelo. (27 July 1871; Berlin, German Empire - 21 May 1953 (aged 81) Freiburg im Breisgau, West Germany) In 1904 he formulated the Axiom of Choice in Set Theory. Years later, when he refused to give the Nazi salute, he was threatened with dismissal from his university position. In reply, he resigned. *VFR
1921 Jonas Kubilius (27 July 1921 – 30 October 2011) was a Lithuanian mathematician who worked in probability theory and number theory. He was rector of Vilnius University for 32 years, and served one term in the Lithuanian parliament.
Kubilius's scientific work was in the areas of number theory and probability theory. The Turán–Kubilius inequality and the Kubilius model in probabilistic number theory are named after him. Eugenijus Manstavičius and Fritz Schweiger wrote about Kubilius's work in 1992, "the most impressive work has been done on the statistical theory of arithmetic functions which almost created a new research area called Probabilistic Number Theory. A monograph devoted to this topic was translated into English in 1964 and became very influential." (The monograph is Probabilistic Methods in the Theory of Numbers.)
Kubilius organized the first mathematical olympiad in Lithuania in 1951, and he wrote books of problems for students to use in preparing for the olympiads. He was a past president of the Lithuanian Mathematical Society.
In addition to his scientific and administrative work, Kubilius was a member of the Seimas (Lithuanian parliament) from 1992 to 1996. *Wik
DEATHS1759 Pierre-Louis Moreau de Maupertuis (17 July 1698 – 27 July 1759) French mathematician, biologist, and astronomer. In 1732 he introduced Newton's theory of gravitation to France. He was a member of an expedition to Lapland in 1736 which set out to measure the length of a degree along the meridian. Maupertuis' measurements both verified Newton's predictions that the Earth would be an oblate speroid, and they corrected earlier results of Cassini. Maupertuis published on many topics including mathematics, geography, astronomy and cosmology. In 1744 he first enunciated the Principle of Least Action and he published it in Essai de cosmologie in 1850. Maupertuis hoped that the principle might unify the laws of the universe and combined it with an attempted proof of the existence of God.*TIS (he died in the home of Johann II Bernoulli.
Johan Bernoulli (above) was born on the day Maupertuis died, but Johann II Bernoulli died on the Calendar date on which Maupertuis was born...)
1844 John Dalton, (6 September 1766 – 27 July 1844) English teacher who, from investigating the physical and chemical properties of matter, deduced an Atomic Theory (1803) whereby atoms of the same element are the same, but different from the atoms of any other element. In 1804, he stated his law of multiple proportions by which he related the ratios of the weights of the reactants to the proportions of elements in compounds. He set the atomic weight of hydrogen to be identically equal to one and developed a table of atomic weights for other elements. He was the first to measure the temperature change of air under compression, and in 1801 suggested that all gases could be liquefied by high pressure and low temperature. Dalton recognized that the aurora borealis was an electrical phenomenon.*TIS |
| *Linda Hall Org |
1931 Jacques Herbrand (12 February 1908 – 27 July 1931) was a French mathematician who died young but made contributions to mathematical logic.*SAU Although he died at only 23 years of age, he was already considered one of "the greatest mathematicians of the younger generation" by his professors Helmut Hasse, and Richard Courant. *Wik
1999 Aleksandr Danilovic Aleksandrov (4 Aug 1912 in Volyn, Ryazan, Russia
- 27 July 1999) approached the differential geometry of surfaces [by extending the notion of the objects studied], extending the class of regular convex surfaces to the class of all convex surfaces ... . In order to solve concrete problems Aleksandrov had to replace the Gaussian geometry of regular surfaces by a much more general theory. In the first place the intrinsic properties (i.e. those properties that appear as a result of measurements carried out on the surface) of an arbitrary convex surface had to be studied, and methods found for the proof of theorems on the connection between intrinsic and exterior properties of convex surfaces. Aleksandrov constructed a theory of intrinsic geometry of convex surfaces on that basis. Because of the depth of this theory, the importance of its applications and the breadth of its generality, Aleksandrov comes second only to Gauss in the history of the development of the theory of surfaces. *SAU
2015 John William Scott Cassels (11 July 1922 – 27 July 2015) initially worked on elliptic curves. After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the Selmer group with Galois cohomology and laying some of the foundations of the modern theory of infinite descent. His best-known single result may be the proof that the Tate-Shafarevich group, if it is finite, must have order that is a square; the proof being by construction of an alternating form. Cassels has often studied individual Diophantine equations by algebraic number theory and p-adic methods.
His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades. *Wik
2021 Enrique Aurelio Planchart Rotundo (3 April 1937 – 27 July 2021) was a Venezuelan mathematician and academic. He was rector of Simón Bolívar University in Caracas from 2009 until his death in 2021.
Planchart graduated as a Bachelor of Science from the Central University of Venezuela and obtained his Doctorate in Mathematics from the University of California, Berkeley, where he was also a visiting professor in its Department of Mathematics between 1986 and 1987. From 1973 he was part of the Department of Pure and Applied Mathematics of the Simón Bolívar University.
While at Simón Bolívar University, between 1989 and 1999 he directed the National Center for the Improvement of Science Education, and from 1999 he directed the Equal Opportunities Program (PIO). In 1989 he was awarded the National Council for Scientific and Technological Research Award.
Throughout his scientific career, Planchart published nine books and nine journal articles and gave thirty lectures *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
.jpg)
