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.
This is the 208th day of the year; 208 is the sum of the squares of the first five primes.
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.
1794 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.
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 contributers 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]
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
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
1667 Johann Bernoulli 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
1801 Sir. George Biddell Airy 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
1844 Ágoston Scholtz 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 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
1849 John Hopkinson 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.
1870 Bertram Borden Boltwood 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 Birthdate of Ernest Friedrich Ferdinand Zermelo. 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 univeristy position. In reply, he resigned. *VFR
1759 Pierre-Louis Moreau de Maupertuis 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, 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 liquified by high pressure and low temperature. Dalton recognised that the aurora borealis was an electrical phenomenon.*TIS
1931 Jacques Herbrand was a French mathematician who died young but made contributions to mathematical logic.*SAU
1999 Aleksandr Danilovic Aleksandrov 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
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum