Giuseppe Peano

Giuseppe Peano was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation; the standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction, he spent most of his career teaching mathematics at the University of Turin. He wrote an international auxiliary language, Latino sine flexione, a simplified version of Classical Latin. Most of his books and papers are in Latin sine flexione, others are in Italian. Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Italy, he attended the Liceo classico Cavour in Turin, enrolled at the University of Turin in 1876, graduating in 1880 with high honors, after which the University employed him to assist first Enrico D'Ovidio, Angelo Genocchi, the Chair of calculus.

Due to Genocchi's poor health, Peano took over the teaching of calculus course within two years. His first major work, a textbook on calculus, was credited to Genocchi. A few years Peano published his first book dealing with mathematical logic. Here the modern symbols for the union and intersection of sets appeared for the first time. In 1887, Peano married Carola Crosio, the daughter of the Turin-based painter Luigi Crosio, known for painting the Refugium Peccatorum Madonna. In 1886, he began teaching concurrently at the Royal Military Academy, was promoted to Professor First Class in 1889. In that year he published the Peano axioms, a formal foundation for the collection of natural numbers; the next year, the University of Turin granted him his full professorship. The Peano curve was published in 1890 as the first example of a space-filling curve which demonstrated that the unit interval and the unit square have the same cardinality. Today it is understood to be an early example of. In 1890 Peano founded the journal Rivista di Matematica, which published its first issue in January 1891.

In 1891 Peano started the Formulario Project. It was to be an "Encyclopedia of Mathematics", containing all known formulae and theorems of mathematical science using a standard notation invented by Peano. In 1897, the first International Congress of Mathematicians was held in Zürich. Peano was a key participant, he started to become occupied with Formulario to the detriment of his other work. In 1898 he presented a note to the Academy about binary numeration and its ability to be used to represent the sounds of languages, he became so frustrated with publishing delays that he purchased a printing press. Paris was the venue for the Second International Congress of Mathematicians in 1900; the conference was preceded by the First International Conference of Philosophy where Peano was a member of the patronage committee. He presented a paper which posed the question of formed definitions in mathematics, i.e. "how do you define a definition?". This became one of Peano's main philosophical interests for the rest of his life.

At the conference Peano gave him a copy of Formulario. Russell was struck by Peano's innovative logical symbols and after the conference he retired in the country "to study every word written by him or his disciples."Peano's students Mario Pieri and Alessandro Padoa had papers presented at the philosophy congress also. For the mathematical congress, Peano did not speak, but Padoa's memorable presentation has been recalled. A resolution calling for the formation of an "international auxiliary language" to facilitate the spread of mathematical ideas, was proposed. By 1901, Peano was at the peak of his mathematical career, he had made advances in the areas of analysis and logic, made many contributions to the teaching of calculus and contributed to the fields of differential equations and vector analysis. Peano played a key role in the axiomatization of mathematics and was a leading pioneer in the development of mathematical logic. Peano had by this stage become involved with the Formulario project and his teaching began to suffer.

In fact, he became so determined to teach his new mathematical symbols that the calculus in his course was neglected. As a result, he was dismissed from the Royal Military Academy but retained his post at Turin University. In 1903 Peano announced his work on an international auxiliary language called Latino sine flexione; this was an important project for him. The idea was to use Latin vocabulary, since this was known, but simplify the grammar as much as possible and remove all irregular and anomalous forms to make it easier to learn. On 3 January 1908, he read a paper to the Academia delle Scienze di Torino in which he started speaking in Latin and, as he described each simplification, introduced it into his speech so that by the end he was talking in his new language; the year 1908 was important for Peano. The fifth and final edition of the Formulario project, titled Formulario mathematico, was published, it contained 4200 formulae and theorems, all stated and most of them proved. The book received little attention.

However, it remains a significant contribution to mathematical literature. The comments

Stairfoot rail accident

The Stairfoot rail accident was a railway accident that took place at Stairfoot, South Yorkshire, England. On 12 December 1870, in Barnsley top yard a rake of 10 goods wagons was standing on a gradient of 1 in 119. A single sprag between the spokes of a wheel was holding them; when two gas tank wagons were shunted against the rake, the sprag broke and the 12 wagons began to move. Two pointsmen made valiant efforts to pin down the brakes to no avail; the wagons gathered speed as the gradient increased to 1 in 72 and passed three signal boxes, none of which had points under their control to deflect the runaways. Meanwhile, a passenger train which had left Barnsley at 18:15 was standing at Stairfoot station one and a half miles away; the runaways struck the rear of the standing train at a speed of at least 40 mph, killing 15 and injuring 59 more. The enquiry by Lieut-Col F. H. Rich found that the goods guard was gravely at fault for not ensuring the standing wagons were better secured; the layout of the yard was criticized as there were no trap points to protect the running lines in the event of such a mishap.

Abergele rail disaster Rolt, L. T. C.. Red for Danger. Newton Abbot: David & Charles. Pp. 184–186. ISBN 0-7153-8362-0. Full report of Enquiry into Accident at Stairfoot on 12 December 1870

Swan Lake Nature Study Area

The Swan Lake Nature Study Area is a small conservation area in Lemmon Valley, Nevada. It contains marsh, alkali mud flats, high desert; the Lahontan Audubon Society describes it as "a nearly unspoiled wetland in the midst of suburban housing and warehouses" and designates it a Nevada Important Bird Area. It is a notable location for birding; the Swan Lake Nature Study Area consists of over 1,800 acres of land, with water supplied by the nearby Reno/Stead Sewage Treatment Plant. The size of the actual wetland varies seasonally and yearly, depending on the amount of precipitation, between 100 and 1,000 acres, it was formally dedicated as a nature study area in 1999, following several years of planning by Reno-area environmentalist/writer/photographer Bob Goodman. The lead organization in planning and creating the conservation area was the Nevada Army National Guard, which contributed about 360 acres and performed preliminary ecological studies. Other sponsoring organizations include: the Bureau of Land Management.

Features include an observational boardwalk into the marsh and educational signs about the local ecology. Swan Lake is located in the midst of the developing suburbs of Stead and Lemmon Valley, near Peavine Peak north of Reno. According to a 1995 study, humans have lived in the area since as early as 400 AD. Steady Hand Creates Reno's Swan Lake Nature Study Area - June 2004 article on the conservation area's development Swan Lake- Lahontan Audubon Society guide Press Release on recent Swan Lake grants