ConseggioLigure/seed-instruct-eng-lij huggingface dataset:
Translate to Genoese:
The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
The Ligurian (Genoese) translation is:
A reçerca neçessäia pe resòlve di problemi de matematica a peu domandâ di anni, ò fiña di secoli, de studdi impegnativi.
What’s the Ligurian translation of this sentence?
Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
The Ligurian (Genoese) translation is:
A matematica a s’é sviluppa con un ritmo abastansa lento fin à l’etæ da Renascion, quande e innovaçioin inte sto campo, insemme a-e neuve scoverte into campo da sciensa, an portou a-a spedia à l’aumento do tasso de scoverta inte l’ambito da matematica, ch’o l’é anæto avanti fin a-a giornâ d’ancheu.
Translate to Genoese:
As evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time—days, seasons, or years.
The Ligurian (Genoese) translation is:
Comme demostra i talli attrovæ in scê òsse, ciù in là de reconosce comme se conta i oggetti fixichi, i pòpoli da preistöia porrieivan avei reconosciuto anche comme contâ de quantitæ astræte, comme o tempo (giorni, stagioin e anni).
Translate this sentence to Genoese:
Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right.
The Ligurian (Genoese) translation is:
À partî da-o secolo VI a.C., co-i discepoli de Pitagora, co-a matematica grega i Greghi antighi an comensou à studiâ scistematicamente a matematica comme matëia separâ.
Translate to Ligurian:
The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse.
The Ligurian (Genoese) translation is:
O ciù grande matematico de l’antighitæ pe-o sòlito o l’é individuou inte Archimede de Sciragusa (c. 287-212 a.C.).
Translate this sentence to Ligurian:
The most notable achievement of Islamic mathematics was the development of algebra.
The Ligurian (Genoese) translation is:
A conquista ciù importante da matematica islamica o l’é stæto o desviluppo de l’algebra.
Translate to Genoese:
During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The Ligurian (Genoese) translation is:
Inta primma etæ moderna, a matematica a l’à comensou à sviluppâse ciù a-a spedia inte l’Euröpa de ponente.
Translate from English to Ligurian:
Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, analysis, differential geometry, matrix theory, number theory, and statistics.
The Ligurian (Genoese) translation is:
Fòscia o matematico ciù importante do secolo XIX o l’é stæto o todesco Carl Friedrich Gauss, ch’o l’à dæto ben ben de contribuçioin inte di campi comme l’algebra, a geometria differençiale, a teorie de matrixe, a teoria di numeri e a statistica.
Translate from English to Genoese:
Mathematical discoveries continue to be made today.
The Ligurian (Genoese) translation is:
De scoverte matematiche vëgnan fæte ancon a-a giornâ d’ancheu.
Translate this sentence to Genoese:
In particular, mathēmatikḗ tékhnē meant "the mathematical art."
The Ligurian (Genoese) translation is:
Ciù into detaggio, mathēmatikḗ tékhnē voeiva dî «l’arte matematica».
Translate to Ligurian:
In English, the noun mathematics takes a singular verb.
The Ligurian (Genoese) translation is:
In ingleise, o sostantivo «mathematics» o veu o verbo a-o scingolare.
Translate to Ligurian:
However, Aristotle also noted a focus on quantity alone may not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart.
The Ligurian (Genoese) translation is:
À tutti i mòddi, Aristòtele o l’à nottou che anche unn’attençion solo che a-a quantitæ a no peu distingue a matematica da de sciense comme a fixica; segondo lê, a matematica a l’é distinta da-e istanse da realtæ pe meo de l’astraçion e do studio da quantitæ comme «separabile da-o pensceo».
Translate to Ligurian (Genoese):
A peculiarity of intuitionism is that it rejects some mathematical ideas considered valid according to other definitions.
The Ligurian (Genoese) translation is:
A particolaritæ de l’intuiçionismo a l’é o refuo de çerte idee matematiche conscideræ valide segondo atre definiçioin.
Translate from English to Genoese:
Haskell Curry defined mathematics simply as "the science of formal systems".
The Ligurian (Genoese) translation is:
Haskell Curry o l’à definio a matematica solo comme «a sciensa di scistemi formali».
Translate to Genoese:
Popper also noted that "I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience."
The Ligurian (Genoese) translation is:
Popper o l’à nottou ascì che «ammettiò che un scistema o segge empirico o scientifico solo s’o peu ëse misso a-a preuva da l’esperiensa».
Can you translate this text to Ligurian?
Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences.
The Ligurian (Genoese) translation is:
L’intuiçion e a sperimentaçion an zugou un ròllo primmäio ascì pe-e ipòtexi tanto che e inta matematica comme inte (atre) sciense.
Can you translate this text to Ligurian?
For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.
The Ligurian (Genoese) translation is:
Pe fâ un exempio, o fixico Richard Feynman o l’à inventou a formulaçion integrale do percorso da mecanica quantistica deuviando unna combinaçion de raxonamento matematico e intuiçion fixica, e a teoria de strinche in veuga a-a giornâ d’ancheu (saieiva à dî unna teoria scientifica ancon in fase de sviluppo ch’a çerca d’azzonze e quattro fòrse fondamentale da natua) a l’inspira ancon da neuva matematica.
Can you translate this text to Ligurian?
A distinction is often made between pure mathematics and applied mathematics.
The Ligurian (Genoese) translation is:
De spesso se distingue fra a matematica pua e quella applicâ.
Translate this sentence to Genoese:
As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.
The Ligurian (Genoese) translation is:
Comme inta ciù parte di campi de studio, l’esploxon da conoscensa inte l’epoca scientifica a l’à portou a-a speçializzaçion: oua gh’é çentenæa d’aree speçializzæ inta matematica e l’urtima Mathematics Subject Classification a l’arriva a-e 46 pagine.
What’s the Genoese translation of this sentence?
Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty.
The Ligurian (Genoese) translation is:
Tanti studioxi de matematica mensoñan l’elegansa da matematica, a seu estetica intrinseca e a seu bellessa interiô.
Translate from English to Ligurian:
G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics.
The Ligurian (Genoese) translation is:
G. H. Hardy iten A Mathematician’s Apology o l’à manifestou a convinçion che ste conscideraçioin estetiche seggian abasta, da pe liatre, pe giustificâ o studio da matematica pua.
Translate to Genoese:
A theorem expressed as a characterization of the object by these features is the prize.
The Ligurian (Genoese) translation is:
Un teorema espresso comme caratterizzaçion de l’oggetto da ste caratteristiche o l’é o premio.
Translate from English to Ligurian:
Euler (1707–1783) was responsible for many of the notations in use today.
The Ligurian (Genoese) translation is:
Eulero (1707-1783) o l’é responsabile de ben ben de nottaçioin deuviæ ancon a-a giornâ d’ancheu.
Translate from English to Genoese:
Mathematical language also includes many technical terms such as homeomorphism and integrable that have no meaning outside of mathematics.
The Ligurian (Genoese) translation is:
O linguaggio matematico o comprende ascì tanti termini speçializzæ comme «omeomorfismo» ò «integrabile», che n’an nisciun scignificato a-o de feua da matematica.
Can you translate this text to Ligurian?
Mathematicians refer to this precision of language and logic as "rigor".
The Ligurian (Genoese) translation is:
I studioxi de matematica fan referensa à sta lògica e à sta preçixon de linguaggio comme «rigô».
Translate from English to Genoese:
This is to avoid mistaken "theorems", based on fallible intuitions, of which many instances have occurred in the history of the subject.
The Ligurian (Genoese) translation is:
Questo o l’é pe evitâ di «teoremi» sbaliæ, basæ in sce de intuiçioin fallibile; di caxi pægi, inta stöia da matëia, se n’é verificou ben ben.
Translate this sentence to Ligurian:
Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics.
The Ligurian (Genoese) translation is:
A fäsa interpretaçion do rigô a l’é a raxon pe-e çerte tra e fäse conceçioin da matematica che s’attreuvan ciù de frequente.
Translate from English to Genoese:
On the other hand, proof assistants allow verifying all details that cannot be given in a hand-written proof, and provide certainty of the correctness of long proofs such as that of the Feit–Thompson theorem.
The Ligurian (Genoese) translation is:
Da l’atra parte, i ascistenti de preuve permettan de verificâ tutti i detaggi che no peuan ëse fornii inte unna preuva scrita à man e dan a çertessa da correttessa de preuve longhe comme quella do teorema de Feit-Thompson.
Translate to Ligurian:
In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
The Ligurian (Genoese) translation is:
In azzonta à ste preoccupaçioin prinçipæ gh’é ascì de sottodivixoin dedicæ à l’esploraçioin di collegamento da-o cheu da matematica +a di atri campi: da-a lògica, a-a teoria di insemmi (fondaçioin), a-a matematica empirica de varie sciense (matematica applicâ) e ciù de reçente a-o studio rigoroso de l’inçertessa.
Translate from English to Ligurian (Genoese dialect):
Some disagreement about the foundations of mathematics continues to the present day.
The Ligurian (Genoese) translation is:
Quarche mancansa d’accòrdio in scî fondamenti da matematica a l’é ancon viva a-a giornâ d’ancheu.
Translate from English to Ligurian (Genoese dialect):
Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science, as well as to category theory.
The Ligurian (Genoese) translation is:
A lògica moderna a se dividde inta teoria da ricorscion, quella di modelli e quella da preuva, a e l’é ligâ streitamente à l’informatica teòrica e a-a teoria de categorie.
Translate to Ligurian:
Computability theory examines the limitations of various theoretical models of the computer, including the most well-known model—the Turing machine.
The Ligurian (Genoese) translation is:
A teoria da computabilitæ a sstudia i limiti de varri modelli teròrichi di computer, compreiso quello ciù conosciuo: a machina de Turing.
Translate to Ligurian:
Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of "infinity".
The Ligurian (Genoese) translation is:
A conscideraçion di numeri naturali a pòrta anche a-i numeri transfinii, che formalizzan o conçetto de «infinio».
Translate to Genoese:
Thus one can study groups, rings, fields and other abstract systems; together such studies (for structures defined by algebraic operations) constitute the domain of abstract algebra.
The Ligurian (Genoese) translation is:
Coscì se peu studiâ di gruppi, di anelli, di campi e di atri scistemi astræti; inte l’insemme, sti studdi (pe struttue definie da de operaçioin algebriche) forman o dominio de l’algebra astræta.
Translate this sentence to Ligurian:
Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions.
The Ligurian (Genoese) translation is:
A trigonometria a l’é a ramma da matematica ligâ a-e relaçioin tra i loei e i angoli di triangoli e co-e fonçioin trigonometriche.
Translate to Genoese:
Lie groups are used to study space, structure, and change.
The Ligurian (Genoese) translation is:
I gruppi de Lie vëgnan deuviæ pe studiâ o spaçio, a struttua e o cangio.
What’s the Ligurian translation of this sentence?
Functions arise here as a central concept describing a changing quantity.
The Ligurian (Genoese) translation is:
Chì e fonçioin se presentan comme un conçetto primmäio ch’o descrive unna quantitæ ch’a cangia.
Translate from English to Ligurian:
One of many applications of functional analysis is quantum mechanics.
The Ligurian (Genoese) translation is:
Uña de tante applicaçioin de l’analixi fonçionale a l’é a mecanica quantica.
Translate this sentence to Ligurian:
Statisticians (working as part of a research project) "create data that makes sense" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data becomes available).
The Ligurian (Genoese) translation is:
I studioxi de statistica (travaggiando inte un progetto de reçerca) crean di «dæti ch’an de senso» pe mezo do campionamento casuale e con di esperimenti randomizzæ; o disegno de un campion statistico ò de un esperimento o speçifica l’analixi di dæti (primma che i dæti mæximi seggian à dispoxiçion).
What’s the Ligurian translation of this sentence?
Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis includes the study of approximation and discretisation broadly with special concern for rounding errors.
The Ligurian (Genoese) translation is:
L’analixi numerica a studia di metodi pe-i problemi d’analixi pe mezo de l’analixi fonçionale e a teoria de l’approscimaçion; l’analixi numerica a comprende o studio de l’approscimaçion e da discretizzaçion latu sensu, con unn’attençion particolare a-i erroî d’arrotondaçion.
Translate to Ligurian:
The Chern Medal was introduced in 2010 to recognize lifetime achievement.
The Ligurian (Genoese) translation is:
A medaggia Chern a l’é stæta introduta do 2010 pe premiâ i successi che meitan d’ëse regordæ pe delongo.
Translate to Ligurian:
This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved.
The Ligurian (Genoese) translation is:
Sta lista a l’à razzonto unna gran çelebritæ tra i studioxi da matematica e a-o manco neuve di problemi an attrovou de soluçion.
What’s the Genoese translation of this sentence?
The value of Pi was first calculated by him.
The Ligurian (Genoese) translation is:
O valô do pi grego o l’é stæto carcolou pe-a primma vòtta da lê.
Can you translate this text to Ligurian?
It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins.
The Ligurian (Genoese) translation is:
O termine «matematica» o l’é stæto cuniou da-i discepoli de Pitagora, co-i quæ comensa o studio da matematica mæxima.
Translate from English to Ligurian (Genoese dialect):
Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles).
The Ligurian (Genoese) translation is:
Apreuvo à unna conteisa politica, a communitæ crestiaña de Lusciandra a l’aiva castigâ, co-o pensâ ch’a fïse interessâ lê ascì; l’aivan despuggiâ e gh’aivan rascciou a scheña con de scheuggioe (gh’é chì dixe con di coppi).
Translate from English to Genoese:
Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences.
The Ligurian (Genoese) translation is:
I finançiamenti pe-a traduçion de testi de sciensa inte de atre lengue vegnivan stançiæ durante o regno de çerti califfi e resultava che çerti studioxi vegnivan di esperti inte euvie che traduxeivan; a seu vòtta reçeveivan ancon do sostëgno pe anâ avanti co-o sviluppo de çerte sciense.
Translate from English to Ligurian:
A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths.
The Ligurian (Genoese) translation is:
Unna caratteritica degna de nòtta de tanti studioxi che travaggian sotta a-o governo mossulman inte l’etæ de mezo a l’ea a seu polimatiçitæ.
Translate to Ligurian:
During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer).
The Ligurian (Genoese) translation is:
Inte sto periodo de tranxiçion da unna coltua prinçipalmente feudale e ecclexiastica à unn’atra prevalentemente secolare, tanti studioxi de matematica degni de nòtta aivan di atri travaggi: Luca Pacioli (fondatô da contabilitæ); Gerolamo Cardano (primmo fondatô da probabilitæ e de l’esprescion binomiale); Robert Recorde (mego) e François Viète (avvocou).
What’s the Ligurian translation of this sentence?
British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Ligurian (Genoese) translation is:
E universcitæ britanniche de quello periodo aivan adottou de metodologie za presente inte quelle italiañe e todesche, ma dæto che de fæto aivan za unna çerta libertæ e autonomia, da liatri i cangi ean za comensæ con l’Etæ di Lummi; e mæxime influense ch’an inspirou Humboldt.
Translate to Genoese:
Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content.
The Ligurian (Genoese) translation is:
I studenti poeivan fâ da reçerca inte di seminäi e labortatöi e comensavan à scrive de texi de dottorato con ciù tanto contegnuo scientifico.
Translate from English to Ligurian:
Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers.
The Ligurian (Genoese) translation is:
I matematichi e i matematichi applicæ en conscideræ i doî representanti de carriere dite STEM (sciensa, tecnologia, inzegnaia e matematica).
Translate to Ligurian:
Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk.
The Ligurian (Genoese) translation is:
I attuäi an da fâ ascì con de costioin finançiäie, comme quelle ligæ a-o livello de contribuçioin penscionistiche neçessäie pe produe un çerto reddito de penscion e o mòddo comme unn’açienda a dovieiva investî de resorse pe mascimizzâ a rendia di investimenti a-a luxe do poscibile reisego.
Translate from English to Ligurian (Genoese dialect):
The hieroglyphic system for Egyptian numerals, like the later Roman numerals, descended from tally marks used for counting.
The Ligurian (Genoese) translation is:
O scistema de geroglifichi che i egiçi deuviavan pe-a representaçion di numeri, comme ascì i numeri romoen che saieivan arrivæ dòppo, ne vegnivan da-i scimboli deuviæ pe contâ.
Translate this sentence to Genoese:
Early number systems that included positional notation were not decimal, including the sexagesimal (base 60) system for Babylonian numerals, and the vigesimal (base 20) system that defined Maya numerals.
The Ligurian (Genoese) translation is:
I primmi scistemi de numeraçion che comprendeivan a numeraçion poxiçionale no ean à base dexe, compreiso quello à base sciuscianta pe i numeri babiloneixi e quelli à base vinti di numeri maya.
What’s the Genoese translation of this sentence?
Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs.
The Ligurian (Genoese) translation is:
Primma de euvie de Euclide (ca. 300 a.c.) i studdi di Greghi in sciâ matematica arrivavan à toccâ e creddense filosòfiche e mistiche.
Translate from English to Ligurian:
The ancient Greeks lacked a symbol for zero until the Hellenistic period, and they used three separate sets of symbols as digits: one set for the units place, one for the tens place, and one for the hundreds.
The Ligurian (Genoese) translation is:
I antighi Greghi n’aivan un scimbolo pe-o zero fin a-o periodo ellenistico, e deuviavan un scistema de trei scimboli pe representâ i numeri: un pe-e unitæ, un pe-e dëxeñe e l’urtimo pe-e çentanæa.
What’s the Ligurian translation of this sentence?
Their long division algorithm was the same, and the digit-by-digit square root algorithm, popularly used as recently as the 20th century, was known to Archimedes (who may have invented it).
The Ligurian (Genoese) translation is:
O seu ritmo de divixon longa o l’ea o mæximo e l’algoritmo de reixe quaddrâ giffra pe giffra, deuviou popolarmente fin a-o secolo XX, o l’ea conosciuo a-o mæximo Archimede (ch’o porriæ fiña aveilo inventou).
Translate from English to Genoese:
The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra.
The Ligurian (Genoese) translation is:
I cineixi antighi aivan di studdi avansæ in sce l’artimetica che remontan a-a dinastia Shang e che van avanti fin à quella Tang, da di numeri di fase fin à l’algebra avansâ.
What’s the Genoese translation of this sentence?
For the hundreds place, they then reused the symbols for the units place, and so on.
The Ligurian (Genoese) translation is:
Pe-e çentanæa an deuviou i scimboli de unitæ, e coscì avanti.
What’s the Ligurian translation of this sentence?
The ancient Chinese were the first to meaningfully discover, understand, and apply negative numbers.
The Ligurian (Genoese) translation is:
I antighi cineixi an descoverto, compreiso e applicou pe-i primmi i numeri negativi de unna forma scignificativi.
Translate this sentence to Genoese:
His contemporary, the Syriac bishop Severus Sebokht (650 AD) said, "Indians possess a method of calculation that no word can praise enough.
The Ligurian (Genoese) translation is:
O seu contemporaneo, o vesco sciriaco Severus Sebokht (650 d.C.), o l’aiva dito: «I indien an un metodo de carcolo che nisciuña poula a saiæ abasta pe lödâlo».
Translate this sentence to Ligurian:
The Arabs also learned this new method and called it hesab.
The Ligurian (Genoese) translation is:
I arabi ascì aivan impreiso sto neuve metodo, e gh’an dæto o nomme de «hesab».
Translate this sentence to Genoese:
The flourishing of algebra in the medieval Islamic world, and also in Renaissance Europe, was an outgrowth of the enormous simplification of computation through decimal notation.
The Ligurian (Genoese) translation is:
O sviluppo de l’algebra into mondo islamico de l’etæ de mezo, e inte l’Euröpa da Renascion ascì, o l’é stæto unna conseguensa de l’enorme semplificaçion do carcolo pe mezo da nottaçion à base dexe.