Mathematicians Sentence Examples
Pascal and P. de Fermat had initiated he brought very nearly to perfection; but the demonstrations are so involved, and the omissions in the chain of reasoning so frequent, that the Theorie analytique (1812) is to the best mathematicians a work requiring most arduous study.
Lessing' in 1773, which purports to have been sent by Archimedes to the mathematicians at Alexandria in a letter to Eratosthenes.
The time thus spent seems to have been on the whole happy, even allowing for warm discussions with the mathematicians and metaphysicians of France, and for harassing controversies in the Netherlands.
A work so widely circulated by the author naturally attracted attention, but in France it was principally the mathematicians who took it up, and their criticisms were more pungent than complimentary.
Modern mathematicians may find on reading this brilliant summary a good many dicta which they will call in question, but, whatever its defects may be, Peacock's report remains a work of permanent value.Advertisement
Thus early commenced the separation between what were long called mathematical and political geography, the one subject appealing mainly to mathematicians, the other to historians.
Roberval was one of those mathematicians who, just before the invention of the infinitesimal calculus, occupied their attention with problems which are only soluble, or can be most easily solved, by some method involving limits or infinitesimals, and in the solution of which accordingly the calculus is always now employed.
In the second, which took place in the Church of St John and St Paul, and lasted three days, he undertook to refute innumerable errors in Aristotelians, mathematicians and schoolmen, to conduct his dispute either logically or by the secret doctrine of numbers, &c. According to Aldus, who attended the debate and published an account of it in his dedication to Crichton prefixed to Cicero's "Paradoxa" (1581), the young Scotsman was completely successful.
This knowledge, joined to what he had gathered by historical reading of equally unusual extent, he carefully digested and gave to the world in his Biographisch-literarisches Handworterbuch zur Geschichte der exacten Wissenschaften, containing notices of the lives and labours of mathematicians, astronomers, physicists, and chemists, of all peoples and all ages.
Of the more immediate successors of Newton in Great Britain Maclaurin is probably the only one who can be placed in competition with the great mathematicians of the continent of Europe at the time.Advertisement
But the desire to obtain general enunciations of theorems without exceptional cases has led mathematicians to employ entities of ever-ascending types of elaboration.
These entities are not created by mathematicians, they are employed by them, and their definitions should point out the construction of the new entities in terms of those already on hand.
This is exactly the same reason as that which has led mathematicians to work with signed real numbers in preference to real numbers, and with real numbers in preference to rational numbers.
In the course of this process, undertaken for the first time with the rigour of mathematicians, some contradictions have become apparent.
Indeed, mathematicians now reserve "continuity" as the term for the latter kind of continuity; the mere property of having an infinite number of terms between any two terms is called "compactness."Advertisement
The classification in question was drawn up by an international committee of eminent mathematicians, and thus has the highest authority.
It was remarkable both for the brilliance of its achievements and for the large number of French mathematicians of the first rank who flourished during it.
Between them the general theory of the complex variable, and of the various "infinite" processes of mathematical analysis, was established, while other mathematicians, such as Poncelet, Steiner, Lobatschewsky and von Staudt, were founding modern geometry, and Gauss inaugurated the differential geometry of surfaces.
In the next and last period the progress of pure mathematics has been dominated by the critical spirit introduced by the German mathematicians under the guidance of Weierstrass, though foreshadowed by earlier analysts, such as Abel.
Leonardo's works are mainly developments of the results obtained by his predecessors; the influences of Greek, Arabian, and Indian mathematicians may be clearly discerned in his methods.Advertisement
His standard work on algebra, written in Arabic, and other treatises of a similar character raised him at once to the foremost rank among the mathematicians of that age, and induced Sultgn Malik-Shgh to summon him in A.H.
Maxwell explained electric and magnetic forces, not by the action at a distance assumed by the earlier mathematicians, but by stresses in a medium filling all space, and possessing qualities like those attributed to the old luminiferous ether.
Few as were the years of work allotted to him, and few as are the printed pages covered by the record of his researches, his name is, and will remain, a household word among mathematicians.
Amongst the brilliant group of mathematicians whose magnanimous rivalry contributed to accomplish the task of generalization and deduction reserved for the 18th century, Lagrange occupies an eminent place.
Recognized as among the first mathematicians of his day, he was also widely known for the universality and depth of his philological and philosophical knowledge.Advertisement
The time had come when the results obtained in the development and application of the law of gravitation by three generations of illustrious mathematicians might be presented from a single point of view.
Although the term " algebra " is now in universal use, various other appellations were used by the Italian mathematicians during the Renaissance.
Investigation of the writings of Indian mathematicians has exhibited a fundamental distinction between the Greek and Indian mind, the former being pre-eminently geometrical and speculative, the latter arithmetical and mainly practical.
It was proposed by Pierre de Fermat to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians.
The Arabians more closely resembled the Hindus than the Greeks in the choice of studies; their philosophers blended speculative dissertations with the more progressive study of medicine; their mathematicians neglected the subtleties of the conic sections and Diophantine analysis, and applied themselves more particularly to perfect the system of numerals, arithmetic and astronomy.
Political and ecclesiastical dissensions occupied the greatest intellects, and the only progress to be recorded is in the art of computing or arithmetic, and the trans pons asinorum of the earlier mathematicians.
Contemporaneously with the remarkable discoveries of the Italian mathematicians, algebra was increasing in popularity in Germany, France and England.
In recent times many mathematicians have formulated other kinds of algebras, in which the operators do not obey the laws of ordinary algebra.
This study was inaugurated by George Peacock, who was one of the earliest mathematicians to recognize the symbolic character of the fundamental principles of algebra.
Liouville, Caspary, Jukovsky, Liapounoff, Kolosoff and others, chiefly Russian mathematicians; and the general solution requires the double-theta hyperelliptic function.
In 1826 he moved to Paris, and during a ten months' stay he met the leading mathematicians of France; but he was little appreciated, for his work was scarcely known; and his modesty restrained him from proclaiming his researches.
Under Abel's guidance, the prevailing obscurities of analysis began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made.
In 1724 he was offered the chair of mathematics in the university of Upsala, which he declined, on the ground that it was a mistake for mathematicians to be limited to theory.
This problem engaged the attention of British as well as continental mathematicians; and its proposal gave rise to a painful quarrel with his brother Jean.
In his dispute with his brother, in his controversies with the English and Scottish mathematicians, and in his harsh and jealous bearing to his son Daniel, he showed a mean, unfair and violent temper.
During the three centuries that have elapsed between Vieta's day and our own several changes of opinion have taken place on this subject, till the principle has at last proved so far victorious that modern mathematicians like to make homogeneous such equations as are not so from the beginning, in order to get values of a symmetrical shape.
Here you find articles in the encyclopedia about British mathematicians.
In like manner, after the French mathematicians had attempted, with more or less ingenuity, to construct a theory of elastic solids from the hypothesis that they consist of atoms in equilibrium under the action of their mutual forces, Stokes and others showed that all the results of this hypothesis, so far at least as they agreed with facts, might be deduced from the postulate that elastic bodies exist, and from the hypothesis that the smallest portions into which we can divide them are sensibly homogeneous.
He was well acquainted with the works of the mathematicians of his own time, and has been called the "English d'Alembert."
His researches on elliptic functions are of considerable elegance, but their great merit lies in the stimulating effect which they had on later mathematicians.
Many of Pell's manuscripts fell into the hands of Dr Busby, master of Westminster School, and afterwards came into the possession of the Royal Society; they are still preserved in something like forty folio volumes, which contain, not only Pell's own memoirs, but much of his correspondence with the mathematicians of his time.
This problem was proposed by Pierre de Fermat first to Bernhard Frenicle de Bessy, and in 1657 to all mathematicians.
These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836-901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola.
Legendre had pursued the subject which would now be called elliptic integrals alone from 1786 to 1827, the results of his labours having been almost entirely neglected by his contemporaries, but his work had scarcely appeared in 1827 when the discoveries which were independently made by the two young and as yet unknown mathematicians Abel and Jacobi placed the subject on a new basis, and revolutionized it completely.
Pfaff's researches bore chiefly on the theory of series, to which he applied the methods of the so-called combinatorial school of German mathematicians, and on the solution of differential equations.
If 1 denotes the logarithm to base e (that is, the so-called "Napierian " or hyperbolic logarithm) and L denotes, as above, " Napier's " logarithm, the connexion between 1 and L is expressed by L = r o 7 loge 10 7 - 10 7 / or e t = I 07e-L/Ia7 Napier's work (which will henceforth in this article be referred to as the Descriptio) immediately on its appearance in 1614 attracted the attention of perhaps the two most eminent English mathematicians then living - Edward Wright and Henry Briggs.
In the preface Robert Napier says that he has been assured from undoubted authority that the new invention is much thought of by the ablest mathematicians, and that nothing would delight them more than the publication of the mode of construction of the canon.
Young men of talent, on the contrary, found his instruction most stimulating, and after Bowditch's death in 1838 Peirce stood first among American mathematicians.
The Premature Death Of Regiomontanus Caused The Design To Be Suspended For The Time; But In The Following Century Numerous Memoirs Appeared On The Subject, Among The Authors Of Which Were Staler, Albert Pighius, Johann Schbner, Lucas Gauricus, And Other Mathematicians Of Celebrity.
The Milanese sculptor, Ambrogio, who worked so much for Federigo, married a lady of Urbino, and was the progenitor of the Baroccio family, among whom were many able mathematicians and painters.
After five years spent in mathematical and astronomical studies, he went to Holland, in order to visit several eminent continental mathematicians.
At the same time, his characteristic exactness makes his collection a most admirable substitute for the texts of the many valuable treatises of earlier mathematicians of which time has deprived us.
The Cronica dei Matematici (published at Urbino in 1707) is an abridgment of a larger work, on which he had bestowed twelve years of labour, and which was intended to contain the lives of more than two hundred mathematicians.
He published a number of these theorems without demonstration as a challenge to contemporary mathematicians.
Here you find articles in the encyclopedia about mathematicians.
The Principia mathematica of Sir Isaac Newton, which chance threw in his way, caused him to prosecute his studies with vigour, and he soon became distinguished among first-rate mathematicians.
The school, however, produced few, if any, great mathematicians between Newton and George Green.
In the course of the ensuing ten years he published a large amount of original work, much of it dealing with the theory of invariants, which marked him as one of the foremost mathematicians of the time.
It was also by his orders that two learned mathematicians undertook the measurement of a degree of the earth's circumference.
No better testimony to the value of the quaternion method could be desired than the constant use made of its notation by mathematicians like Clifford (in his Kinematic) and by physicists like ClerkMaxwell (in his Electricity and Magnetism).
Coulomb's work received better publication than Cavendish's at the time of its accomplishment, and provided a basis on which mathematicians could operate.
He soon showed mathematical powers, but these were not fostered by the careful training mathematicians usually receive, and it may be said that in after years his attention was directed to the higher mathematics mainly by force of circumstances.
In this he was an innovator against the excessively analytic tendency of Cambridge mathematicians.
Jacobi and other mathematicians have developed to a great extent, and as a question of pure mathematics only, Hamilton's processes, and have thus made extensive additions to our knowledge of differential equations.
With the view of stimulating mathematicians to write annotations on this admirable work, the celebrated 's Gravesande published a tract, entitled Specimen Commentarii in Arithmeticam Universalem; and Maclaurin's Algebra seems to have been drawn up in consequence of this appeal.
In June 1696 Bernoulli addressed a letter to the mathematicians of Europe challenging them to solve two problems - (1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P 1, P 2, then AP 1 m +AP 2 m will be constant.
The six months elapsed without any solution being produced; but he received a letter from Leibnitz, stating that he had "cut the knot of the most beautiful of these problems," and requesting that the period for their solution should be extended to Christmas next, that the French and Italian mathematicians might have no reason to complain of the shortness of the period.
Thus we speak of counting up to a certain number; and similarly mathematicians speak of high and ascending powers, while engineers speak of high pressure, high speed, high power, &c. This tendency is probably aided by the use of bricks or cubes in elementary number-teaching.
Unlike most mathematicians, De Morgan always laid much stress upon the importance of logical training.
Throughout his logical writings De Morgan was led by the idea that the followers of the two great branches of exact science, logic and mathematics, had made blunders, - the logicians in neglecting mathematics, and the mathematicians in neglecting logic. He endeavoured to reconcile them, and in the attempt showed how many errors an acute mathematician could detect in logical writings, and how large a field there was for discovery.
In this position he acquired a wide knowledge of Chinese religion and civilization, and especially of their mathematics, so that he was able to show that Sir George Homer's method (1819) of solving equations of all orders had been known to the Chinese mathematicians of the 14th century.
The modifications of which these are susceptible he reports to be " inexhaustible and truly infinite, extension alone affording a boundless field to the mathematicians."
The business of drawing up the new calendar was entrusted to the president of the committee of public instruction, Charles Gilbert Romme (1750-1795), who was aided in the work by the mathematicians Gaspard Monge and Joseph Louis Lagrange, the poet Fabre d'Eglantine and others.
Numerous new fields were opened up, and have been diligently explored by many mathematicians.
When the subject was taken up by the continental mathematicians, using the analytical method, the question naturally arose whether the motions of three bodies under their mutual attraction could not be determined with a degree of rigour approximating to that with which Newton had solved the problem of two bodies.
Both irregularities had been noted, a century earlier, by Edmund Halley; both had, since that time, vainly exercised the ingenuity of the ablest mathematicians; both now almost simultaneously yielded their secret to the same fortunate inquirer.
But one may well believe that there was in his mind at any rate a foreshadowing of some of the ideas by which modern mathematicians have finally laid to rest the traditional difficulties connected with infinity and continuity."
These discoveries were unknown in western Europe for many centuries, and were re-invented and developed by many European mathematicians.
Mathematicians are rarely represented in main stream media, and when they are they don't exactly appear glamorous.
Mathematicians undoubtedly use probability in a way that fits well with the propensity interpretation, but they leave it undefined.
How to use the mailroom Did you ever want to ask the Pure Mathematicians a tough question?
The American mathematical Society has much mathematical information and links to many other web pages of interest to mathematicians.
The Institute of Mathematics and its Applications is the professional and learned society for qualified and practicing mathematicians.
The conference will bring together mathematicians, physicists, and engineers of varying backgrounds and occupations.
He had many students; now some of them are among leading mathematicians.
In fact, there are areas of mathematics that have been developed by mathematicians on the assumption that the Riemann Hypothesis is true.
It was studied by ancient mathematicians due to its frequent appearance in geometry.
Without a doubt, the future for applied mathematicians looks very, very good.
A close friendship developed between the two Swiss mathematicians in exile.
Here, too, he made the acquaintance of Claude Mydorge, one of the foremost mathematicians of France, and renewed an early intimacy with Malin Mersenne (q.v.), now Father Mersenne, of the order of Minim friars.
The stranger, Isaac Beeckman, principal of the college of Dort, offered to do so into Latin, if the inquirer would bring him a solution of the problem, - for the advertisement was one of those challenges which the mathematicians of the age were accustomed to throw down to all corners, daring them to discover a geometrical mystery known as they fancied to themselves alone.
He began by reading, with the most profound admiration and attention, the whole of Faraday's extraordinary self-revelations, and proceeded to translate the ideas of that master into the succinct and expressive notation of the mathematicians.
When this fundamental truth had been fully grasped, mathematicians began to inquire whether algebras might not be discovered which obeyed laws different from those obtained by the generalization of arithmetic. The answer to this question has been so manifold as to be almost embarrassing.
Notwithstanding these and other idiosyncratic appellations, European mathematicians have adhered to the older name, by which the subject is now universally known.
The Arabians more closely resembled the Hindus than the Greeks in the choice of studies; their philosophers blended speculative dissertations with the more progressive study of medicine; their mathematicians neglected the subtleties of the conic sections and Diophantine analysis, and applied themselves more particularly to perfect the system of numerals (see Numeral), arithmetic and astronomy.
In that year Adriaan van Roomen gave out as a problem to all mathematicians an equation of the 45 th degree, which, being recognized by Vieta as depending on the equation between sin 4 and sin 43/45, was resolved by him at once, all the twenty-three positive roots of which the said equation was capable being given at the same time (see Trigonometry).
The French mathematicians, Coulomb, Biot, Poisson and Ampere, had been content to accept the fact that electric charges or currents in conductors could exert forces on other charges or conductors at a distance without inquiring into the means by which this action at a distance was produced.
James Clerk Maxwell (1831-1879) entered on his electrical studies with a desire to ascertain if the ideas of Faraday, so different from those of Poisson and the French mathematicians, could be made the foundation of a mathematical method and brought under the power of analysis.3 Maxwell started with the conception that all electric and magnetic phenomena are due to effects taking place in the dielectric or in the ether if the space be vacuous.
To instruct his captains, pilots and other pioneers more fully in the art of navigation and the making of maps and instruments he procured, says Barros, the aid of one Master Jacome from Majorca, together with that of certain Arab and Jewish mathematicians.
Scientists, mathematicians, musicians, artists, and sculptors have all proven over the centuries that you can find the Golden Ratio in everything, even our solar system.
Although mathematicians have actually carried the value of the Golden Ratio to 100,000,000,000 places, it is generally expressed as 1.618 and is known as Phi.
As an infinite number, the value of Phi goes on indefinitely and mathematicians have actually carried its value to 100 billion places.
No one is exactly certain when mathematicians discovered Phi, also known as the Golden Number, ancient people have used this number throughout history since the time the Egyptians built the pyramids in approximately 2575 B.C.
ProTeacher.org provides a helpful suggestion for beginning mathematicians.
The Mayans were mathematicians, great scholars, accomplished astronomers and astrologers.
Historically, astrologers were mathematicians who performed complex calculations based on specific formulas.
Encouraging children to create reports or even stories about famous mathematicians such as Richard Feynman, Einstein, or Pythagoras might also appeal to kids who aren't wanting to focus on numbers themselves, but on the history of math.
The number 13 is an oddity and is considered an imperfection from artists to astrologers to mathematicians.
Autistic prodigious savants include musicians, mathematicians and linguists.
He was a member of almost every learned society in Europe, and one of the first mathematicians of a mathematical age.
His two sons, Jean and Jacques, are the last noted mathematicians of the family.
That principle had been made use of by the Greek authors of the classic age; but of later mathematicians only Hero, Diophantus, &c., ventured to regard lines and surfaces as mere numbers that could be joined to give a new number, their sum.
He is justly regarded as one of the greatest of mathematicians.
He had been much helped by his opportunities of intercourse with the great architects, engineers and mathematicians who frequented the court of Milan - Bramante, Alberghetti, Andrea di Ferrara, Pietro Monti, Fazio Cardano and, above all, Luca Pacioli.
His mathematical genius gained for him a high place in the 'esteem of Jean Bernoulli, who was at that time one of the first mathematicians in Europe, as well as of his sons Daniel and Nicolas Bernoulli.
In 1735 a problem proposed by the academy, for the solution of which several eminent mathematicians had demanded the space of some months, was solvecdby Euler in three days,but the effort threw him into a fever which endangered his life and deprived him of the use of his right eye.