Tristes picadas, coisas pequenas, 
Almas de esquemas, entropia, sentada no fim do teu dia. 
E persistes, teimosia inconsequente, morte de repente 
E o que fica é uma picada de mosca, uma coisa tosca.

considering the history of modern mathematics two questions at once arise: 

(1) what limitations shall be placed upon the term Mathematics; 

(2) what force shall be assigned to the word Modern? 

In other words, how shall Modern Mathematics be defined?

In these pages the term Mathematics will be limited to the domain of pure science. 

Questions of the applications of the various branches will be considered only incidentally. 

Such great contributions as those of Newton in the realm of mathematical physics, of Laplace in celestial mechanics, of Lagrange and Cauchy in the wave theory, and of Poisson, Fourier, and Bessel in the theory of heat, belong rather to the field of applications.


In particular, in the domain of numbers reference will be made to certain of the contributions to the general theory, to the men who have placed the study of irrational and transcendental numbers upon a scientific foundation, and to those who have developed the modern theory of complex numbers and its elaboration in the field of quaternions and Ausdehnungslehre. 

In the theory of equations the names of some of the leading investigators will be mentioned, together with a brief statement of the results which they secured. 

The impossibility of solving the quintic will lead to a consideration of the names of the founders of the group theory and of the doctrine of determinants. 

This phase of higher algebra will be followed by the theory of forms, or quantics. 

The later development of the calculus, leading to differential equations and the theory of functions, will complete the algebraic side, save for a brief reference to the theory of probabilities. 

In the domain of geometry some of the contributors to the later development of the analytic and synthetic fields will be mentioned, together with the most noteworthy results of their labors. 

Had the author’s space not been so strictly limited he would have given lists of those who have worked in other important lines, but the topics considered have been thought to have the best right to prominent place under any reasonable definition of Mathematics.

Modern Mathematics is a term by no means well defined. 

Algebra cannot be called modern, and yet the theory of equations has received some of its most important additions during the nineteenth century, while the theory of forms is a recent creation. 

Similarly with elementary geometry; the labors of Lobachevsky and Bolyai during the second quarter of the century threw a new light upon the whole suBject, and more recently the study of the triangle has added another chapter to the theory. 

Thus the history modern mathematics must also be the modern history of ancient branches, while subjects which seem the product of late generations have roots in other centuries than the present.

How unsatisfactory must be so brief a sketch may be inferred from a glance at the Index du Répertoire Bibliographique des Sciences Mathématiques (Paris, 1893), whose seventy-one pages contain the mere enumeration of subjects in large part modern, or from a consideration of the twenty-six volumes of the Jahrbuch über die Fortschritte der Mathematik, which now devotes over a thousand pages a year to a record of the progress of the science. 

1

The seventeenth and eighteenth centuries laid the foundations of much of the subject as known to-day. The discovery of analytic geometry by Descartes, the contributions to the theory of numbers by Fermatto algebra by Harriot, to geometry and mathematical physics by Pascal, and the discovery of the differential calculus by Newton and Leibniz, all contributed to make the seventeenth century memorable. 

The eighteenth century was naturally one of great activities. 

Euler and the Bernoulli family in Switzerland, d’Alembert, Lagrange, and Laplace in Paris, and Lambert in Germany, popularized Newton’s great discovery, and extended both its theory and its applications. Accompanying this activity, however, was a too implicit faith in the calculus and in the inherited principles of mathematics, which left the foundations insecure and necessitated their strengthening by the succeeding generation.


The nineteenth century has been a period of intense study of first principles, of the recognition of necessary limitations of various branches, of a great spread of mathematical knowledge, and of the opening of extensive fields for applied mathematics. 

Especially influential has been the establishment of scientific schools and journals and university chairs. 

The great renaissance of geometry is not a little due to the foundation of the École Polytechnique in Paris (1794-5), and the similar schools in Prague (1806), Vienna (1815), Berlin (1820), Karlsruhe (1825), and numerous other cities. 

About the middle of the century these schools began to exert a still greater influence through the custom of calling them mathematicians of high repute, thus making Zürich, Karlsruhe, Munich, Dresden, and other cities well known as mathematical centers.

In 1796 appeared the first number of the Journal de l’ École Polytechnique. Crelle’s Journal für die reine und angewandte Mathematik appeared in 1826, and ten years later Liouville began the publication of the Journal de Mathématiques pures et appliquées, which has been continued by Resal and Jordan. 


The Cambridge Mathematical Journal was established in 1839, and merged into the Cambridge and Dublin Mathematical Journal in 1846. 

Of the other periodicals which have contributed to the spread of mathematical knowledge, only a few can be mentioned: the Nouvelles Annales de Mathématiques (1842), Grunert’s Archiv der Mathematik (1843), Tortolini’s Annali di Scienze Matematiche e Fisiche (1850), 

Schlömilch’s Zeitschrift für Mathematik und Physik (1856), the Quarterly Journal of Mathematics (1857), Battaglini’s Giornale di Matematiche (1863), the Mathematische Annalen (1869), the Bulletin des Sciences Mathématiques (1870), the American Journal of Mathematics (1878), the Acta Mathematica (1882), and the Annals of Mathematics (1884). 

To this list should be added a recent venture, unique in its aims, namely, 

 and two annual publications of great value, the Jahrbuch already mentioned (1868), and the 

(1892).


To the influence of the schools and the journals must be added that of the various learned societies whose published proceedings are widely known, together with the increasing liberality of such societies in the preparation of complete works of a monumental character.


The study of first principles, already mentioned, was a natural consequence of the reckless application of the new calculus and the Cartesian geometry during the eighteenth century. 


This development is seen in theorems relating to infinite series, in the fundamental principles of number, rational, irrational, and complex, and in the concepts of limit, continuity, function, the infinite, and the infinitesimal. 


But the nineteenth century has done more than this. 


It has created new and extensive branches of an importance which promises much for pure and applied mathematics. 

Foremost among these branches stands the theory of functions founded by Cauchy, Riemann, and Weierstrass, followed by the descriptive and projective geometries, and the theories of groups, of forms, and of determinants.

The nineteenth century has naturally been one of specializations. 


At its opening one might have hoped to fairly compass the mathematical, physical, and astronomical sciences, as did Lagrange, Laplace, and Gauss. 

But the advent of the new generation, with Monge and Carnot, Poncelet and Steiner, Galois, Abel, and Jacobi, tended to split mathematics into branches between which relations were long to remain obscure. 


In this respect, recent years have seen a reaction, the unifying tendency again becoming prominent through the theories of functions and groups. 

 

 

1 The foot-notes give only a few of the authorities which might easily be cited. They are thought to include those from which considerable extracts have been made, the necessary condensation of these extracts making any other form of acknowledgment impossible.


2 For a list of current mathematical journals see the Jahrbuch über die Fortschritte der Mathematik. A small but convenient list of standard periodicals is given in Carr’s Synopsis of Pure Mathematics, p. 843; Mackay, J. S., Notice sur le journalisme mathématique en Angleterre, Association française pour l’Avancement des Sciences, 1893, II, 303; Cajori, F., Teaching and History of Mathematics in the United States, pp. 94, 277; Hart, D. S., History of American Mathematical Periodicals, The Analyst, Vol. II, p. 131.


3 For a list of such societies consult any recent number of the Philosophical Transactions of Royal Society of London. Dyck, W., Einleitung zu dem für den mathematischen Teil der deutschen Universitäts Ausstellung ausgegebenen Spezialkatalog, Mathematical Papers Chicago Congress (New York, 1896), p. 41.

4 Klein, F., The Present State of Mathematics, Mathematical Papers of Chicago Congress (New York, 1896), p. 133.


Godspeed.😍

Cada texto cada contexto é apresentado 

Não há telefone que toque, 

Cognitive meningeal carcinomatosis.
Analogue, vague, revival of vinyl...meia hora.
Tarde para boa noite, cedo para boa semana. 
Incompetência.
Inapetência patológica pré-ordenada a que nível, a que plano...
Nem faço palavras cruzadas, as minhas letras presas naquele quadradinhos castradores e competitivos, 
Amigos do mérito, querido perdido no pretërito rito. Sem umlaut. 
Pretérito.
Que não move moinhos, quais, de vento, de correntes, de desalento, 
Moinhos deste momento onde o sentido é o ondular da miragem.

Mãe está entrando na carruagem
O assento isolado da última viagem.

A minha filha tira alusiva fotografia
Para que eu possa emoldurar um dia
Fotografias na sala de estar, céus,
Não há alma que não tenha quem a adore!
Que se fodam os da maioria, há quem chore
E lamente sem esconder, nem ficar doente,
E nem se qualifique como ausência de sentimento.

Esse trem tem doce para me levar, apita Chopin (Noc. Op 48 n.1)
Esse diesel apita com o vapor que sobe do inferno,
A linha curva tão linda à esquerda, céu laranja escuro
E eu contente por saber que vou lá ter ao apeadeiro,

Humilde paragem de quem nasceu pequeno,
E parte com um ínfimo suspiro do que visitou
Não gostou mas deixou lembranças, como um toque,
Pétalas escassas, descendentes, fortes,
Devaneios em tom lilás que a arte olvidou.

Nunca este autor achou o que não procurou.

Contra minha esperança, acordei vivo e indiferente, 
Como que triste por ainda existir, persistir neste caminho, 
Não poder sair para comprar umas caixas de vinho,
Não ter que comer excepto alguns ovos, que odeio,
Não nada fazer para inverter, antes subverter a realidade.

Uma tristeza desprevenida sem seguro de vida
Uma atitude cada vez menos ativa,um atrofiar,
Ódio revolta negativa e me querer encontrar na raiva de me findar.
Na raiva ou desespero ou alegria ou ironia, quero acabar se eu me fizer esse favor
Deitado de lado num pardieiro que sujei inteiro, vou limpar para quê, 
Um sem propósito a não ser negar_vos
Um despropósito de não querer existir convosco 
No paradoxo de nem sempre querer estar sozinho 
Alheio à crueza das pessoas e à maldade do gatos contagiados
Tocados pelo mal das pessoas vivas...
Podia assassinar como meio para acabar com isto. 

Chegou a hora de deixar de aprender 
Como fazer não vou fazer
L'heure de la départe est arrivée
J'espère, mais, franchement, je suis désolé d'être vivante 
Il s'impose une heure d'hommage à une vie terminée qui se refuse à accepter.
On insiste en se lever après se coucher dans l'espérance de décéder innocent,
Partir dans un vent de l'inconscient dormant. 
Un homme qui n'a pas ni au moins une amante,
Um filho da puta que quer seguir a trilha do levante,
Foder a Rosa dos ventos, essa inconstante,
Pisar o petulante galo até cala-lo.
Cansado de andar a atura-lo nas suas orientaçöes, 
Quase tanto como de vcs, me_dusa, cabrões.

Como vos tenho distanciado!
E vcs cabrões, voltam, desenhadas preocupações,
Cabrões, insensíveis pedaços de pão, 
Pão de fome não me digam tome
Toma tu 
Eu não tomo, já tomei!
Agora só tomo porrada
Agora só quero facada, 
Sendo que a porra da vossa tortura
É lenta e preparada 
Serei obrigado a tomar a iniciativa
Numa simples passada, uma rua tropeçada
Uma lámina descontrolada, 
Tanto sugerem que aceito.
Aceito o vosso pleito de casa na colina,
Aceito-vos como ovelhas de faca pristina.
Aceitem-me longe longe longe, longe da vista, longe da circulação, longe da Cristina 
Longe da Capela Sistina, longe deste plano plaino cheio de engano,
Onde toda esta dor que me cortam, em que me golpeiam, se esvai como sangue saudável numa hemorragia de um vaso, sem mialgia, hyperalgesia, you pick, I fall. 
Sick of death me walking.