Quotes
"Bilim adamı olabilmek için tutku gerekir."
Cahit Arf
"... As you know, Faust in Goethe's story was offered whatever he wanted (in his case the love of a beautiful woman), by the devil, in return for selling his soul. Algebra is the offer made by the devil to the mathematician. The devil says: 'I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.' (Nowadays you can think of it as a computer!)"
Special Article Mathematics in the 20th Century - M. Atiyah
"According to A. Grothendieck one really does not need a space to do geometry, all one needs is a category of sheaves on this would-be space."
Spectral Theory and Analytic Geometry over Non-Archimedean Fields - V. G. Berkovich
"Or, as suggested by Don Zagier: “Most hyperelliptic curves are pointless”."
Most hyperelliptic curves over Q have no rational points - M. Bhargava
"... It looks like okay well we've solved 66 percent of the problem. 660.000 dollars. The Clay institute does not agree."
What is the Birch and Swinnerton-Dyer conjecture and what is known about it? - M. Bhargava
"Sometimes it is fun to drive around in a Model T Ford but one should be aware there are much faster cars on the road."
Higher Regulators, Algebraic K-Theory, and Zeta Functions of Elliptic Curves - S. J. Bloch
"Just the combinatorics, please."
Moduli Spaces of Curves: Classical and Tropical - M. Chan
"Thy soul, Diophantus, be with Satan because of the difficulty of your other theorems and particularly of the present theorem."
J. Chortasmenos
"... although one Frobenius may be best, all are good."
"Rigid analysis was created to provide some coherence in an otherwise totally disconnected p-adic realm. Still, it is often left to Frobenius to quell the rebellious outer provinces."
Dilogarithms, Regulators and p-adic L-functions - R. Coleman
"We would also like to thank David Rohrlich for providing us with an independent check of the sign (and two bottles of kahlua)."
Stable reduction of Fermat Curves and Jacobi sum Hecke characters - R. Coleman & W. McCallum
"This paper is the outcome of a discussion during a hike at Oberwolfach."
Rational surfaces and the canonical dimension of PGL_6 - J. L. Colliot-Thélène & N. A. Karpenko & A. S. Merkurjev
"... Le choix naturel est de poser Log p = 0, ce qui nous donne le logarithme d’Iwasawa que nous noterons log_p , mais du simple point de vue de l’intégration p-adique, aucun choix ne semble vraiment meilleur qu’un autre."
Intégration sur les variétés p-adiques - P. Colmez
"When Bloch wrote the paper [1] which renewed the study of zero cycles on rational surfaces, he made an unpleasant technical assumption."
Every rational surface is separably split - K. R. Coombes
"There are no bad primes, really."
From his talk in Groningen - N. Dogra
"... About twenty years later, in 1890, Hilbert generalised the result of Gordan to a system of several homogeneous forms in a finite number of variables. His proof was non-constructive and did not provide any tools to determine such finite bases. Hilbert 'only' proved that these finite bases existed, to which Gordan reacted with the famous exclamation:
'Das ist nicht Mathematik. Das ist Theologie.'
Hilbert returned to the problem and in 1893 gave a proof which was this time constructive. Eventually Gordan appreciated Hilbert's new ideas,
remarking
'I have convinced myself that Theology also has its merits.' "
Invariants of binary forms - M. I. P. Draisma
"... our aim is to make publicity for p-adic cohomology, because we think that it has an undeserved reputation of being complicated and not so useful; the truth is precisely the opposite."
Point counting after Kedlaya - B. Edixhoven
"The theory of schemes is widely regarded as a horribly abstract algebraic tool that hides the appeal of geometry to promote and overwhelming and often unnecessary generality. By contrast, experts know that schemes make things simpler."
The Geometry of Schemes - D. Eisenbud & J. Harris
"We prove the result in the title for Noetherian fppf stacks, ..."
Finiteness of coherent cohomology for proper fppf stacks - G. Faltings
"Then, just when you are about to surrender, when you no longer have the desire to go on counting, you come across another pair of twin primes, clutching each other tightly."
The Solitude of Prime Numbers - P. Giordano
"If I were a Springer-Verlag Graduate Text in Mathematics, I would be Joe Harris's Algebraic Geometry: A First Course."
From his personal website - E. Z. Goren
" "At that time, blowups were the poor man's tool to resolve singularities." This phrase of the late 21st century mathematician J.H.Φ. Leicht could become correct. In our days, however, blowups are still the main device for resolution purposes."
Seven short stories on blowups and resolutions - H. Hauser
"... if C has no k-rational points, then it is not difficult(!) to prove that C(k) is finite."
Diophantine Geometry - An Introduction - M. Hindry & J. H. Silverman
"Algebraic geometry starts with cubic polynomial equations."
The geometry of cubic hypersurfaces - D. Huybrechts
"The reader will notice that the cover of this thesis does not contain any illustrations. It is intentionally left blank white in contrast to the gray skies of Groningen, which were the biggest obstacle in front of the completion of this thesis."
From his PhD thesis - M. D. Kaba
"The reader cannot have failed to notice the purely formal nature of most of our arguments."
Crystalline Cohomology, Dieudonné Modules, and Jacobi Sums - N. Katz
"Initially, the uniformity conjecture was considered somewhat outrageous; this implication was initially taken as possible evidence against the Lang–Vojta conjecture and led to a frenzied hunt for examples (or better: families) of curves with many points."
Diophantine and tropical geometry, and uniformity of rational points on curves - E. Katz & J. Rabinoff & D. Zureick-Brown
"The words 'adele' and 'idele' are sometimes spelled 'adèle' and 'idèle' (as in Neukirch), but not as far as I know by anyone who speaks French (e.g., Lang)."
Math 254B, Adeles and Ideles - K. Kedlaya
"God made the integers, all else is the work of man."
L. Kronecker
"Like a p-adic, one step at a time, still trapped In the unit ball."
A mathematical haiku - A. Kulkarni
"It is possible to write endlessly on elliptic curves. (This is not a threat.)"
Elliptic Curves: Diophantine Analysis - S. Lang
"Different people at different times will use the different techniques for different purposes."
Introduction to Arakelov Theory - S. Lang
"The main application of Pure Mathematics is to make you happy."
H. Lenstra
"I have a soft spot for del Pezzo surfaces."
From his personal website - Dan Loughran
"There is no deeper meaning to the adjective "tropical". It simply stands for the French view of Brazil."
"Tropical geometry is a marriage between algebraic and polyhedral geometry."
Introduction to Tropical Geometry - D. Maclagan & B. Sturmfels
"Number theory swarms with bugs, waiting to bite the tempted flower-lovers who, once bitten, are inspired to excesses of effort!"
Number Theory as Gadfly - B. Mazur
"A major theme in the development of Number Theory has been to try to bring R somewhat more into line with the p-adic fields; a major mystery is why R resists this attempt so strenuously."
On the passage from local to global in number theory - B. Mazur
"... It also seemed, at the outset, that this would be a relatively routine project. The project has proved to be anything but routine, ..."
On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer - B. Mazur & J. Tate & J. Teitelbaum
"... Note that this last is not actually a absolute value, because it doesn’t satisfy the triangle law. There are various ways of getting around this problem the best of which is simply to ignore it."
Algebraic Number Theory - J. Milne
"The most interesting object in mathematics Arguably, it is π_1(X,x), where X is the projective line over Q (not C!) with the three points 0, 1, ∞ removed."
Lectures on Étale Cohomology - J. Milne
"Groups, as men, will be known by their actions."
G. Moreno
"... These examples suggest that an answer to the mathematician’s riddle: 'How is a set different from a door?' should be: 'A door must be either open or closed, and cannot be both, while a set can be open, or closed, or both, or neither!'"
Topology - J. Munkres
"Selmer groups are dead. Long live Selmer complexes!"
Selmer Complexes, Introduction - J. Nekovář
"Algebraic curves were created by God and algebraic surfaces by the Devil."
M. Noether
"We need some new obstructions!"
Rational Points on Varieties - B. Poonen
"Kurt Hensel (1861-1941) discovered or invented the p-adic numbers around the end of the nineteenth century."
A Course in p-adic Analysis - A. M. Robert
"Bazen insan matematik yaparken içinin ürperdiğini hissediyor."
Kaç Tane Asal Sayı Var, Bilim ve Teknik Dergisi, Sayı 635 - S. Sertöz
"Hiçbir problem üzerine bodoslama gidilerek çözülmez."
İpler, Keçiler ve Koca Dünya, Bilim ve Teknik Dergisi, Sayı 655 - S. Sertöz
"Differentials want to be integrated."
Arithmetic of Hyperelliptic Curves - M. Stoll
"There is a general philosophy in Number Theory that 'all completions are created equal' and should have the same rights."
p-adic Analysis in Arithmetic Geometry - M. Stoll
“The only reason that we like complex numbers is that we don’t like real numbers.”
B. Sturmfels
"If your research adviser gives you a problem involving del Pezzo surfaces of degree 2 and 1, it means he really hates you.”
P. Swinnerton-Dyer
"A lifetime of mathematical activity is a reward in itself."
On receiving the Steele Prize for Lifetime Achievement - J. Tate
"This remarkable conjecture relates the behavior of a function L, at a point where it is not at present known to be defined, to the order of a group Ш, which is not known to be finite."
On the Birch-Swinnerton-Dyer Conjecture - J. Tate
"... If there are topologies to consider, we assume the action is continuous, though we shall mostly ignore continuity questions except to say that all maps, actions etc. are continuous when they should be."
Modular Forms and Fermat's Last Theorem, Galois Cohomology - L. Washington
"There is no P2C2E in this book."
Lectures on Polytopes - G. M. Ziegler