Journal of the American Mathematical Society
The Journal of the American Mathematical Society, is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988; this journal is abstracted and indexed in: Mathematical Reviews Zentralblatt MATH Science Citation Index ISI Alerting Services CompuMath Citation Index Current Contents/Physical, Chemical & Earth Sciences. Bulletin of the American Mathematical Society Memoirs of the American Mathematical Society Notices of the American Mathematical Society Proceedings of the American Mathematical Society Transactions of the American Mathematical Society Official website
Boris Zilber is a Soviet-British mathematician who works in mathematical logic. He is a professor of mathematical logic at the University of Oxford, he obtained his doctorate from the Novosibirsk State University in 1975 under the supervision of Mikhail Taitslin and his habilitation from the Saint Petersburg State University in 1986. He received the Pólya Prize from the London Mathematical Society. Prof. Zilber's homepage
Ehud Hrushovski is a mathematical logician. He is a Merton Professor of Mathematical Logic at the University of Oxford and a Fellows Merton College, Oxford, he is Professor of Mathematics at the Hebrew University of Jerusalem. Hrushovski's father, Benjamin Harshav, was a literary theorist, a Yiddish and Hebrew poet and a translator, Professor at Yale University and Tel Aviv University in comparative literature. Ehud Hrushovski earned his PhD from the University of California, Berkeley in 1986 under Leo Harrington, he was Professor of Mathematics at the Massachusetts Institute of Technology until 1998 before he went to Jerusalem. Hrushovski is well known for several fundamental contributions to model theory, in particular in the branch that has become known as geometric model theory, its applications, his PhD thesis revolutionized stable model theory. Shortly afterwards he found counterexamples to the Trichotomy Conjecture of Boris Zilber and his method of proof has become well known as Hrushovski constructions and found many other applications since.
One of his most famous results is his proof of the geometric Mordell–Lang conjecture in all characteristics using model theory in 1996. This deep proof was a landmark in geometry, he has had many other famous and notable results in model theory and its applications to geometry and combinatorics. Hrushovski is a fellow of the American Academy of Arts and Sciences, Israel Academy of Sciences and Humanities, he is a recipient of the Erdős Prize of the Israel Mathematical Union in 1994, the Rothschild Prize in 1998, the Carol Karp Prize of the Association of Symbolic Logic in 1993, the Carol Karp Prize in 1998. He was a Plenary speaker of the ICM in 1998. Zariski geometry Homepage Prof. Ehud Hrushovski Ehud Hrushovski at the Hebrew University of Jerusalem
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a 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.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to