David Masser | |
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David Masser | |

Born | London, United Kingdom | 8 November 1948

Nationality | British |

Alma mater | University of Cambridge |

Known for | abc conjecture |

Awards | Humboldt Prize (1991) Fellow of the Royal Society (2005) Member of the Academia Europaea (2014) |

Scientific career | |

Fields | Mathematics |

Institutions | University of Basel |

Doctoral advisor | Alan Baker |

Doctoral students | Philipp Habegger |

**David William Masser** (born 8 November 1948) FRS is Professor Emeritus in the Department of Mathematics and Computer Science at the University of Basel.^{ [1] } He is known for his work in transcendental number theory, Diophantine approximation, and Diophantine geometry. With Joseph Oesterlé, Masser formulated the abc conjecture which has been called "the most important unsolved problem in Diophantine analysis".^{ [2] }

Masser was born on 8 November 1948 in London, England.^{ [3] } He graduated from Trinity College, Cambridge with a B.A. (Hons) in 1970.^{ [3] } In 1974, he obtained his M.A. and Ph.D. at the University of Cambridge,^{ [3] } with a doctoral thesis under the supervision of Alan Baker titled *Elliptic Functions and Transcendence*.^{ [4] }

Masser was a Lecturer at the University of Nottingham from 1973 to 1975, before spending the 1975-1976 year as a Research Fellow of Trinity College at the University of Cambridge.^{ [3] } He returned to the University of Nottingham to serve as a Lecturer from 1976 to 1979 and then as a Reader from 1979 to 1983.^{ [3] } He was a Professor at the University of Michigan from 1983 to 1992.^{ [3] } He then moved to the Mathematics Institute at the University of Basel and became emeritus there in 2014.^{ [1] }^{ [3] }^{ [5] }

Masser's research focuses on transcendental number theory, Diophantine approximation, and Diophantine geometry.^{ [5] }

With Joseph Oesterlé in the 1980s, Masser formulated the *abc* conjecture, which has been called "the most important unsolved problem in Diophantine analysis".^{ [2] } The *abc* conjecture originated as the outcome of attempts by Oesterlé and Masser to understand the Szpiro conjecture about elliptic curves.^{ [6] }

Masser was an invited speaker at the International Congress of Mathematicians in Warsaw in 1983.^{ [3] }^{ [5] } In 1991, he received the Humboldt Prize.^{ [3] } He was elected as a Fellow of the Royal Society in 2005.^{ [3] }^{ [5] } In 2014, he was elected as a Member of the Academia Europaea.^{ [3] }^{ [5] }

The ** abc conjecture** is a conjecture in number theory, first proposed by Joseph Oesterlé (1988) and David Masser (1985). It is stated in terms of three positive integers,

In mathematics, the **arithmetic of abelian varieties** is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has become a very substantial area of arithmetic geometry both in terms of results and conjectures. Most of these can be posed for an abelian variety *A* over a number field *K*; or more generally.

In mathematics, **Diophantine geometry** is the study of points of algebraic varieties with coordinates in the integers, rational numbers, and their generalizations. These generalizations typically are fields that are not algebraically closed, such as number fields, finite fields, function fields, and *p*-adic fields. It is a sub-branch of arithmetic geometry and is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry.

In mathematics and computer science, **computational number theory**, also known as **algorithmic number theory**, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program.

**Klaus Friedrich Roth** was a German-born British mathematician who won the Fields Medal for proving Roth's theorem on the Diophantine approximation of algebraic numbers. He was also a winner of the De Morgan Medal and the Sylvester Medal, and a Fellow of the Royal Society.

**Serge Lang** was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential *Algebra*. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group.

**Joseph Oesterlé** is a French mathematician who, along with David Masser, formulated the *abc* conjecture which has been called "the most important unsolved problem in diophantine analysis".

**John William Scott** "**Ian**" **Cassels**, FRS was a British mathematician.

**Paul Alan Vojta** is an American mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation.

In mathematics, **arithmetic geometry** is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.

This is a glossary of **arithmetic and diophantine geometry** in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.

A **height function** is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties to the real numbers.

In arithmetic geometry, the **Bombieri–Lang conjecture** is an unsolved problem conjectured by Enrico Bombieri and Serge Lang about the Zariski density of the set of rational points of an algebraic variety of general type.

**Kurt Mahler** FRS was a mathematician who worked in the fields of transcendental number theory, diophantine approximation, *p*-adic analysis, and the geometry of numbers.

**Gisbert Wüstholz** is a German mathematician internationally known for his fundamental contributions to number theory and arithmetic geometry.

In number theory, **Szpiro's conjecture** relates the conductor and the discriminant of an elliptic curve. In a slightly modified form, it is equivalent to the well-known abc conjecture. It is named for Lucien Szpiro who formulated it in the 1980s. Szpiro's conjecture and its equivalent forms have been described as "the most important unsolved problem in Diophantine analysis" by Dorian Goldfeld, in part to its large number of consequences in number theory including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem.

**Alan Baker** was an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.

**Lucien Serge Szpiro** was a French mathematician known for his work in number theory, arithmetic geometry, and commutative algebra. He formulated Szpiro's conjecture and was a Distinguished Professor at the CUNY Graduate Center and an emeritus Director of Research at the CNRS.

In mathematics, the **analytic subgroup theorem** is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's theorem on linear forms in logarithms. Gisbert Wüstholz proved it in the 1980s. It marked a breakthrough in the theory of transcendental numbers. Many longstanding open problems can be deduced as direct consequences.

**Umberto Zannier** is an Italian mathematician, specializing in number theory and Diophantine geometry.

- 1 2 "Prof. Dr. David Masser".
*University of Basel*. Retrieved 5 March 2021. - 1 2 Goldfeld, Dorian (March–April 1996), "Beyond the last theorem",
*The Sciences*,**36**(2): 34–40, doi:10.1002/j.2326-1951.1996.tb03243.x . - 1 2 3 4 5 6 7 8 9 10 11 "Curriculum Vitae and Publication list of D. W. Masser" (PDF).
*University of Basel*. 14 February 2020. Retrieved 5 March 2021. - ↑ David Masser at the Mathematics Genealogy Project
- 1 2 3 4 5 "David W. Masser".
*Institute for Advanced Study*. Retrieved 5 March 2021. - ↑ Fesenko, Ivan (2015), "Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki" (PDF),
*European Journal of Mathematics*,**1**(3): 405–440, doi:10.1007/s40879-015-0066-0, S2CID 52085917 .

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