Daniel Alan Goldston (born January 4, 1954 in

Oakland, California Oakland is the largest city and the county seat of Alameda County, California, United States. A major West Coast of the United States, West Coast port, Oakland is the largest city in the East Bay region of the San Francisco Bay Area, the third ...

) is an American mathematician who specializes in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

. He is currently a professor of mathematics at

San Jose State University San José State University (San Jose State or SJSU) is a public university in San Jose, California. Established in 1857, SJSU is the oldest public university on the West Coast and the founding campus of the California State University (CSU) sys ...

Early life and education

Daniel Alan Goldston was born on January 4, 1954 in Oakland, California. In 1972, he matriculated to the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, where he earned his bachelor's degree and, in 1981, a Ph.D. in mathematics. His doctoral advisor at Berkeley was Russell Sherman Lehman; his dissertation was entitled "Large Differences between Consecutive Prime Numbers".

Career

After earning his doctorate, Goldston worked at the

University of Minnesota Duluth The University of Minnesota Duluth (UMD) is a public university in Duluth, Minnesota. It is part of the University of Minnesota system and offers 16 bachelor's degrees in 88 majors, graduate programs in 25 different fields, and a two-year progr ...

and then spent the next academic year (1982–83) at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

(IAS) in Princeton. He has worked at

since 1983, save for stints at the IAS (1990), the

University of Toronto The University of Toronto (UToronto or U of T) is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution ...

(1994), and the

Mathematical Sciences Research Institute The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Califo ...

in Berkeley (1999).

Research

Goldston is best known for the following result that he,

János Pintz János Pintz (born 20 December 1950 in Budapest) is a Hungary, Hungarian mathematician working in analytic number theory. He is a fellow of the Alfréd Rényi Institute of Mathematics, Rényi Mathematical Institute and is also a member of the Hun ...

, and

Cem Yıldırım Cem Yalçın Yıldırım (born 8 July 1961) is a Turkish mathematician who specializes in number theory. He obtained his B.Sc from Middle East Technical University in Ankara, Turkey and his PhD from the University of Toronto in 1990. His advisor ...

proved in 2005: :

\liminf_\frac=0

where

p_n

denotes the n^th

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

. In other words, for every

c>0\

, there exist infinitely many pairs of consecutive primes

p_n\

and

p_\

which are closer to each other than the average distance between consecutive primes by a factor of

c\

, i.e.,

p_-p_n .

This result was originally reported in 2003 by Goldston and Yıldırım but was later retracted. Then Pintz joined the team and they completed the proof in 2005.

In fact, if they assume the

Elliott–Halberstam conjecture In number theory, the Elliott–Halberstam conjecture is a conjecture about the distribution of prime numbers in arithmetic progressions. It has many applications in sieve theory. It is named for Peter D. T. A. Elliott and Heini Halberstam, who st ...

, then they can also show that primes within 16 of each other occur infinitely often, which is related to the

twin prime conjecture A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

Recognition

In 2014, Goldston won the

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number ...

, shared with

Yitang Zhang Yitang Zhang (; born February 5, 1955) is a Chinese American mathematician primarily working on number theory and a professor of mathematics at the University of California, Santa Barbara since 2015. Previously working at the University of New ...

and colleagues Cem Yildirim and

, for his contributions to

. Also, Goldston was named to the 2021 class of fellows of the American Mathematical Society "for contributions to analytic number theory".

References

External links