David Mumford facts for kids

Quick facts for kids David Mumford
David Mumford in 2010
Born	(1937-06-11) 11 June 1937 (age 88) Worth, West Sussex, England
Nationality	American
Alma mater	Harvard University
Known for	Algebraic geometry Mumford surface Deligne-Mumford stacks Mumford–Shah functional
Awards	Putnam Fellow (1955, 1956) Sloan Fellowship (1962) Fields Medal (1974) MacArthur Fellowship (1987) Shaw Prize (2006) Steele Prize (2007) Wolf Prize (2008) Longuet-Higgins Prize (2005, 2009) National Medal of Science (2010) BBVA Foundation Frontiers of Knowledge Award (2012)
Honours	Hong Kong University of Science and Technology (Honoris Causa)
Scientific career
Fields	Mathematics
Institutions	Brown University Harvard University
Thesis	Existence of the moduli scheme for curves of any genus (1961)
Doctoral advisor	Oscar Zariski
Doctoral students	Avner Ash Henri Gillet Tadao Oda Emma Previato Malka Schaps Michael Stillman Jonathan Wahl Song-Chun Zhu

David Bryant Mumford (born 11 June 1937) is an American mathematician. He is famous for his important work in algebraic geometry. This is a field of mathematics that uses algebra to study geometric shapes. Later, he also did research in computer vision and pattern theory.

Mumford has received many top awards for his work. These include the Fields Medal and the National Medal of Science. He is currently a professor at Brown University.

Early Life and Learning

David Mumford was born in Worth, West Sussex, England. His father was English, and his mother was American. His father, William, started a special school in Tanzania. He also worked for the United Nations, which had just been created.

Mumford went to Phillips Exeter Academy for high school. There, he won a prize for a computer project he built using relays. After that, he studied at Harvard University. He was a student of a famous mathematician named Oscar Zariski.

While at Harvard, Mumford was named a Putnam Fellow in 1955 and 1956. This is a special honor for top math students. He earned his PhD (a high-level university degree) in 1961. His main research for this degree was about how to describe certain mathematical shapes.

His Research Work

David Mumford's research has greatly influenced mathematics. He combined older ideas about geometry with newer ways of using algebra.

Algebraic Geometry Discoveries

Mumford worked a lot on moduli spaces. These are mathematical spaces that help organize and classify different geometric objects. He wrote a key book called Geometric Invariant Theory. This book helped explain how to use algebra to understand these spaces.

He also studied abelian varieties and algebraic surfaces. These are special types of geometric shapes. His books, like Abelian Varieties and Curves on an Algebraic Surface, brought together old and new mathematical ideas.

Mumford's notes on scheme theory were very important. They helped many students learn about this complex topic. These notes were later published as The Red Book of Varieties and Schemes.

He also helped bring back the study of theta functions. These are special mathematical functions used in geometry. Mumford showed how they could be understood using modern algebra. He also helped create toroidal embedding theory. This theory helps mathematicians study complex shapes using simpler building blocks.

Understanding Difficult Cases in Geometry

Mumford also looked at "pathologies" in algebraic geometry. These are cases where things don't behave as simply as expected. He wrote several papers about these unusual situations.

Problems in Characteristic p

One area he studied was called "characteristic p." This refers to a specific type of number system used in algebra. Mumford showed that some geometric ideas that work well in one number system might not work the same way in characteristic p. For example, he found shapes where certain rules of geometry seemed to break down.

He showed that some expected properties of shapes, like how they relate to each other, could be different in characteristic p. This helped mathematicians understand the limits of certain theories.

Issues with Moduli Spaces

Mumford also found unexpected behaviors in Hilbert schemes. These are mathematical spaces that describe collections of geometric objects. He showed that these spaces could be more complicated than first thought. For example, they could have multiple parts or unexpected structures.

Later research by other mathematicians showed that these "pathologies" were not rare. They could happen quite often in complex geometric problems.

Classifying Surfaces

Between 1969 and 1976, Mumford worked on classifying smooth projective surfaces. He extended a system that was used for complex numbers to other types of algebraic fields. He found that the classification was mostly the same, but with a few important differences.

These differences included "non-classical" surfaces and quasi-elliptic surfaces. These are special types of surfaces that appear in certain number systems. His work helped create a complete way to sort and understand all these different geometric surfaces.

Awards and Recognitions

David Mumford in 1975

David Mumford has received many top awards for his contributions to mathematics.

• In 1974, he was awarded the Fields Medal. This is one of the highest honors a mathematician can receive.
• He was a MacArthur Fellow from 1987 to 1992. This fellowship provides support to talented individuals in various fields.
• He won the Shaw Prize in 2006, often called the "Nobel Prize of the East."
• In 2007, he received the Steele Prize for Mathematical Exposition. This award is for excellent mathematical writing.
• In 2008, he was awarded the Wolf Prize. When he received this prize, he donated half of the money to Birzeit University in the Palestinian territories. He gave the other half to Gisha, an Israeli group that helps Palestinians move freely.
• In 2010, he received the National Medal of Science. This is the highest scientific honor in the United States.
• In 2012, he became a fellow of the American Mathematical Society.
• He also received the BBVA Foundation Frontiers of Knowledge Award in 2012.

Mumford has also received many other honors. He was elected to the United States National Academy of Sciences in 1975. He is an honorary member of the London Mathematical Society and The Royal Society. He has received honorary degrees from many universities around the world.

From 1995 to 1999, he served as the President of the International Mathematical Union. This is a global organization for mathematicians.

See also