Ronald Graham facts for kids
Quick facts for kids
Ronald Graham
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Graham in 1998
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Ronald Lewis Graham
October 31, 1935 Taft, California, U.S.
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| Died | July 6, 2020 (aged 84) San Diego, California, U.S.
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| Thesis | On Finite Sums of Rational Numbers (1962) |
| Doctoral advisor | Derrick Henry Lehmer |
Ronald Lewis Graham (born October 31, 1935 – died July 6, 2020) was an American mathematician. He was known as a key person in the fast growth of discrete mathematics around the world. Discrete mathematics deals with things that can be counted, like numbers, graphs, and codes.
Graham was the president of two important math groups: the American Mathematical Society and the Mathematical Association of America. He won the Leroy P. Steele Prize for his amazing work in math and was chosen to be part of the National Academy of Sciences.
He studied at the University of California, Berkeley. After that, he worked for many years at Bell Labs and later at the University of California, San Diego. He made big discoveries in areas like how to schedule tasks on computers, computational geometry (using computers to solve geometry problems), and Ramsey theory (finding order in chaos). Many math ideas are named after him.
Ronald Graham wrote six books and about 400 papers. He worked with nearly 200 other scientists. Many of his projects were with his wife, Fan Chung, and with the famous mathematician Paul Erdős.
He was even featured in Ripley's Believe It or Not! because he was not only a top mathematician but also a great trampolinist and juggler! He was even the president of the International Jugglers' Association.
Contents
Life Story of Ronald Graham
Ronald Graham was born in Taft, California, on October 31, 1935. His father worked in oil fields and later on ships. Even though Ronald became good at gymnastics, he was small and not very athletic when he was young.
He moved a lot between California and Georgia, often skipping grades in school. He never stayed at one school for more than a year. As a teenager, he moved to Florida with his mother. He didn't finish high school there. Instead, at age 15, he won a special scholarship from the Ford Foundation to go to the University of Chicago. There, he learned gymnastics but didn't take any math classes.
After three years, his scholarship ended. He then went to the University of California, Berkeley. He planned to study electrical engineering but also learned about number theory from Derrick Henry Lehmer. While there, he became the California state trampoline champion.
In 1955, when he was old enough, he joined the United States Air Force. He left Berkeley without a degree and was sent to Fairbanks, Alaska. In 1959, he finally earned a bachelor's degree in physics from the University of Alaska Fairbanks.
He returned to the University of California, Berkeley for graduate school. In 1962, he earned his Ph.D. (a high-level degree) in mathematics. His main project was about "Finite Sums of Rational Numbers." While studying, he earned money by performing trampoline acts in a circus. He married Nancy Young, a math student, and they had two children.
After getting his Ph.D., Graham started working at Bell Labs in 1962. Later, he became the Director of Information Sciences at AT&T Labs in New Jersey. In 1963, he met the very productive Hungarian mathematician Paul Erdős. They became close friends and often worked together on research. Graham was surprised when Erdős, who was already middle-aged, beat him at ping-pong. Graham decided to get better at the game and eventually became the Bell Labs champion!
Graham later made the idea of the Erdős number popular. This number shows how "close" a mathematician is to Paul Erdős based on who they've worked with. Graham worked with Erdős on many projects, including two books about unsolved math problems.
Graham divorced in the 1970s. In 1983, he married Fan Chung, who was also a mathematician at Bell Labs and often worked with him.
While at Bell Labs, Graham also taught at Rutgers University starting in 1986. He was president of the American Mathematical Society from 1993 to 1994. In 1995, he became the Chief Scientist at Bell Labs.
He retired from AT&T in 1999 after 37 years. Then, he moved to the University of California, San Diego (UCSD) as a professor. At UCSD, he also became the chief scientist at the California Institute for Telecommunications and Information Technology. From 2003 to 2004, he was president of the Mathematical Association of America.
Ronald Graham passed away on July 6, 2020, at the age of 84, in La Jolla, California.
Amazing Math Discoveries
Ronald Graham made many important discoveries in different areas of mathematics and computer science. He wrote about 400 papers and six books. One famous book is Concrete Mathematics, which he wrote with Donald Knuth and Oren Patashnik. He worked with almost 200 other authors. He also guided nine students who were getting their Ph.D.s.
Many math ideas are named after Graham, including:
- The Erdős–Graham problem about fractions.
- Graham's number, which is a very, very large number.
- The Graham–Pollak theorem and Graham's pebbling conjecture in graph theory (the study of networks).
- The Coffman–Graham algorithm for scheduling tasks and drawing graphs.
- The Graham scan algorithm for finding the "outline" of a group of points.
He also started studying "primefree sequences" (sequences of numbers where none of the numbers are prime) and the "Boolean Pythagorean triples problem."
Number Theory Work
Graham's first major math work was in number theory, which is about numbers and their properties. His Ph.D. paper was about Egyptian fractions (fractions like 1/2 + 1/3 + 1/7). The Erdős–Graham problem asks if you can always find a group of numbers whose fractions add up to one. A mathematician named Ernie Croot proved this in 2003.
In 1964, Graham started the study of primefree sequences. He showed that you can create number sequences, similar to the Fibonacci numbers, where none of the numbers are prime. Other mathematicians, like Donald Knuth, later worked on this challenge.
Ramsey Theory
Ramsey theory is about finding order even in messy situations. The Graham–Rothschild theorem, which Graham published with Bruce Lee Rothschild in 1971, is a key idea in this area.
Graham used a huge number as a limit for a problem related to this theorem. This number is now called Graham's number. It was once listed in the Guinness World Records as the largest number ever used in a math proof! Even larger numbers have been found since then, like TREE(3).
Graham even offered a money prize for solving the Boolean Pythagorean triples problem, another problem in Ramsey theory. Someone claimed the prize in 2016. Graham also wrote two books about Ramsey theory.
Graph Theory Contributions
into five complete bipartite subgraphs, according to the Graham–Pollak theoremThe Graham–Pollak theorem, which Graham published with Henry O. Pollak in 1971 and 1972, is about how you can break down a complete graph (where every point is connected to every other point). It says you need a certain number of special smaller graphs to do this. Even though the problem sounds like it's about counting, all known proofs use linear algebra, a type of advanced math.
Graham also worked on "quasi-random graphs" with his wife, Fan Chung. These are graphs that look random but have some hidden order.
Graham's pebbling conjecture, from a 1989 paper by Chung, is about how many "pebbles" you need to move around on a graph. This problem is still unsolved today!
Scheduling and Algorithms
Graham's early work was about job shop scheduling, which is about figuring out the best way to do tasks in a certain order. He looked at the "worst-case" situations to see how well different ways of scheduling would work. This helped create the idea of "approximation algorithms," which find good, but not always perfect, solutions to problems.
The Coffman–Graham algorithm, which Graham published with Edward G. Coffman Jr. in 1972, is a great way to schedule tasks for two computers. It also helps with more computers. This algorithm is also used in drawing graphs in layers.
In 1979, Graham and his co-authors created a special way to classify different scheduling problems. This system is sometimes called "Graham notation."
Geometry and Computers
The Graham scan is a popular and useful way to find the "convex hull" of a set of points. Imagine putting a rubber band around a group of nails on a board; the shape the rubber band makes is the convex hull. Graham published this algorithm in 1972.
Graham also studied the "biggest little polygon" problem. This asks for the polygon with the largest area for a given width. Surprisingly, the answer isn't always a regular shape!
In 1975, Graham and Erdős looked at how to fit small squares into a larger square. They found that if you tilt the small squares, you can fit them better and leave less empty space.
Juggling Skills
Ronald Graham became a skilled juggler when he was 15. He could juggle up to six balls! He even taught Steve Mills, a champion juggler, how to juggle. Their work together helped Mills create a famous juggling pattern called "Mills' Mess."
Graham also made important contributions to the math behind juggling, including ideas about "siteswaps" (a way to describe juggling patterns). In 1972, he was elected president of the International Jugglers' Association.
Awards and Honors
In 2003, Ronald Graham received the Leroy P. Steele Prize for his lifetime achievements in mathematics. The award recognized his work in discrete mathematics, how he made math popular through his talks and writing, his leadership at Bell Labs, and his service as president of the American Mathematical Society.
He was one of the first five people to win the George Pólya Prize from the Society for Industrial and Applied Mathematics. He also won the Euler Medal.
Graham was chosen to be part of the National Academy of Sciences in 1985. In 1999, he became an ACM Fellow for his important work in analyzing algorithms and scheduling. In 2009, he became a Fellow of the Society for Industrial and Applied Mathematics for his contributions to discrete mathematics. In 2012, he became a Fellow of the American Mathematical Society.
He was invited to speak at the International Congress of Mathematicians in 1982. He also gave the important Josiah Willard Gibbs Lectureship twice, in 2001 and 2015.
The Mathematical Association of America gave him two awards for his papers: the Carl B. Allendoerfer Prize for "Steiner Trees on a Checkerboard" (1989) and the Paul R. Halmos – Lester R. Ford Award for "A whirlwind tour of computational geometry" (1990). His book Magical Mathematics, which he wrote with Persi Diaconis, won the Euler Book Prize.
Conferences were held to celebrate Graham's 70th and 80th birthdays, and books were published in his honor.
See also
In Spanish: Ronald Graham para niños
Images for kids
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Graham in 1998
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Ronald Graham, his wife Fan Chung, and Paul Erdős in Japan, 1986
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Partition of the edges of the complete graph
into five complete bipartite subgraphs, according to the Graham–Pollak theorem -
The Graham scan algorithm for convex hulls
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Ronald Graham juggling a four-ball fountain (1986)
