G. Baley Price (14 March 1905,

Brookhaven, Mississippi Brookhaven is a small city in Lincoln County, Mississippi, United States, south of the state capital of Jackson. The population was 12,520 at the 2010 U.S. Census. It is the county seat of Lincoln County. It was named after the town of Brookhaven ...

– 7 November 2006,

Lawrence, Kansas Lawrence is the county seat of Douglas County, Kansas, Douglas County, Kansas, United States, and the sixth-largest city in the state. It is in the northeastern sector of the state, astride Interstate 70, between the Kansas River, Kansas and Waka ...

) was an American mathematician and historian of American mathematics. He was a president of the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

.MAA presidents: Griffith Baley Price
/ref>

Career

After graduating with an A.B. from

Mississippi College Mississippi College (MC) is a private Baptist university in Clinton, Mississippi. Founded in 1826, MC is the second-oldest Baptist-affiliated college or university in the United States and the oldest college or university in Mississippi. Histor ...

in 1925, G. B. Price went to

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, where he received his M.A. in 1928 and his Ph.D. in 1932 under G. D. Birkhoff with thesis ''Double Pendulum and Similar Dynamical Systems''. Apart from a period of service with the U.S. Army Air Force in England in World War II, Price was a mathematics professor at the

University of Kansas The University of Kansas (KU) is a public research university with its main campus in Lawrence, Kansas, United States, and several satellite campuses, research and educational centers, medical centers, and classes across the state of Kansas. Tw ...

from 1937 to 1975 and chair of the mathematics department from 1951 to 1970. He was the co-author of two textbooks (published in 1966 and 1968) and the author of a history of the department of mathematics of the University of Kansas and several articles related to the role of mathematics and mathematicians in World War II. He was president of the Mathematical Association of America (MAA) for the two years 1957–1958 and received the MAA's distinguished service award in 1970. Price based his book about multicomplex spaces and functions on

Corrado Segre Corrado Segre (20 August 1863 – 18 May 1924) was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry. Early life Corrado's parents were Abramo Segre and Estella De Ben ...

's work where

\Complex_n

has n

imaginary unit The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...

i_1, \ i_2, \dots, i_n

all of which commute. But the book primarily treats

bicomplex number In abstract algebra, a bicomplex number is a pair of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate (w,z)^* = (w, -z), and the product of two bicomplex numbers as :(u,v)(w,z) = (u w - v z, u z ...

\Complex_2 \ .

Since

(i_1 i_2)^2 = +1

the numbers

e_1 = \tfrac(1 + i_1i_2)

and

e_2 = \tfrac(1 - i_1i_2)

are

idempotent Idempotence (, ) is the property of certain operation (mathematics), operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence ...

. The idempotents provide an alternate basis for the bicomplexes: :

z_1 + z_2 i_2 = (z_1 - i_1 z_2)e_1 + (z_1 + i_1 z_2)e_2 .

(page 19) Differentiable bicomplex functions f are shown to correspond to a pair of differentiable complex functions f₁ and f₂: :

f(z_1-i_1z_2) = f_1(z_1-i_1z_2)e_1 + f_2(z_1+i_1z_2)e_2 .

(page 131)

Works

* 1935: "On reversible dynamical systems",

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...

37(1): 51–59, , * 1947: "Some identities in the theory of determinants",

American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an e ...

54:75–90, * 1951: "Bounds for determinants with dominant principal diagonal",

Proceedings of the American Mathematical Society ''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages. According to the ' ...

2: 497–502, , * 1976: , link from

Google Books Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical c ...

* 1984: * 1991:

References

{{DEFAULTSORT:Price, Griffith Baley 1905 births 2006 deaths American centenarians Men centenarians 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni Mississippi College alumni People from Brookhaven, Mississippi Presidents of the Mathematical Association of America University of Kansas faculty