Hoi Toan hoc Hoa Ky (tieng Anh: American Mathematical Society, viet tat la AMS) la mot Hoi cac nha toan hoc chuyen nghiep nham thuc đay viec nghien cuu phat trien Toan hoc. Hoi xuat ban nhieu an pham va to chuc nhieu hoi nghi chuyen đe, cung nhu trao nhieu giai thuong hang nam cho cac nha toan hoc xuat sac.
Hoi nay la mot trong 4 thanh phan cua Joint Policy Board for Mathematics (Ban chinh sach chung cho Toan hoc) va la thanh vien cua Conference Board of the Mathematical Sciences (Ban Hoi nghi cac khoa Toan hoc).


Lich su Hoi đuoc thanh lap nam 1888 duoi ten Hoi Toan hoc New York, san pham tri oc cua Thomas Fiske, nguoi co an tuong sau sac ve Hoi Toan hoc London nhan mot chuyen vieng tham nuoc Anh. John Howard Van Amringe la chu tich va Thomas Fiske la thu ky đau tien cua hoi. Hoi som quyet đinh xuat ban mot to bao, nhung bi mot vai phan khang do canh tranh voi to American Journal of Mathematics, nen thay vao đo hoi xuat ban tap san Bulletin of the New York Mathematical Society do Fiske lam truong ban bien tap.
Thang 7 nam 1894, hoi to chuc lai, đoi ten nhu tren va tro thanh mot hoi toan quoc. Nam 1951, hoi doi tru so chinh tu thanh pho New York sang thanh pho Providence, Rhode Island va mo them mot van phong o Ann Arbor, Michigan nam 1984 va mot o Washington, D.C. nam 1992.
Tinh pho bien cua tap san cua hoi đa dan đen viec xuat ban cac to Transactions of the American Mathematical Society va Proceedings of the American Mathematical Society, tren thuc te cung la cac bao. Chua toi nam 1988 hoi xuat ban tiep to Journal of the American Mathematical Society voi y đinh se la to bao hang đau cua Hoi.
Hoi no luc cai thien chat luong viec giang day toan hoc o Hoa Ky. Vi du, nam 1954 hoi đa yeu cau thiet lap mot cap hoc moi: cap bang "Doctor of Arts in Mathematics", tuong tu nhu bang Ph.D. nhung khong co luan đe nghien cuu.


Cac cuoc hop Hoi Toan hoc Hoa Ky, cung voi Hiep hoi Toan hoc Hoa Ky (Mathematical Association of America) va cac to chuc khac to chuc cuoc hop nghien cuu toan hoc hang nam lon nhat the gioi: Joint Mathematics Meeting (Cuoc hop Toan hoc chung) vao đau thang Gieng. Nam 2008 cuoc hop Toan hoc chung đa co so nguoi tham du ky luc la 5.500 nguoi. Moi phan ban trong 4 phan ban vung cua hoi (vung Trung, Đong, Tay va Đong Nam) đeu to chuc cac cuoc hop vao mua xuan va mua thu hang nam. Hoi cung cung đo đau cho cac cuop hop voi cac hoi toan hoc quoc te khac.


Cac an pham Hoi xuat ban tap chi Mathematical Reviews, mot co so du lieu cua reviews cac an pham toan hoc, nhieu bao va sach. Nam 1997 hoi đa mua Cong ty xuat ban Chelsea đe xuat ban sach bao.
Cac bao:

Thong thuong
Bulletin of the American Mathematical Society - xuat ban hang quy,
Electronic Research Announcements of the American Mathematical Society - online,
Journal of the American Mathematical Society - xuat ban hang quy,
Notices of the American Mathematical Society – xuat ban hang thang, mot trong cac bao toan hoc đinh ky đuoc đoc nhieu nhat,
Proceedings of the American Mathematical Society – xuat ban hang thang,
Transactions of the American Mathematical Society – xuat ban hang thang,
Chu đe rieng
Mathematics of Computation - xuat ban hang quy,
Conformal Geometry and Dynamics - chi online,
Representation Theory - chi online.


Cac giai thuong Hoi trao cac giai thuong sau. Mot vai giai trao chung voi cac to chuc Toan hoc khac:

Giai tuong niem Bocher
Giai Cole
Giai Frank va Brennie Morgan cho Nghien cuu Toan hoc xuat sac cua sinh vien chua tot nghiep
Giai Fulkerson
Giai Leroy P. Steele
Giai Toan hoc ung dung Norbert Wiener
Giai Hinh hoc Oswald Veblen


Cac chu tich Hoi Toan hoc Hoa Ky đuoc lanh đao boi mot chu tich, đuoc bau ra cho mot nhiem ky 2 nam, va khong đuoc đam nhiem 2 nhiem ky lien tiep.


= 1888 – 1900 =
John Howard Van Amringe (New York Mathematical Society) (1888-1890)
Emory McClintock (New York Mathematical Society) (1891-94)
George Hill (1895-96)
Simon Newcomb (1897-98)
Robert Woodward (1899-1900)


= 1901 – 1950 =
Eliakim Moore (1901-02)
Thomas Fiske (1903-04)
William Osgood (1905-06)
Henry White (1907-08)
Maxime Bocher (1909-10)
Henry Fine (1911-12)
Edward Van Vleck (1913-14)
Ernest Brown (1915-16)
Leonard Dickson (1917-18)
Frank Morley (1919-20)
Gilbert Bliss (1921-22)
Oswald Veblen (1923-24)
George Birkhoff (1925-26)
Virgil Snyder (1927-28)
Earle Raymond Hedrick (1929-30)
Luther Eisenhart (1931-32)
Arthur Byron Coble (1933-34)
Solomon Lefschetz (1935-36)
Robert Moore (1937-38)
Griffith C. Evans (1939-40)
Marston Morse (1941-42)
Marshall Stone (1943-44)
Theophil Hildebrandt (1945-46)
Einar Hille (1947-48)
Joseph Walsh (1949-50)


= 1951 – 2000 =
John von Neumann (1951-52)
Gordon Whyburn (1953-54)
Raymond Wilder (1955-56)
Richard Brauer (1957-58)
Edward McShane (1959-60)
Deane Montgomery (1961-62)
Joseph Doob (1963-64)
Abraham Albert (1965-66)
Charles B. Morrey, Jr. (1967-68)
Oscar Zariski (1969-70)
Nathan Jacobson (1971-72)
Saunders Mac Lane (1973-74)
Lipman Bers (1975-76)
R. H. Bing (1977-78)
Peter Lax (1979-80)
Andrew Gleason (1981-82)
Julia Robinson (1983-84)
Irving Kaplansky (1985-86)
George Mostow (1987-88)
William Browder (1989-90)
Michael Artin (1991-92)
Ronald Graham (1993-94)
Cathleen Morawetz (1995-96)
Arthur Jaffe (1997-98)
Felix Browder (1999-2000)


= 2001 – =
Hyman Bass (2001-02)
David Eisenbud (2003-04)
James Arthur (2005-06)
James Glimm (2007-08)
George E. Andrews (2009–2010)


Tham khao Lien ket ngoai The AMS website
A Semicentennial History of the American Mathematical Society, 1888–1938 Luu tru ngay 6 thang 12 nam 2006 tai Wayback Machine – by Raymond Clare Archibald
MacTutor: The New York Mathematical Society Luu tru ngay 30 thang 10 nam 2019 tai Wayback Machine
MacTutor: The American Mathematical Society Luu tru ngay 16 thang 3 nam 2013 tai Wayback Machine
American Mathematical Society tai trang PlanetMath.org.