Scott W. Williams

Born: April 22, 1943

Birthplace: Staten Island, New York (raised in Baltimore, Maryland)

here is a professional photo

B.S. Mathematics (minor in Humanities) 1964 Morgan State College; M.S. Mathematics (1967) Lehigh University.

Research Interests: Topology, Set Theory, Dynamics

Ph.D. Topology (minor in Algebra) 1969 Lehigh University
thesis: The Transfinite Cardinal Covering Dimension; Advisor: Samuel Gulden

: Professor of Mathematics, University at Buffalo, SUNY

university URL:

For additional material on Scott Williams, see:

  1. NextWave article;
  2. Faces in Science web site;
  3. SUMMA web site;
  4. Brief autobiography;
  5. Williams' personal Web Site; .

When he was 12, Scott Williams' mother [see background] took him to see the Massachusetts Institute of Technology during a family trip to Boston. After her description of the Institute as a great place of mathematics learning, he said, "Mom, I will get a Ph.D. in Mathematics." By the time Scott Williams received a B.S. in Mathematics from Morgan State College (1964) he had solved 4 advanced problems in The Mathematical Monthly, a publication of the Mathematical Association of America, and had co-authored two papers on Non-Associative Algebra with his undergraduate advisor Dr. Volodymir Bohun-Chudyniv. The Morgan State University 1964 graduating class was distinguished by many students scoring never before highs on the Advanced Mathematics Graduate Record Exam. Williams' 96% and publications as an undergraduate assured him he would be accepted into the Yale University Ph.D. program. However, for reasons unknown he was not accepted to Yale (who had "never heard of Morgan State"), so after working in the Product Testing Division of International Business Machines, he entered Lehigh University's graduate program and distinguished himself in his first year by creating many new examples in Dr. Albert Wilansky's Ph.D. student topology seminar. While at Lehigh University, he founded (along with the other three Black students enrolled in the university) and lead the Black Uhuru Society which later became the university's Black Student Union. He earned an M. S. in Mathematics from Lehigh University (1967) and a Ph.D. in Mathematics from Lehigh University (1969). Dr. Scott W. Williams' personal home page:

Dr. Williams served as a Research Associate in the Department of Mathematics at Pennsylvania State University - University Park, from 1969 to 1971. He was appointed an Assistant Professor of Mathematics at State University of New York (SUNY) in Buffalo 1971. Excerpts of Dr. Williams 1975-77 struggle to overcome racism and to obtain tenure is contained within an article On Affrimative Action.. He was easily promoted to Full Professor at SUNY at Buffalo in 1985.

In 2004, Science Spectrum Magazine and Career Communications Group, Inc. selected Dr. Williams as one of the 50 Most Important Blacks in Research Science.

Dr. Williams Ph.D. thesis was in General Topology. His work in the paper The G-delta -topology on compact spaces, Fundamenta Mathematicae 83 (1974), 143-149 first established him as one of the rising stars in General Topology. In 1975 he became the first topologist to apply the notion of scales (now known as b=d) to give a partial solution of the famous and still (2005) unsolved Box Product Problem. This began his work in the relatively new field of Set-theoretic Topology. His 1978 work on Boolean Algebras began the now popular technique of using trees to study Cech-Stone Remainders. His 1987 work with Jan Pelant of the Czech Academy of Sciences solved two 30 year old problems in the field of Topological Dynamics. He as also written in the field of Set Theory. A list of reviewed publications can be found below and a complete list of Scott Williams' more than 40 papers (as well as a list of his Topology Atlas columns) can be found on his Professional Resumé web page. Here is a basic WWW book on elementary topology.

Dr. Williams is one of two founders of Black and Third World Mathematicians, the first African American Mathematics Society, which in 1971 became The National Association of Mathematicians (NAM).

Dr. Williams has served on the Editorial Board of the Notices of the American Mathematical Society, the Advisory Board for the Summer Conferences on Topology and Applications. He is a regular columnist and a graphics images editor with the world wide web journal Topology Atlas, and presently Editor of the National Association of Mathematics.

Scott Williams has also worked as an Artist Blacksmith (1972-1983). His work has appeared in numerous art galleries and craft shows around the U.S. including the Renwick Gallery of The Smithsonian. Williams has published poetry and short stories. He is involved in the African American community at the grass-roots level. He is also involved in community work in Buffalo, and was honored, in Buffalo, with the Fatherhood and Family Award of the Year (1997).

Selected Professional Honors

Ford Foundation Senior Research Fellow, 1980-81

National Science Foundation research grant, 1983-87

Chancellor's Award for Excellence in Teaching, State University of New York (1982)

1986-1987 Fulbright-Lecturer (Prague Czechoslovakia)

1997 Keynote Address, A Sly Fox Approach to Racism, Conference on Black History, Queens University, Kingston, Ontario, February

2004, selected as one of the 50 Most Important Blacks in Research Science.

Professor Williams has published 32 papers, given over eighty-five invited conference lectures, colloquia, and seminar lectures on his mathematics research at fifty-eight institutions in eight countries, and has lectured to high ability high school students.

Selected Invited Lectures:

All talks were in Mathematics unless otherwise noted.

Special session on set-theoretic topology, AMS Summer Meeting, Kalamazoo MI, August 1975

University of Toronto September 1976

Annual Spring Topology Conference, Athens, OH, March 1979

University of Washington, Seattle, WA, June 1981

NATO Conference on Topology and Order, Amsterdam, The Netherlands, August 1981

12th Winter School for Abstract Analysis, Srni, Czechoslovakia, January 1984

Topology Seminar, Oxford University, England August 1987

Beijing Normal University, Beijing, China, 18 lectures, May-June 1988

Colloquium Sichuan University, Chengdu, China, July 1988

Northwest University, Xian, China, July 1988

The Claytor Lecture, National Association of Mathematicians, Louisville, KY, January 1990

University of Delaware, Newark DE,Colloquium, October 1995

Lincoln University, Lincoln PA, Lecture to student body, October 1995

University of North Carolina, Wilmington NC, Colloquium, February 1996

2nd Conference for African American Research in the Mathematical Sciences, DIMACS, Rutgers University, New Brunswick, New Jersey, June 1996

University of Toronto, Toronto, Ontario, Canada, October 1996

CUNY - City College, New York, New York, May 1997

The Wilkins Lecture, National Asscoiation of Mathematicians, Baltimore, MD October 2000

Non-Research Publications

  1. Williams, Scott W. Million-buck problems. Math. Intelligencer 24 (2002), no. 3, 17--20.
  2. Williams, Scott W. Compact! A tutorial, Contemp. Math., 275, Amer. Math. Soc., 161--171, Providence, RI, 2001.
  3. Williams, Scott W. Black research mathematicians in the United States. African Americans in mathematics, II (Houston, TX, 1998), Contemp. Math., 252,, 165--168 Amer. Math. Soc., Providence, RI, 1999.
  4. Williams, Scott W. Some dynamics on the irrationals. African Americans in mathematics (Piscataway, NJ, 1996), 83--103, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 34, Amer. Math. Soc., Providence, RI, 1997.
  5. Williams, Scott W. Box products. Handbook of set-theoretic topology, 169--200, North-Holland, Amsterdam-New York, 1984.

Research Publications

  1. Williams, Scott W.; Zhou, Haoxuan Order-like structure of monotonically normal spaces. Comment. Math. Univ. Carolin. 39 (1998), no. 1, 207--217.
  2. Pelant, Jan and Williams, Scott W. Examples of recurrence. Papers on general topology and applications (Gorham, ME, 1995), 316--332, Ann. New York Acad. Sci., 806, New York Acad. Sci., New York, 1996.
  3. Williams, Scott W.; Zhou, Hao Xuan Strong versions of normality. General topology and applications (Staten Island, NY, 1989), 379--389, Lecture Notes in Pure and Appl. Math., 134, Dekker, New York, 1991.
  4. Roitman, Judith and Williams, Scott The paracompactness of spaces related to uncountable box products. Topology Proc. 15 (1990), 135--141.
  5. Williams, S. W. Special points arising from self-maps. General topology and its relations to modern analysis and algebra, VI (Prague, 1986), 629--638, R & E Res. Exp. Math., 16, Heldermann, Berlin, 1988.
  6. Yang, Shou Lian and Williams, Scott W. On box products of small ordinal spaces. Kexue Tongbao (English Ed.) 33 (1988), no. 7, 554--556.
  7. Yang, Shou Lian and Williams, Scott W. On box products of small families of spaces of ordinal numbers. (Chinese) Kexue Tongbao (Chinese) 32 (1987), no. 14, 1051--1053.
  8. Yang, Soulian and Williams, Scott W. On the countable box product of compact ordinals. Proceedings of the 1987 Topology Conference (Birmingham, AL, 1987). Topology Proc. 12 (1987), no. 1, 159--171.
  9. Balcar, Bohuslav; Kalá\v sek, Pavel and Williams, Scott W. On the multiple Birkhoff recurrence theorem in dynamics. Comment. Math. Univ. Carolin. 28 (1987), no. 4, 607--612.
  10. Friedler, L. M.; Martin, H. W.; Williams, S. W. Paracompact $C$-scattered spaces. Pacific J. Math. 129 (1987), no. 2, 277--296.
  11. Williams, Scott W. More realcompact spaces. Rings of continuous functions (Cincinnati, Ohio, 1982), 289--300, Lecture Notes in Pure and Appl. Math., 95, Dekker, New York, 1985.
  12. Williams, Scott W. Paracompactness in box products. Proceedings of the 12th winter school on abstract analysis (Srní, 1984). Rend. Circ. Mat. Palermo (2) 1984, Suppl. No. 6, 313--328.
  13. Williams, S. W. Orderable subspaces of compact $F$-spaces. Topology and order structures, Part 2 (Amsterdam, 1981), 91--105, Math. Centre Tracts, 169, Math. Centrum, Amsterdam, 1983.
  14. Williams, S. W. Coabsolutes of \v Cech\mhy Stone remainders and orderable spaces. General topology and its relations to modern analysis and algebra, V (Prague, 1981), 699--705, Sigma Ser. Pure Math., 3, Heldermann, Berlin, 1983.
  15. van Mill, Jan; Williams, Scott W. A compact $F$-space not co-absolute with $\beta\bold N-\bold N$. Topology Appl. 15 (1983), no. 1, 59--64.
  16. Williams, Scott Orderable subspaces of \v Cech-remainders. Proceedings of the 1982 Topology Conference (Annapolis, Md., 1982). Topology Proc. 7 (1982), no. 2, 301--327.
  17. Williams, Scott W. Trees, Gleason spaces, and coabsolutes of $\beta {N}\sim {N}$. Trans. Amer. Math. Soc. 271 (1982), no. 1, 83--100.
  18. Gewand, Marlene E. and Williams, Scott W. Covering properties of linearly ordered topological spaces and their products. Topology and order structures, Part 1 (Lubbock, Tex., 1980), pp. 119--132, Math. Centre Tracts, 142, Math. Centrum, Amsterdam, 1981.
  19. Williams, Scott W. Coabsolutes with homeomorphic dense subspaces. Canad. J. Math. 33 (1981), no. 4, 857--861.
  20. Williams, Scott W. Spaces with dense orderable subspaces. Topology and order structures, Part 1 (Lubbock, Tex., 1980), pp. 27--49, Math. Centre Tracts, 142, Math. Centrum, Amsterdam, 1981.
  21. Williams, Scott W. Boxes of compact ordinals. Topology Proc. 2 , no. 2(1978), 631--642 .
  22. Williams, Scott W. Is $\sp{\omega }(\omega +1)$ paracompact? Topology Proceedings, 1 (1977), 141--146.
  23. Williams, Scott W. Paracompactness and products. General Topology and Appl. 6 (1976), no. 2, 117--125. (Reviewer: H. R. Bennett) 54D20 (54F05) [26] 51 #11449
  24. Williams, Scott W. A technique for reducing certain covers on certain L.O.T.S. and their products. TOPO 72---general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. De Groot), pp. 586--590. Lecture Notes in Math., Vol. 378, Springer, Berlin, 1974.
  25. Fleischman, William; Williams, Scott The $G\sb{\delta }$-topology on compact spaces. Fund. Math. 83 (1974), no. 2, 143--149.
  26. Williams, Scott Transfinite cardinal dimension and separability. Portugal. Math. 32 (1973), 139--145. (Reviewer: A. Appert) 54F45 [29] 42 #5224
  27. Williams, Scott W. The liberation of the $Q$-gap. Proceedings of the University of Houston Point Set Topology Conference (Houston, Tex., 1971), pp. 179--186. Univ. Houston, Houston, Tex., 1971.
  28. Williams, Scott W. Completeness for all. 1970 Proc. Washington State Univ. Conf. on General Topology (Pullman, Wash., 1970) pp. 127--136, Dept. of Math., Washington State Univ., Pullman, Wash.

Some Background materials

Scott Williams comes from a line of academics and political activists. His paternal grandfather supported his family of six as both a the sole Black public school teacher in Harrisburg, Pennsylvania and as a bell-hop in the segregated William Penn Hotel (which refused to serve Scott and other African Americans in 1970) in the capitol of Pennsylvania. Scott's maternal grandfather, whose own grandfather has emigrated in the 1840's to Nova Scotia Canada from the Caribbean, was a pullman porter whose childhood friend "Billy" W.E.B. Dubois, influenced him considerably. In 1908, his maternal grandmother, an Algonquin Indian, began the Colored Women's Literary Society, the first reading group for minorities in Bangor, Maine.

By 1960, all of the siblings of Scott Willams' parents had a graduate degree in some subject. In 1935, Williams' mother became the first Black to graduate from the University of Maine (mathematics with a minor in music - the Cello), where she earned her Masters Degree in Mathematics in 1937 (in 1956, earned a Masters Degree in English from Johns Hopkins University). Her work for the African American community in Baltimore has given her the honor of being awarded as one of the 10 most important Black women in the History of the State of Maryland. Scott Williams' father's graduate work at Pennsylvania State University - College Park was interrupted by World War II; however, in 1946 he became one of the first Blacks to earn a Ph.D. in Psychology.

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