David Blackwell

{{Short description|American mathematician and statistician (1919–2010)}}

{{for|the American football coach|David Blackwell (American football)}}

{{Infobox scientist

| image = David_Blackwell_1999_(re-scanned,_cropped).jpg

| image_size =

| caption = Blackwell in 1999

| birth_name = David Harold Blackwell

| birth_date = {{Birth date|1919|04|24}}

| birth_place = Centralia, Illinois, U.S.

| death_date = {{death date and age|2010|07|08|1919|04|24}}{{cite news |last=Sorkin |first=Michael |date=July 14, 2010 |title=David Blackwell fought racism; become world-famous statistician |url=http://www.stltoday.com/news/local/obituaries/article_8ea41058-5f35-5afa-9c3a-007200c5c179.html |work=St. Louis Post-Dispatch |language=en-US |access-date=April 10, 2024}}

| death_place = Berkeley, California, U.S.

| field = Probability
Statistics
Logic
Game theory
Dynamic programming

| work_institution = University of California, Berkeley

| education = University of Illinois at Urbana-Champaign (BA, MA, PhD)

| thesis_title = Some properties of Markoff chains

| thesis_url = https://www.worldcat.org/oclc/493477066

| thesis_year = 1941

| doctoral_advisor = Joseph Leo Doob{{MathGenealogy}}

| known_for = Rao–Blackwell theorem
Blackwell channel
Blackwell's contraction mapping theorem
Blackwell order
Arbitrarily varying channel
Bayesian statistics
Dirichlet distribution
Games of imperfect information
Mathematical economics
Recursive economics
Sequential analysis

| prizes = John von Neumann Theory Prize (1979)
R. A. Fisher Lectureship (1986)
National Medal of Science (2012)

| doctoral_students = {{plainlist|1=

}}

David Harold Blackwell (April 24, 1919 – July 8, 2010) was an American statistician and mathematician who made significant contributions to game theory, probability theory, information theory, and statistics.{{Google scholar id}} He is one of the eponyms of the Rao–Blackwell theorem,Roussas, G.G. et al. (2011) [https://www.ams.org/notices/201107/rtx110700912p.pdf A Tribute to David Blackwell], NAMS 58(7), 912–928. and is also known for the Blackwell channel, Blackwell's contraction mapping theorem, Blackwell's approachability theorem, and the Blackwell order. He was the first African American inducted into the National Academy of Sciences, the first African American full professor with tenure at the University of California, Berkeley,{{cite news |last=Cattau |first=Daniel |date=July 2009 |title=David Blackwell 'Superstar' |work=Illinois Alumni |language=en-US |pages=32–34 |publisher=University of Illinois Alumni Association}}{{cite web |title=Joseph Thomas Gier; "Wasn't David Blackwell First?" |url=https://eecs.berkeley.edu/about/history/gier |website=Joseph Gier Memorial Project |publisher=Berkeley EECS |access-date=September 26, 2023}} and the seventh African American to receive a Ph.D. in mathematics.{{Cite web |last=Schoemig |first=Skylar |date=February 25, 2020 |title='A Berkeley hero': UC Berkeley professors, alumnus reflect on legacy of David Blackwell |url=https://www.dailycal.org/2020/02/25/a-berkeley-hero-uc-berkeley-professors-alumnus-reflect-on-legacy-of-david-blackwell/ |website=The Daily Californian |language=en-US |access-date=June 18, 2021}} In 2012, President Barack Obama posthumously awarded Blackwell the National Medal of Science.

Blackwell was also a pioneer in textbook writing. He wrote one of the first Bayesian statistics textbooks, his 1969 Basic Statistics. By the time he retired, he had published over 90 papers and books on dynamic programming, game theory, and mathematical statistics.

Early life and education

David Harold Blackwell was born on April 24, 1919, in Centralia, Illinois, to Mabel Johnson Blackwell, a full-time homemaker, and Grover Blackwell, an Illinois Central Railroad worker.{{Cite book|url=https://archive.org/details/mathmathematicia00brun|title=Math and mathematicians : the history of math discoveries around the world|last=C.|first=Bruno, Leonard|orig-year=1999|year=2003|publisher=U X L|others=Baker, Lawrence W.|isbn=0787638137|location=Detroit, Mich.|oclc=41497065|url-access=registration}} He was the eldest of four children{{cite book|author=Marlow Anderson|title=Who Gave You the Epsilon?: And Other Tales of Mathematical History|url=https://books.google.com/books?id=WwFMjsym9JwC&pg=PA98|date=31 March 2009|publisher=MAA|isbn=978-0-88385-569-0|pages=98–}} with two brothers, J. W. and Joseph, and one sister, Elizabeth. Growing up in an integrated community, Blackwell attended "mixed" schools, where he distinguished himself in mathematics. During elementary school, his teachers promoted him beyond his grade level on two occasions. It was in a high school geometry course, however, that his passion for mathematics began.{{Cite web |title=Blackwell, David Harold (1919-2010) {{!}} The Black Past: Remembered and Reclaimed |url=http://www.blackpast.org/aah/blackwell-david-harold-1919-2010 |website=Black Past |language=en-US |date=July 27, 2010 |access-date=September 26, 2017}} An exceptional student, Blackwell graduated high school in 1935 at the age of sixteen.

Blackwell entered the University of Illinois at Urbana-Champaign with the intent to study elementary school mathematics and become a teacher. He was a member of Alpha Phi Alpha, a black fraternity that housed him for his full six years as a student. He earned his bachelor's degree in mathematics in three years in 1938 and, a year later, a master's degree in 1939. He was awarded a Doctor of Philosophy in mathematics in 1941 at the age of 22.{{cite book |last1=Kessler |first1=James H. |last2=Kidd |first2=J. S. |last3=Kidd |first3=Renée A. |last4=Morin |first4=Katherine A. |year=1996 |title=Distinguished African American Scientists of the 20th Century |url=https://archive.org/details/distinguishedafr00kess |location=Phoenix, AZ |publisher=Oryx Press |isbn=0-89774-955-3}}{{cite news |last=Grime |first=David |date=July 17, 2010 |title=David Blackwell, Scholar of Probability, Dies at 91 |url=https://www.nytimes.com/2010/07/17/education/17blackwell.html |url-access=registration |work=The New York Times |language=en-US |access-date=April 10, 2024}} His doctoral advisor was Joseph L. Doob. At the time, Blackwell was the seventh African American to earn a Ph.D. in mathematics in the United States and the first at the University of Illinois at Urbana-Champaign. His doctoral thesis was on Markov chains.

Career and research

= Postdoctoral study and early career =

Blackwell completed one year of postdoctoral research as a fellow at the Institute for Advanced Study (IAS) at Princeton in 1941 after receiving a Rosenwald Fellowship, which was a fund to aid black scholars. There he met John von Neumann, who asked Blackwell to discuss his Ph.D. thesis with him.{{cite book|title=A Mathematical View of Our World|year=2007|publisher=Cengage Learning|isbn=9780495010616|page=32|author=Gary Musser, Lynn Trimpe|author2=Gary Musser |author3=Lynn Trimpe |editor=Harold R. Parks}} Blackwell, who believed that von Neumann was just being polite and not genuinely interested in his work, did not approach him until von Neumann himself asked him again a few months later. According to Blackwell, "He (von Neumann) listened to me talk about this rather obscure subject and in ten minutes he knew more about it than I did."{{cite book|title=Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical|year=2005|publisher=Cambridge University Press|isbn=9780883855546|page=225|author=Steven Krantz}}

While a postdoc at IAS, Blackwell was prevented from attending lectures or undertaking research at nearby Princeton University, which the IAS has historically collaborated with in research and scholarship activities,{{cite web |title=Mission and History |url=http://www.ias.edu/about/mission-and-history |website=Institute for Advances Studies |date=March 15, 2016}}

because of his race.

File:Shabazz Blackwell Wilkins.jpg, David Blackwell, and J. Ernest Wilkins Jr. at the Conference for African American Researchers in the Mathematical Sciences in June 1995.]]

Seeking a permanent position elsewhere, he wrote letters of application to 104 historically black colleges and universities in 1942, and received a total of only three offers. He felt at the time that a black professor would be limited to teaching at black colleges.{{cite book |last=Albers |first=Donald J. |year=2008 |chapter=David Blackwell |editor-last1=Albers |editor-first1=Donald J. |editor-last2=Alexanderson |editor-first2=Gerald L. |editor-link2=Gerald L. Alexanderson |title=Mathematical People: Profiles and Interviews |edition=2nd |publisher=A K Peters |isbn=978-1-56881-340-0}}

Having been highly recommended by his dissertation advisor Joseph L. Doob for a position at the University of California, Berkeley, he was interviewed by statistician Jerzy Neyman. Neyman supported his appointment, and Griffith C. Evans, the head of the mathematics department, at first agreed and even convinced university president Robert Sproul that it was the correct decision, only to subsequently balk, citing the concerns of his wife. It was customary for Evans and his wife to invite the members of the department over for dinner and "she was not going to have any darkie in her house."{{Cite web |date=2010-03-12 |title=David Blackwell: Berkley [sic] |url=https://www.youtube.com/watch?feature=youtu.be&v=Mqpf9tw44Xw&app=desktop |website=YouTube |access-date=2020-06-10}}{{cite book |last=Black |first=Robert |year=2019 |title=David Blackwell and the Deadliest Duel |location=Unionville, NY |publisher=Royal Fireworks Press |pages=57–59}}

He was offered a post at Southern University at Baton Rouge, which he held in from 1942 to 1943, followed by a year as an Instructor at Clark College in Atlanta.

= Howard University =

Blackwell joined the Mathematics Department at Howard University in 1944. When he joined, he was one of four faculty members and within three years he was appointed full professor and head of the department. He remained at Howard until 1954. In 1947, while at Howard, Blackwell published the paper "Conditional Expectation and Unbiased Sequential Estimation", which outlined a technique that later became known as the Rao-Blackwell theorem.{{Cite journal |last=Blackwell |first=David |year=1947 |title=Conditional expectation and unbiased sequential estimation |journal=Annals of Mathematical Statistics |volume=18 |issue=1 |pages=105–110 |doi=10.1214/aoms/1177730497 |mr=19903 |zbl=0033.07603 |doi-access=free}} The theorem provides a method for improving statistical estimates by potentially reducing their mean squared error.

From 1948 to 1950, Blackwell spent his summers at RAND Corporation with Meyer Abraham Girshick and other mathematicians exploring the game theory of duels. In 1954, Girshick and Blackwell published Theory of Games and Statistical Decisions.{{Cite book |last1=Blackwell |first1=David |last2=Girshick |first2=M. A. |year=1954 |title=Theory of Games and Statistical Decisions |location=New York |publisher=John Wiley & Sons}} Aside from von Neumann and Girshick, other Blackwell collaborators and mentors included Leonard J. Savage, Richard E. Bellman, and Nobel Laureate Kenneth J. Arrow.Arrow, K. J., D. Blackwell and M. A. Girshick “Bayes and Minimax Solutions of Sequential Decision Problems” Econometrica Vol. 17, No. 3/4 (Jul. - Oct., 1949), pp. 213-244.

= University of California, Berkeley =

Blackwell took a position at the University of California, Berkeley as a visiting professor in 1954, and was hired as a full professor in the newly created Department of Statistics in 1955. He became the Statistics department chair in 1957.{{cite journal |last=DeGroot |first=Morris H. |year=1986 |title=A conversation with David Blackwell |journal=Statistical Science |volume=1 |issue=1 |pages=40–53 |doi=10.1214/ss/1177013814 |doi-access=free}}{{Cite web |title=David Blackwell |url=https://math.illinois.edu/david-blackwell |website=Mathematics at Illinois |access-date=November 3, 2021}}

Blackwell bridged topology and game theory via a game-theoretic proof of Kuratowski's coreduction principle for analytic subsets of a metric space in 1967.{{cite journal |last1=Blackwell |first1=David |year=1967 |title=Infinite Games and Analytic Sets |journal=Proceedings of the National Academy of Sciences |volume=58 |issue=5 |pages=1836–1837 |doi=10.1073/pnas.58.5.1836 |pmid=16578685 |pmc=223869 |bibcode=1967PNAS...58.1836B |doi-access=free}} Blackwell only briefly extended his research beyond zero-sum games to explore the sure-thing principleJeffrey, Richard (1982). "The Sure Thing Principle". Proceedings of the Biennial Meeting of the Philosophy of Science Association. 1982 (2): 719–730. [https://www.journals.uchicago.edu/doi/10.1086/psaprocbienmeetp.1982.2.192456 10.1086/psaprocbienmeetp.1982.2.192456.][https://www.jstor.org/stable/192456 JSTOR 192456.][https://www.semanticscholar.org/paper/The-Sure-Thing-Principle-Jeffrey/5808f28ca437b53c18a71270d93676851b4276dc S2CID 124506828].Pearl, Judea (December 2015). [https://ftp.cs.ucla.edu/pub/stat_ser/r466.pdf "The sure-thing principle"] (PDF). UCLA Cognitive Systems Laboratory, Technical Report R-466. as introduced by Jimmie Savage,Savage, L. J. (1954), The foundations of statistics. John Wiley & Sons Inc., New York. primarily due the real-world societal implications of the mathematical result,{{what?|date=October 2022}}7. Blyth, C. (1972). "On Simpson's paradox and the sure-thing principle". Journal of the American Statistical Association. 67 (338): 364–366. [https://www.tandfonline.com/doi/1972.10482387 10.2307/2284382]. [https://www.jstor.org/stable/2284382 JSTOR 2284382]. particularly for nuclear disarmament{{how?|date=October 2022}} at the inception of the Cold War.{{cite journal |last1=Agwu |first1=Nkechi |last2=Smith |first2=Luella |last3=Barry |first3=Aissatou |date=February 2003 |title=Dr. David Harold Blackwell, African American Pioneer |journal=Mathematics Magazine |volume=76 |issue=1 |pages=3–14 |doi=10.1080/0025570X.2003.11953941 |s2cid=120904626 |url=http://eblackcu.net/portal/archive/files/blackwell-article-jstor_f4b0f250fc.pdf}}

Blackwell wrote one of the first Bayesian textbooks, his 1969 Basic Statistics. It inspired the 1995 textbook Statistics: A Bayesian Perspective by the biostatistician Donald Berry.

He spent the rest of his career at UC Berkeley, retiring in 1988 at age 70, which at that time was the mandatory retirement age. Over the course of his career, he mentored over 60 students.

Personal life and death

Blackwell married Annlizabeth Madison, a 1934 graduate of Spelman College, on December 27, 1944. They had eight children together,[https://radar.auctr.edu/islandora/object/sc.001.messenger%3A1950.04?search=spelman%2520messenger Spelman Messenger] Spelman College three sons and five daughters: Ann, Julia, David, Ruth, Grover, Vera, Hugo, and Sara.

David Blackwell died of complications from a stroke on July 8, 2010, at Alta Bates Summit Medical Center in Berkeley, California.{{Cite news |last=Brown |first=Emma |date=July 16, 2010 |title=David H. Blackwell dies at 91; pioneering statistician at Howard and Berkeley |url=https://www.washingtonpost.com/wp-dyn/content/article/2010/07/15/AR2010071506274.html |newspaper=The Washington Post |language=en-US |issn=0190-8286 |access-date=September 26, 2017}} He was 91 years old.

Honors and awards

In his lifetime, Blackwell received 12 honorary doctorates.

Invited Speaker at the International Congress of Mathematicians, 1954
President of the Institute of Mathematical Statistics, 1956
Elected a member of the National Academy of Sciences (NAS), 1965
Elected a member of the American Academy of Arts and Sciences (AAAS), 1968
President of the Bernoulli Society for Mathematical Statistics and Probability, 1975-1977
Honorary Fellow of the Royal Statistical Society (RSS) in 1976
Vice President of the American Statistical Association (ASA) in 1978
Awarded the John von Neumann Theory Prize in 1979{{cite web|url=https://www.informs.org/Recognizing-Excellence/Award-Recipients/David-Blackwell|title=David Blackwell|work=Recognizing Excellence/Award Recipients|publisher=INFORMS|access-date=12 June 2019}}
Awarded the R. A. Fisher Lectureship in 1986{{cite web|url=https://community.amstat.org/copss/awards/fisher-lecturer#FisherPastRecipients|title=R.A. Fisher Award and Lectureship - Past Recipients|publisher=Committee of Presidents of Statistical Societies|access-date=12 June 2019}}
Elected a member of the American Philosophical Society, 1990{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=David+Blackwell&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2022-04-19 |website=search.amphilsoc.org}}
Fellow of the Institute for Operations Research and the Management Sciences, 2002{{citation|url=https://www.informs.org/Recognizing-Excellence/Fellows/Fellows-Alphabetical-List|title=Fellows: Alphabetical List|publisher=Institute for Operations Research and the Management Sciences|access-date=2019-10-09}}
Awarded the National Medal of Science (posthumous), 2012{{cite web|title=Laureates - David Blackwell|url=http://nationalmedals.org/laureates/david-blackwell|website=National Science & Technology Medals Foundation|access-date=21 May 2018}}

Legacy

The Mathematical Association of America's MathFest, in coordination with the National Association of Mathematicians, features an annual MAA-NAM David Blackwell Lecture. Blackwell offered the inaugural address in 1994; and subsequent lecturers are researchers who "exemplif[y] the spirit of Blackwell in both personal achievement and service to the mathematical community."{{Cite web |title=MAA-NAM Blackwell Lecture |url=https://www.nam-math.org/blackwell-lecture.html |website=www.nam-math.org |access-date=2021-06-18 |archive-date=2021-06-23 |archive-url=https://web.archive.org/web/20210623200049/https://www.nam-math.org/blackwell-lecture.html |url-status=dead}}

The Blackwell-Tapia prize is named in honor of David Blackwell and Richard A. Tapia.

The University of California, Berkeley named an undergraduate residence hall in his honor, named David Blackwell Hall. The residence hall opened in Fall 2018.{{cite web |last1=Kane |first1=Will |date=February 8, 2018 |title=New dorm to honor Berkeley's first tenured black professor |url=http://news.berkeley.edu/2018/02/08/new-dorm-to-honor-berkeleys-first-tenured-black-professor/ |website=UC Berkeley |language=en-US |access-date=May 21, 2018}}

An educational book about his life titled David Blackwell and the Deadliest Duel was published in 2019.

Blackwell made the following statement about his values and work in a 1983 interview for a project called "Mathematical People":

Basically, I'm not interested in doing research and I never have been....I'm interested in understanding, which is quite a different thing. And often to understand something you have to work it out yourself because no one else has done it.

In March 2024, Nvidia announced its Blackwell GPU architecture, named in honour of David Blackwell.{{Cite web |title=Nvidia Blackwell Platform Arrives to Power a New Era of Computing |url=http://nvidianews.nvidia.com/news/nvidia-blackwell-platform-arrives-to-power-a-new-era-of-computing |website=Nvidia Newsroom |language=en-US |access-date=2024-03-18}}{{Cite web |last=Leswing |first=Kif |date=2024-03-18 |title=Nvidia CEO Jensen Huang announces new AI chips: 'We need bigger GPUs' |url=https://www.cnbc.com/2024/03/18/nvidia-announces-gb200-blackwell-ai-chip-launching-later-this-year.html |website=CNBC |language=en-US |access-date=2024-03-18}}

Bibliography

= Books =

{{Cite book |last1=Blackwell |first1=David |last2=Girshick |first2=M. A. |year=1954 |title=Theory of Games and Statistical Decisions |location=New York |publisher=John Wiley & Sons}}
{{cite book |last1=Blackwell |first1=D.|year=1969 |title=Basic Statistics |publisher=McGraw Hill}}

= Journal articles =

{{Cite journal |last1=Blackwell |first1=David |year=1947 |title=Conditional Expectation and Unbiased Sequential Estimation |journal=The Annals of Mathematical Statistics |volume=18 |issue=1 |pages=105–110 |doi=10.1214/aoms/1177730497 |mr=19903 |zbl=0033.07603 |doi-access=free}}
{{cite journal |last1=Arrow |first1=K. J. |last2=Blackwell |first2=David |last3=Girshick |first3=M. A. |year=1949 |title=Bayes and Minimax Solutions of Sequential Decision Problems |journal=Econometrica |volume=17 |issue=3/4 |pages=213–244|doi=10.2307/1905525 |jstor=1905525 }}
{{cite journal |last1=Blackwell |first1=David |year=1953 |title=Equivalent Comparisons of Experiments |journal=The Annals of Mathematical Statistics |volume=24 |issue=2 |pages=265–272|doi=10.1214/aoms/1177729032 }}
{{cite journal |last1=Blackwell |first1=David |last2=Koopmans |first2=Lambert |year=1957 |title=On the Identifiability Problem for Functions of Finite Markov Chains |journal=The Annals of Mathematical Statistics |volume=28 |issue=4 |pages=1011–1015|doi=10.1214/aoms/1177706802 }}
{{cite journal |last1=Blackwell |first1=David |year=1962 |title=Discrete Dynamic Programming |journal=The Annals of Mathematical Statistics |volume=33 |issue=2 |pages=719–726 |doi=10.1214/aoms/1177704593 |doi-access=free}}
{{cite journal |last1=Blackwell |first1=David |year=1965 |title=Discounted Dynamic Programming |journal=The Annals of Mathematical Statistics |volume=36 |issue=1 |pages=226–235|doi=10.1214/aoms/1177700285 |doi-access=free }}
{{cite journal |last1=Blackwell |first1=David |last2=Ferguson |first2=T. S. |year=1968 |title=The Big Match |journal=The Annals of Mathematical Statistics |volume=39 |issue=1 |pages=159–163|doi=10.1214/aoms/1177698513 |doi-access=free }}
{{cite journal |last1=Blackwell |first1=David |year=1973 |title=Discreteness of Ferguson Selections |journal=The Annals of Statistics |volume=1 |issue=2 |pages=356–358|doi=10.1214/aos/1176342373 }}

References

External links

[https://web.archive.org/web/20150121033153/http://www.amstat.org/about/statisticiansinhistory/index.cfm?fuseaction=biosinfo&BioID=20 Biographical sketch] from the American Statistical Association
{{cite web |url=http://www.stat.berkeley.edu/images/stories/docs/blackwell%20packet.pdf |title=Dr. David Blackwell Biography Packet |others=(5.21 MB) |publisher=provided by the Department of Statistics at the University of California, Berkeley |archive-url=https://web.archive.org/web/20100622110021/http://www.stat.berkeley.edu/images/stories/docs/blackwell%20packet.pdf |archive-date=June 22, 2010 |url-status=dead }}
[http://www.visionaryproject.com/blackwelldavid David Blackwell's oral history video excerpts] at The National Visionary Leadership Project
A volume dedicated to [http://celebratio.org/Blackwell_DH/cover/3/ David H. Blackwell], Celebratio Mathematica
[https://www.informs.org/content/view/full/268692 Biography of David Blackwell] from the Institute for Operations Research and the Management Sciences (INFORMS)
[https://stat.illinois.edu/news/2020-07-17/david-h-blackwell-profile-inspiration-and-perseverance David H. Blackwell: A Profile of Inspiration and Perseverance], University of Illinois Urbana-Champaign College of Liberal Arts & Science Department of Statistics
[https://www.britannica.com/biography/David-Blackwell David Blackwell - American statistician and mathematician] from Britannica