Charles T. Gidiney

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Charles T. Gidiney
Members of the Official Board of the A.M.E. Zion Church, and Trustees in Trust, 1887-88.jpg
Members of the Official Board of the A.M.E. Zion Church, and Trustees in Trust, 1887-88; "C. T. Gidney" is on the front row, third from the right
Born (1813-09-05)September 5, 1813
Milton, New York, US
Disappeared June 4, 1900 (aged 86)
Milton, New York, US
Other names Charles F. Gidiney; Chas T. Gidiney; Charles T. Gideney; Charles T. Gidney; C. T. Gidney; Charles L. Gedney
Occupation Laborer; Whitewasher; Class Leader; Sexton
Known for Untrained mathemathian who discovered a unique algebraic equation to determine the value of π
Home town Troy, New York, US
Spouse(s) Thodosia Ball (married March 20, 1837); Harriet A. Gidiney (married 1855 - September 11, 1890)

Charles T. Gidiney (September 5, 1813 – June 1900) was an untrained African-American mathematician who made his living as a whitewasher. He became a local celebrity when he claimed to have found an algebraic formula for the value of π. Though his suggestions proved incomplete, he furthered scientific discussions with a formula that has been since used in other studies.[2]

Personal life[edit]

Gidiney and his wife, Harriet, were members of the African Methodist Episcopal (A.M.E.) Zion Church of Seventh Street in Troy, New York.

Life in documents[edit]

Most of Gidiney's life can be found in official records, but unintended modifications to his name may prove research difficult.


The first document to mention Gidiney (27 years old) is the Federal Census of 1840, who was listed as the head of a household of nine unnamed “free colored people”,[3] the largest of its kind in the Shaker community of New Lebanon, New York. Gidiney decided to move to Troy around that time, where the abolitionist paper National Watchman was established two years later and where the first Negro State Convention and play Tom Shows, based on the 1852 book Uncle Tom's Cabin, were held.


A decade later, records stated that Gidiney (37) the “laborer” was born in 1813 New York and likely had a son, John T. Gidiney (11), while in the Third Ward of the City of Troy. The Gidineys lived with two other household members: Anna Hardy (3), the only one from Pennsylvania, and Mary C. Hardy (22).[4][a] The 1855 census of New York was the first to mention Harriet A. Gidiney (36) of Schoharie County as Gidiney's wife while Gidiney's birthplace was pinpointed at Columbia County, his year of birth in 1815, his residence at the First Ward of the City of Troy, and his job as a whitewasher. Both have lived in Troy for 2 years and Harriet was illiterate.[5]


In 1860, Chas T. Gidiney (45), still recorded as born in 1815, but residing in the Seventh Ward this time,[6] was in proximity of Harriet Tubman, who was on her way to an abolitionist meeting in Boston.[citation needed] A year later, Gidiney shows up in the Troy City directory “as a at house number 156 Green”[1] and continued living there up to 1868.[b] The 1865 census of New York lists the Gidineys still living in the Seventh Ward, each having been married twice with at least one child, and is the only census to have dated Charles' birth back to 1808 instead of 1813 and located Harriet's birthplace to Broome.[7][8]

Gidiney sent a letter to the mayor of Troy on July 18, 1863 in the wake of the draft riots during the Civil War, where civilians either joined the Union Army or paid $300 in support.[citation needed] Possibly preserved at the Rensselaer County Historical Society,[citation needed] the letter was an appeal to stop the mob, where rioters consisting mostly of Irish-Americans infiltrated the city of Troy from factories to the Troy Daily Times' offices. He writes:

As I learn that you are in town I now inform you of my Grief, and no doubt all the rest of my people are under the same grievances. I have been advised by white gentlemen and ladies for to stay in my house and not to be seen in the streets because it is not safe the Irish mob was going about seeking the coloured peoples lives. Since the mob, I cannot go out to get groceries but there is something thrown at my head, I have been staying in my house for two days. And we are afraid of our lives being destroyed. Therefore I now pray to you for protection so that I may walk the streets undisturbed you know that I cannot live without my daily labor. And when I pass through the streets I heard them say Kill the Nigger, Kill the Nigger, Kill the Nigger. And even yesterday little boys stood before my door at a short distance and my wife stood in her door, and there they stood with clubs and saying Nigger, Nigger, Shaking their clubs at her and etc. I pray you to forthwith put out a proclamation against all such offenses so that we Coloured people may walk the street in perfect Peace and etc.

Yours most respectably etc.,

Chas. T Gidiney[9][c]


In 1870, Gidney[d] (56) of Rensselaer, about 9 miles away from Troy, lived alone with Harriet (52), a real estate value of $2,000, and a personal estate value of $200.[citation needed] Two years later, the Troy City directory found them at 52 North Third Street and continued to list that information for several more years.[citation needed] Then the 1875 New York census renamed the Gidineys to Charles L. Gedney (62)[e] and Harretta Gedney (58). The census also added a 17-year-old “daughter”, Melicia Johnson, and a 52-year-old “broader”, William H. Brown, to the household,[10] which is the only time they appear in records with the Gidiney family. Troy's directory in 1877 listed Gidiney as “Gideney”.[11]


Religious activity started to appear in the Gidineys' records around the 1880s. Gidiney had already been a vice president of the “Seventh street Methodist church” for 4 years.[12] In 1884, Mrs. Harriet Gidiney became “president of the Female Benevolent Society, a society for African American women that met the 'First Tuesday evening of each month.'”[1] On March 27, 1886, the New York Freeman reported that Charles Gidiney was elected for the board of trustees of the A.M.E. Zion Church of Seventh Street (est. 1830s), which was well known for its archive of literacy and even held some math lectures.[citation needed] For two years after that, the Gidiney couple were recorded as members of the church, including Charles as a “Class Leader”.[13] During that time, the Gidineys moved to 2168 Sixth Ave,[citation needed] where they stayed for 6 years with a property value of $1,000.


Harriet Gidiney (72) suddenly died four days after Charles' birthday party (September 5, 1890) and the church held her funeral at 3 p.m. in September 11,[14] led by Rev. Decker and pastor Rev. Geo. E. Smith.[citation needed] A year later, Gidiney was invited for dinner at the Bingham house on 1632 Sixth Avenue.[citation needed] In the city directories of 1893 and 1895, Gidiney appeared as a sexton,[citation needed] but was also noted as the chairman of the A.M.E. Zion church in 1894.[15]


It was eventually around June 1900 when the last details of widowed “Charles F. Gidiney”[f] were documented on a ward census in Milton, about 30 miles away from Troy. The census also pointed out that neither Gidiney, nor the people in the ward, save for one, had ever attended school,[16] which was already noted in the news.[17]

Periodical records[edit]

Despite the abundance of newspapers that mentioned Gidiney, he was still little-known among a number of Gidneys and African-American mathematicians. The first paper to ever mention Gidiney is in the Troy Daily Whig of March 30, 1837, when he married Thodosia Ball ten days before, led by Reverend Daniel Vandervere.[18][19]


On the matter of π[edit]

On October 20, 1877, the Troy, New York, Daily Times' Saturday afternoon paper reported that Gidiney “discovered the true and exact ratio between the diameter and circumference of a circle”, known as π today. Two days later, the New York Times republished that article as “A Negro Mathematician's Claim”.

The Troy Times of Saturday says: “A colored man named Gidney, residing on North Third street, below Jacob, claims to have discovered the true and exact ratio between the diameter and circumference of a circle. According to the accepted rule, with the diameter or circumference alone given, the other cannot be exactly told. The ratio is 3.14159 plus, or as commonly used, 3.1416 plus. Mr. Gidney claims that by an algebraic calculation he has discovered the exact ratio, and he has in preparation a book on the subject which he intends shortly to publish. The demonstration of this interesting discovery is now receiving the attention of competent mathematicians, and whether it amounts to anything or not will soon be determined. Mr. Gidney possesses little or no education except in mathematics, and in this branch it is said he is able to solve most difficult problems.”[17]

So far, no book under Gidiney's writing has been found, giving the impression that he never got to publish it. The New York Times republished another Troy Times article exactly a year after the original article above under "A Colored Man's Solution".

Now, take two different circles. Let the letter w represent the diameter and the letter x the circumference of one circle; and the letter y the diameter and the letter z the circumference of the second circle. From this, we form the proportion w:x::y:z. Reducing this, we find that wx=yz, and these products must always be equal. Thus we see that if we take any two different circles, and multiply the diameter of the first by the [circumference] of the second, and the circumference of the first by the diameter of the second, these products will be exactly equal. In illustration of this Mr. Gidiney takes two circles; the diameter of the first he considers 113 feet, and the diameter of the second 7. By a long series of ingeniously-constructed equations he finds the exact circumferences of these circles to the 348 5*12 and 21 7*12 respectively, or 113:348 5*12 : : 7:21 7*12. Reduce this, and 2,438 11*12 = 2,438 11*12. In solving this and kindred problems, Mr. Gidiney uses over 1,350 different equations, all of which prove themselves correct from beginning to end. Another, as 7:21 7*12 : : 7 5*37:22. Multiplying the means and the extremes to-gether, their products will be exactly equal. Thus 7 5*37x21 7*12=7x22, or 154 equals 154.[20]

Various newspapers shared the news over time in different ways, including

  • Indianapolis Sentinel (Indiana) – October 24, 1877[citation needed]
  • Jersey Journal (New Jersey) – October 29, 1877[citation needed]
  • Weekly Louisianian (New Orleans) – November 3, 1877[citation needed]
  • The Troy Evening Standard (New York) – October 2, 1878[g]
The Historic Magazine and Notes and Queries compared Gidiney's result from this article (3.15135+) with others' finds and was not one of the twenty who got the first 13 digits correct.[22] Nevertheless, an uneducated person reaching this close to the answer of π is rare.
  • The Chicago Tribune (Illinois) – October 26, 1878[23]
  • The Valley Republican (Kinsley, Kansas) – November 2, 1878[24]
  • Arkansas City Weekly Traveler (Kansas) – November 6, 1878[25]
  • Belleville Telescope (Kansas) – November 7, 1878[26]
  • The Osage City Free Press (Kansas) – November 8, 1878[27]
  • St. Albans Daily Messenger (Vermont) – March 1, 1879[citation needed]
  • The Rome Sentinel (New York) - March 4, 1879

C. T. Gidiney,[h] of Troy, N.Y., a poor man more than sixty years old, announces that he has discovered the ratio between the diameter and circumference of a circle, and that it is worked out by laws immutable. Jealous of his discovery[,] he is guarding it until he can secure the protection of the law to prevent others from wresting it from him.[28]

  • The Athens Messenger (Ohio) – March 6, 1879[29]
  • State Journal (Harrisburg) – July 26, 1884[citation needed]

Other publications[edit]

On February 11, 1843, Gidiney published a formula to extract the fourth root under “A Concise Formula to Extract the Fourth Root: Example” in The New York State Mechanic, a Journal of the Manual Arts, Trades, and Manufactures. Interestingly, he writes from New Lebanon Springs, also about 30 miles away from Troy.

RULE.–Separate the given number into periods, of four figures each, by putting a point over the unit figure, and every fourth figure from the place of units to the left, and if there be decimals, to the right hand. Find the greatest biquadrate in the left hand period, and place its root in the quotient. Subtract the biquadrate thus found from the said period, and to the remainder bring down the next period, calling this the dividend. Multiply the cube of the quotient by 4000, calling it the imperfect divisor. Find how often the imperfect divisor may be had in the dividend, and place the result in the quotient. Then multiply the square of the former quotient by the last quotient figure, and that product by 600, calling it the first triple product, and place it under the imperfect divisor; then multiply the square of the last quotient figure by the former quotient, and that product by 40, calling it the second triple product, and place it under the first triple product; then cube the last quotient figure, and place it under the second triple product, and the sum of these four called a perfect divisor. Multiply the perfect divisor by the last quotient figure, calling the product the subtractend. Place this regularly under the dividend, and subtract, bring down the next period for a new dividend. Then to find another imperfect divisor, (instead of cubing the quotient and multiplying it by 4000,) add to the last perfect the first triple product, and twice the second triple product, and three times the cube of the last quotient figure, placing three cyphers to the right hand of their sum. Then proceed as above directed, remembering at every period brought down to find your imperfect divisor, according to the above direction.[30]

Other mentions[edit]

The Troy Daily Times put his name in a “list of letters remaining in the Troy Post Office, May 16, 1853,”[31] placed his real estate under two city tax sales in 1872[32][33] and a county tax sale in 1876.[34] The paper also posted Gidiney's ad for whitewashing under the Miscellaneous section on May 11, 1885.[35] The property of Gidiney's wife, located in the Third Assessors' District, was also posted in county tax sales: one in 1893 for $22.47[36] and in 1901 for $9.40.[37]


  1. ^ Not to be confused with the Gidney in Newburgh
  2. ^ With the exception of 1863, when he simply lived near it.[citation needed]
  3. ^ Not to be confused with Mr. Chas. Gidney
  4. ^ Not to be confused with Dr. E. Gidney
  5. ^ Not to be confused with the applicant of a safety device and a check valve
  6. ^ Not to be confused with the Gidiney from Kansas
  7. ^ Republished by Sylvester Clark Gould's bibliography[21]
  8. ^ Not to be confused with the one from King's Lynn


  1. ^ a b c Cooper-Rompato, Christine (January 1, 2014). "A Forgotten African American Mathematician: Charles T. Gidiney of Troy, New York [Public]". Afro-Americans in New York Life and History. Retrieved June 30, 2014. 
  2. ^ "A Negro Mathematician's Claim". October 22, 1877. Retrieved November 26, 2015. 
  3. ^ Bureau of the Census; United States. (December 19, 1840). "Schedule of the whole number of persons within the division allotted to J. N. N.". 1840 New York Federal Population Census Schedules - Columbia County. Washington : National Archives and Records Service, General Services Administration. p. 64. Retrieved August 10, 2014. 
  4. ^ "Charles T. Gidiney, United States Census, 1850". September 14, 1850. Retrieved June 27, 2014. 
  5. ^ "New York, State Census, 1855 - Rensselaer - Troy City, Ward 1". FamilySearch. 1855. p. 41. Retrieved August 4, 2014. 
  6. ^ "Chas T Gidney - United States Census, 1860". FamilySearch. 1860. p. 58. Retrieved August 4, 2014. 
  7. ^ "1865 New York State Census - Rensselaer County - Troy - 7th Ward - Dun to Greer". ConnorsGenealogy. Retrieved July 27, 2014. 
  8. ^ "New York, State Census, 1865 - Rensselaer - Troy, Ward 07". FamilySearch. 1865. p. 29. Retrieved August 4, 2014. 
  9. ^ Williams, Oscar (2012). "Racial Violence in the New York State 1860-1863" (PDF). The Harabi. 7 (1): 10. 
  10. ^ "Charles L. Gedney, New York, State Census, 1875". June 1875. p. 14. Retrieved June 27, 2014. 
  11. ^ "Troy, New York 1877 City Directory". 1877. p. 77. Retrieved July 27, 2014. 
  12. ^ "Meeting of the Rensselaer County Bible Society - Treasurer's Report - Election of Officers." (PDF). The Troy Daily Times. Troy, N.Y. January 20, 1876. Retrieved July 31, 2014. 
  13. ^ Hillman, Joseph (1888). Members of the Official Board of Zion Church, 1887-88. Troy, N.Y.: Troy. p. 277. 
  14. ^ "Surnames Beginning with the Letter Ga-Gi". Troy Irish Genealogy Society. Retrieved July 27, 2014. 
  15. ^ "Continuing Anniversary Exercises - A Historical Meeting." (PDF). The Troy Daily Times. Troy, N.Y. October 3, 1894. p. 1. Retrieved August 7, 2014. 
  16. ^ Herbert E. Gollamer (June 4, 1900). "Charles F Gidiney in household of Charles Spaulding". p. 242B. Retrieved June 27, 2014. 
  17. ^ a b "A NEGRO MATHEMATICIAN'S CLAIM". The New York Times. New York City, N.Y.: The Troy Evening Standard. 22 October 1877. Retrieved June 27, 2014. 
  18. ^ "Troy Irish Genealogy Society- Troy Daily Whig Marriages 1834-1838". Retrieved July 29, 2014. 
  19. ^ "Married." (PDF). The Troy Daily Times. Troy, NY. March 30, 1837. p. 2. Retrieved August 4, 2014. 
  20. ^ "A Colored Man's Solution.". The New York Times. New York City, N.Y.: The Troy Evening Standard. 20 October 1878. p. 2. Retrieved June 13, 2014. 
  21. ^ Gould, Sylvester Clark (1888). Bibliography on the polemic problem: What is the value of [symbol for pi]. Manchester, New Hampshire. p. 13. 
  22. ^ Gould, S. C. & L. M. (1888). "Bibliography - Cyclometry and Quadratures.". Historic Magazine and Notes and Queries: A Monthly of History, Folk-lore, Mathematics, Literature, Art, Arcane Societies, Etc, Volumes 5-6. Manchester, N.H. 5: 125. Retrieved August 8, 2014. 
  23. ^ "News". The Chicago Tribune. Chicago, Illinois. October 26, 1878. p. 11. Retrieved August 5, 2014. 
  24. ^ "A Colored Plan's Solution.". The Valley Republican. Kinsley, Kansas. November 2, 1878. p. 1. Retrieved July 31, 2014. 
  25. ^ "A Colored Man's Solution.". Arkansas City Weekly Traveler. Arkansas City, Kansas. November 6, 1878. p. 4. Retrieved July 31, 2014. 
  26. ^ "News". Belleville Telescope. Belleville, Kansas. November 7, 1878. p. 4. Retrieved August 5, 2014. 
  27. ^ "A Colored Man's Solution". The Osage City Free Press. Osage City, Kansas. November 8, 1878. p. 3. Retrieved July 8, 2014. 
  28. ^ "State News" (PDF). The Rome Sentinel. Rome, New York. March 4, 1879. Retrieved June 29, 2014. 
  29. ^ "General News of the Week". The Athens Messenger. Athens, Ohio. March 6, 1879. p. 1. Retrieved August 5, 2014. 
  30. ^ Gidiney, Charles T. (February 1843). "A CONCISE METHOD OF EXTRACTING THE FOURTH ROOT". The New York State Mechanic, a Journal of the Manual Arts, Trades, and Manufactures (1841-1843). 2 (12): 94. 
  31. ^ "The List of Letters" (PDF). The Troy Daily TImes. Troy, N.Y. May 16, 1853. Retrieved July 31, 2014. 
  32. ^ "Third District - City Tax Sale" (PDF). The Troy Daily Times. Troy, N.Y. April 19, 1872. Retrieved July 31, 2014. 
  33. ^ Burdett, Geo. C. (May 20, 1872). "City Tax Sale" (PDF). Troy Daily Times. Troy, N.Y. Retrieved July 17, 2014. 
  34. ^ "County Notices" (PDF). The Troy Daily Times. Troy, N.Y. February 24, 1876. Retrieved July 31, 2014. 
  35. ^ Gidiney, Charles (May 11, 1885). "Whitening" (PDF). The Troy Daily Times. Retrieved June 29, 2014. 
  36. ^ "Third District - County Tax Sale" (PDF). The Troy Daily Times. Troy, N.Y. 1893. p. 7. Retrieved August 7, 2014. 
  37. ^ "Third Assessors' District - County Tax Sale" (PDF). The Troy Daily Times. Troy, N.Y. June 21, 1901. p. 5. Retrieved July 31, 2014.