A Forgotten African American Mathematician: Charles T. Gidiney of Troy, New York.

Cooper-Rompato, Christine

African American men made considerable contributions to the field of mathematics in the 1700s and 1800s) The earliest African American mathematician is thought to be the slave Thomas Fuller (d. 1790), whose obituary termed him "the famous Africa Calculator" who could, among other feats, "give the number of months, days, weeks, hours, minutes and seconds in any period of time that any person chose to mention, allowing in his calculation for all leap years that happened in the time." (2) Better known is Benjamin Banneker (d. 1806), who taught himself advanced mathematics and astronomical calculations and created a famous almanac featuring astronomical predictions.(3)

In 1849, Charles Reason (d. 1893) became the first African American professor at a predominately white college, namely Central College in McGrawville, Cortland County, New York. He was professor of belles lettres, Greek, Latin, and French, and appointed as an adjunct professor of mathematics.(4) Edward Alexander Bouchet (d. 1918) was the first African American to earn a PhD in the U.S. (in geometrical optics, a branch of physics, from Yale University in 1876).(5) In 1886, Kelly Miller (d. 1939) was the first African American to study mathematics at the graduate level, at Johns Hopkins University.(6) In 1925, the first African American to earn a PhD in pure mathematics, from Cornell University, was Elbert Frank Cox (d. 1969).(7) These men, whether informally or formally educated, are famous for their mathematical achievements. One story that has not been told, however, is that of a lesser known and non-formally educated African American man who also was actively involved in the field of mathematics, Charles T. Gidiney. (8)

On Saturday afternoon, October 20, 1877, the Troy Times reported a mathematical discovery in its local news section, "Home Matters": Charles T. Gidney [sic], a resident of Troy, New York, claimed to have calculated "The True Ratio Between a Diameter and Circumference of a Circle," or pi (11). This article was then reprinted in the October 22, 1877 issue of the New York Times under the title "A Negro Mathematician's Claim":

  The Troy Times of Saturday says: "A colored man named Giciney,
  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 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." (9)

Notices about this discovery also appeared in several newspapers across the nation. Both the Indianapolis Sentinel of October 24, 1877 (10) and the New Orleans' Weekly Louisianian of November 3, 1877 repeat the Times notice, with an error in the latter claiming that the ratio of pi is "4.14159 plus". (11) The October 29, 1877 Jersey Journal of New Jersey summarizes Gidiney's findings in a section dedicated to humorous and/or unusual news items, quipping that "a Troy publisher is printing a book on the subject. Several lunatics on this subject have already been fed at the State's expense, and the thing is about played out." (12) The March 1, 1879 issue of the Si. Albans Daily Messenger of Vermont focuses on both the poverty and vulnerability of the inventor, claiming that Gidiney, "a poor man, more than sixty years old" is "jealous of his discovery" and thus "is guarding it until he can secure the protection of the law to prevent others from wresting it from him." (13) Five years later, an article titled "A Colored Mathematician" appearing in the State Journal of Harrisburg, Pennsylvania, repeated the information of the Times article, adding that Gidiney "has devoted years to the problem and will soon publish in book form the results of his labor." (14) That this news item was republished repeatedly over an eight-year time span suggests that it had resonance with readers across the country. The story was attractive on so many levels: an informally educated African American genius, a "poor man" by at least one account, planning to publish his life's work but jealously guarding his discovery against those who would attempt to claim it for their own.

Unfortunately, it is not immediately known whether or not Charles Gidiney did produce such a book, and if he did, whether or not it was ever published. However, S. C. Gould's Bibliography on The Polemic Problem: What is the Value of (17), published in 1888, reports under Gidiney's name the title "The Ratio of Circumference to the Diameter of the Circle," with the publication details as "Troy (N. Y.) Standard, October 2, 1878," referring to the newspaper the Evening Standard, whose first issue was published in 1877. (15) As Gould's bibliographic reference records, "Mr. Gidney works by a series of algebraic equations numbering 1350, from which he develops the ratio, 3.135135+. (16) This would suggest that either Gidiney did write a publication by the title "The Ratio of Circumference to the Diameter of the Circle" that was mentioned in the October 2, 1878 issue of the Evening Standard, or that this article published his results and observed therein that the number of expressions totaled 1,350. Regrettably, no copies of this particular newspaper issue survive in any form that I have been able to locate, so what was reported in the paper must be left to our imagination. (17)

As far as I have been able to discern, Gidiney's discovery is only mentioned in a few sources between the 1880s and the 1960s. In addition to Gould's 1888 Bibliography on The Polemic Problem, a verbatim citation appears in S.C. Gould and L.M. Gould's periodical The Bizarre Notes and Queries in History, Folk-Lore, Mathematics, Mysticism, Art, Science, Etc., also published in 1888.18 Decades later, in a very short article published in 1963 by Underwood Dudley on the value of pi, Gidiney is credited with being part of a long but important tradition of those who helped us "[keep] track of IT' in the nineteenth century. (19) However, since the 1960s, it appears no one has remembered this mathematician or considered some of the important questions raised by and surrounding his remarkable efforts.

A large part of the interest in Gidiney's discovery for newspaper audiences across the country may have been readers' familiarity with the concept of pi and attempts to define it. Searching for the value of pi, or the ratio of a circle's circumference to its diameter, had occupied hundreds if not thousands of enthusiasts since ancient times. This appears to have been such an intriguing problem for so many people over the centuries because what seems at first glance to be deceptively simple is actually beyond the power of human calculation; as we now know, pi is actually an irrational number that cannot be precisely determined with absolute accuracy. We may use approximations such as the ratio 22/7 or 3.14 for convenience sake, but in fact the decimal continues on indefinitely in no predictable pattern. But the very hope that the value could be determined was enough to motivate many; certainly computing the value of pi with absolute precision would be attractive, as it appears in many formulae and its value is intrinsic to trigonometry. (20)

By 1853, the British amateur mathematician William Shank, collaborating with mathematician of the Royal Military Academy William Rutherford, had calculated pi to the 607 (th) digit, and by 1873 Shank had increased pi to the 707 (th) digit, although approximately the last 200 or so of these digits were later found to be incorrect. (21) Shank and Rutherford's amazing feat did not preclude others from attempting to refine pi in the mid to late nineteenth century, or from reproducing some of the same results as earlier publications through a different series of calculations. Some who were working on the value of pi were well-known figures, including noted mathematicians and other professionals. For example, in 1861, Dr. Philip H. Van der Weyde, prominent electrician and future editor of The Manufacturer and Builder, demonstrated that pi is equal to 3.1415926535+. (22) In 1862, the philosopher, writer, and geometrist Professor Lawrence Sluter Benson argued that pi is equal to 3.141592+. (23) Even aristocracy was not exempt from the desire to define pi: The 11" Duke of Somerset, Edward Adolphus St. Maur, wrote a treatise in 1843 calculating the properties of the ellipse and the circle. (24) Still others were publishing their results on pi under pseudonyms such as "Futurus" at 3.1238093 11/21 (in 1853) and "A. Finality" at 3.16666 2/3 (in 1872), no doubt leading audiences to wonder at the authors' true identities. (25)

This late nineteenth-century drive to define pi and the related problem of squaring the circle, or making a square with the same area as a given circle using only a compass and a straight edge, culminated in the infamous "Indiana Pi Bill" of 1897. This bill was brought to session by an amateur mathematician, Dr. Edward J. Goodwin, who believed he had squared the circle and wished to legislate his results for the benefit of Indiana (all other states were to pay a tax to Indiana for using Goodwin's discovery). Although the bill was an extremely confusing and contradictory piece of legislation containing several definitions of pi, it passed the House but fortunately was postponed indefinitely in the Senate after a math professor from Purdue University pointed out its erroneous logic.26 Although the Indiana Pi Bill is usually considered to be an example of what happens when government attempts to legislate science, it can also be read as an example of the public's intense and popular interest in long-standing mathematical challenges. (27) Trying to define pi was a kind of participatory math problem, as amateurs and professionals alike believed they could make valuable contributions to the field.

To return to the case of Charles T. Gidiney, who contributed his algebraic proof of pi to the larger mathematical discussion, we see that many questions are raised by the New York Times article, and especially the non-extant Troy Evening Standard article. The New York Times (quoting the Troy Times) states that Gidiney had received little or no education, except in mathematics. How and where did he learn his mathematics? As a free African American, had he received formal and/or informal training as a child or adult, or was he an autodidact? How did he publicize his discovery, and what was the response of the local community to his work? Who were the "competent mathematicians" who examined it, and what were their conclusions? Did Gidiney or the other mathematicians reviewing his work have any connection to nearby universities or colleges, namely Rensselaer Polytechnic Institute and the short-lived Troy University, which was operated by the Methodist Episcopal Church between 1858 and 1 86 1? (28) In what ways did Gidiney publically practice mathematics in his community, thereby earning him a reputation for mathematics? Unfortunately, none of these questions are easy to answer without further evidence to illuminate them.

Fortunately, Charles T. Gidiney has left a number of biographical records including those found in census records, city directories, church records, and local newspaper articles, and these provide brief glimpses into the circumstances of his life. Much can be surmised from the records, but even more is left unknown. In the following pages I will present the extant biographical evidence and life records in rough chronological order, making conjectures whenever possible to shed some light on Gidiney's mathematical accomplishments.

The first time Gidiney appears in any written document is the Federal Census of 1840, where he is listed as living in New Lebanon, Columbia [County], New York. According to the census, there were nine -free colored persons" living in the household: two males under the age of ten, two men between 24 and 35 (of which Charles Gidiney, head of household was one), one female under ten, two females between the ages of ten and 23, one female 24 through 35, and one between 36 and 54. None of the other names in the household are given, so their relationships to Gidiney are not easy to discern. (29) It is tempting to imagine that Charles Gidiney was living with his wife, mother, and several children; the other man between 24 and 35 could of course be a relative or unrelated boarder.

New Lebanon, well known in the nineteenth century for its vibrant Shaker community, lies over twenty miles southeast of Albany, and in the early-mid nineteenth century a number of free African Americans lived in this general area of upstate New York. According to North Star Country: Upstate New York and the Crusade for African American Freedom, in 1840 Columbia County had 1,156 free African American men and women living within its confines; however, as the census reveals, the number of African Americans living in New Lebanon itself was quite small, fewer than 30. Gidiney's household was by far the largest with its nine residents. (30) As Charles Gidiney does not appear in any earlier documents that I have found, it is not clear whether he was raised in New Lebanon as a child, of if he relocated to New Lebanon as an adult. If Gidiney was raised in upstate New York, perhaps he attended one of several segregated schools in the area for African American children, where he would no doubt have learned the fundamentals of algebra and geometry. (31)

A decade later Charles T. Gidiney appears in the 1850 census as a "laborer," age 37, with the estimated year of birth 1813. His birthplace is listed as New York. He is recorded as dwelling in house number 1226 (census numbering) of the Third ward of Troy in Rensselaer County. In addition to Gidiney, three other people are included in the household:

  Mary C. Hardy, female, age 22, birthplace New York Anna Hardy,
  female, age 3, birthplace Pennsylvania John T. Gidiney, male,
  age 11, birthplace New York"

John T. may possibly be Charles Gidiney's son, who would have been one year old at the time of the 1840 census. Mary Hardy may be a partner, relative, or unrelated acquaintance. According to census data, in 1850 Rensselaer County had 1,019 free blacks living within its confines; the dwelling in which the Gidiney and Hardy family resided was home to several other African American families. (33)

Charles Gidiney's move to Troy in the 1840s may have proved quite important to the development and expression of his mathematical ability. The city of Troy and its inhabitants played an important role in the abolitionist movement; for example, the Liberty Street Presbyterian Church was one of the stops on the Underground Railroad, and the abolitionist paper the National Watchman was first published in Troy in 1842. (34) Troy was the first city where Uncle Tom 's Cabin was produced (in 1852), and Troy was also the host of the first Negro State Convention (in 1841). (35) Certainly its abolitionist activity must have been attractive to many, and it is tempting to imagine Gidiney as capitalizing on this atmosphere to pursue his mathematical ambitions. (36)

Because of the influx of immigrants to New York, the state held extra censuses in the nineteenth century. In the 1855 New York state census, Charles F. Gidiney [spelled Gidney], age 40, is recorded as living in the First Ward of Troy, with a birthplace of Columbia County and the occupation of whitewasher. He is married to Harriet A. Gidney, age 36, with a birthplace of Schoharie County. (37)

Gidiney appears in a number of documents in the 1860s. The 1860 federal census lists a "Chas T Gidney," with a residence in the Seventh Ward City of Troy in Rensselaer, New York. His age is given as 45 years and his birthplace is New York state. (38) This year, Rensselaer County had 1058 free blacks living in the county, according to census data. (39) This is the year that Harriet Tubman stayed over in Troy on her way to an abolitionist meeting in Boston and helped to rescue an escaped slave, Charles Nalle, who was about to be sent back to Virginia under the Fugitive Slave Law of 1850. (40) In the 1861 Troy City directory, Charles T. Gidiney appears as a whitewasher (an unskilled labor position involved with painting and construction), living at house number 156 Green.41 The 1863 city directory states "Charles T. Gidiney," "house rear 156 Green." (42)

In July 1863, Charles Gidiney wrote a letter to the mayor of Troy expressing his fear about the well-being of his family and other African Americans during the Troy Civil War draft riots. This letter is now preserved at the Rensselaer County Historical Society. The draft riots began when federal legislation passed stating that all able-bodied men between the ages of 20 and 45 should serve in the Union Army, with the exception that a man could either provide a substitute or pay three hundred dollars for an exemption. Riots commenced in New York City, and soon the mob, composed largely of Irish-American immigrants, violently attacked African American men, women, and children. According to the front page articles in the New York Times on July 14, 1863, "As soon as one of these unfortunate people was spied, whether on a cart, a railroad car, or in the street, he was immediately set upon by a crowd of men and boys, and unless some men of pluck came to his rescue ... he was inhumanly beaten and perhaps killed." (43)

Riots soon spread to Boston and Troy. The following is a description of the riots in Troy that came to a head on Wednesday, July 15:

  On Wednesday morning, about four hundred men, averse
  to the draft, formed a procession at the Nail Factory...
  and marched through the city northward as far as Mount
  Olympus. Along the line of march mechanics and other
  workmen were solicited to the part in take part in the
  demonstration which was evidently intended primarily
  to be a display of the number of persons in the city
  opposed to the making of a draft to recruit the
  armies in the field. This intention was soon changed
  to one less peaceful in expression. (44)

Rioting and looting was rampant, and the offices of the Troy newspaper, the Troy Daily Times, were ransacked, as were private residences. The rioters in Troy targeted African Americans with particular vehemence. As Arthur James Weise records, "Wherever found, without any distinction of age or sex, they [African Americans] were stoned and otherwise maltreated." (45) Charles T. Gidiney's letter, which was written on Saturday, July 18, to the mayor of Troy, describes the violence he and his wife were facing and eloquently requests the mayor's assistance:

  City of Troy July 18th 1863 To the Mayor of Troy City Mr.
  Wm L. Van Alstyne Esq. Honorable Sir. 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 some thing thrown at my head, I have been staying
  in my house 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 with
  out 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 there clubs at her &c.

  I pray you to forthwith put out a Proclamation against all such
  offenses so the we Coloured people may walk the street in perfect
  Peace &c.

  Yours Most Respectfully &c. &c.

  Chas. T. Gidiney (46)

The letter attests to the cruel and menacing treatment he and his family were receiving at the hands of the rioters, and makes an appeal to the mayor to restore order by making a proclamation "against all such offenses" so that all the African American men and women of Troy can return unmolested to their work and lives. The letter shows Charles Gidiney to be a careful rhetorician, balancing accounts of his wife's and his own personal experiences with formal requests of aid, to urge the major to act to protect Troy's African American community. Gidiney begins by stating that he has listened to white men and women who have instructed him to stay inside, and then ends the letter with the image of little white boys holding clubs and menacing his wife. The letter seems to suggest that surely the mayor should be able to control "little boys," if not their parents.

Gidiney next appears in a census document two years later. Charles T. Gidiney is included in the 1865 New York state census as a resident of the Seventh Ward of Troy. He is listed as head of household and is 57 years old. According to the document, he has three children, has been married twice, and is currently married. His birthplace is given as Columbia [County, New York], and his occupation is -white washer."

Immediately following his entry is listed -Harriet Gidiney," age 46, from Broome [County], which lies west of Rensselaer. She is recorded as having one child, has been twice married, and is now currently married.'" Although the entry for Charles Gidiney suggests he was born somewhat earlier than the other censuses (approximately 1808), the remaining details are similar to other censuses. In the 1865, 1866, 1867, and 1868 Troy City directories, Charles T. Gidiney appears as a "whitewasher" living at the street address of 156 Green. (48)

In the 1870 census, he appears as Charles T. Gidney of Rensselaer, New York, age 56. His occupation is listed as "whitewashing walls." His household includes Harriet M. Gidney, age 52; the couple lives alone. The value of their real estate is given as two thousand dollars, and their personal estate is worth two hundred. (49) Assuming these census figures are correct, this would put Charles Gidiney about age 63 or 64 when the Troy Times first reported his mathematical discovery. In the 1872 directory of Troy City, Charles T. uicuncy is listed as a whitewasher living at h. 52 North Third. (50) This is repeated for the Troy City Directories of 1872, 1873, 1874, 1875, and 1878. (51)

In the 1875 New York state census for Troy, a listing is given for "Charles L. Gedney," age 62, whitewasher, and "Harretta Gedney," age 58, housekeeper, as well as a "daughter" named "Melicia Johnson," age 17 and "William H. Brown," age 52, "boarder." (52) The value of their framed dwelling is given as one thousand dollars. It is not clear whose daughter Melicia is, and she does not appear again under this name in future censuses. As Harriet and Charles Gidiney were married by 1855, is does not seem possible that Melicia Johnson is their biological daughter. However, she may be an adopted daughter, or even the daughter of the boarder (although her name is listed after the Gidineys and before the boarder.)

Gidiney does not appear in the records of the 1880 census. However, his name is included in the subsequent city directories. In 1881, 1882, and 1883, Charles T. Gidiney appears as a whitewasher living at h. 52 North Third. (53) In 1886 he is listed as "Chas T.," still with the same occupation and address. (54) In 1887 Chas. T. Gidiney has moved to 2168 Sixth Ave, where his directory listing remains unchanged until 1893. (See records for 1888, 1889, 1890, 1892, and 1893.) (55) The Saturday, October 2 issue of the New York Freeman in 1886 lists his property as valued at one thousand dollars. (56)

A number of records frorr the 1880s attest to the Gidineys' involvement in their community and church. In the 1884 Troy City Directory, Mrs. Harriet Gidiney is listed as the president of the Female Benevolent Society, a society for Atrican American women that met the "First Tuesday evening of each month." (57) The original African Female Benevolent Society of Troy was formed in 1833, and was designed to give aide to the poor as well as "to break down the barrier of prejudice and raise themselves to an equality 'with those fellow beings who differ from us in complexion alone.'" (58) It is not clear whether society over which Harriet Gidiney presided was an unbroken continuation of the African Female Benevolent Society, or whether the society was disbanded earlier and then reorganized at some point in the mid-1880s.

The Gidineys were very active in their church in the 1880s. The New York Freeman of March 27, 1886, reported on Charles Gidiney's recent election to the board of trustees of the A. M. E. (African Methodist Episcopal) Zion Church of Seventh Street, Troy. (59) In 1887-1888, Charles T. Gidiney and his wife Harriet appear in a list of members of the Church; Charles is also listed as a "Class Leader" as well as a "Trustee" of the Church. (60) The A.M.E. Church was originally founded in New York City in 1822, and in the early- to mid-nineteenth century African American worshippers brought independent congregations to upstate New York; the Troy A.M.E. Zion Church was established in the 1830s. (61) A photograph of Charles T. Gidiney appears in the book The History of Methodism in Troy, New York in which he is seated with members and the Church Board and the Church Trustees. (62) References to Troy's A.M.E. Zion Church in newspapers provide valuable evidence of the rich, literate community of the congregation, as articles on the topics of sermons and social events appeared regularly in the New York Freeman and the New York Age. These articles demonstrate the close connections between the African American churches in the area, particularly with the Liberty Street Presbyterian Church. The Gidineys' A.M.E. Zion Church was a significant site of learning and literacy; for example, a summary of the 1886 quarterly report of the Church included the mention of over 300 books in the library. (63)

One sermon of that may have been of particular interest to mathematician Charles Gidiney is referenced in a New York Freeman article on December 6, 1890, which states that the pastor of the Church, George E. Smith, "delivered an instructive sermon last Sunday upon 'Gospel Arithmetic,' beginning at addition and he purposes to conclude at division." (64) Although the title of this sermon is somewhat vague, it may have focused on the many numerate acts modeled in the Gospels--for example, the multiplication of the loaves and fishes, Christ's reference to Peter that he should forgive his brother "seventy times seven" times, and so on. Indeed, it is tempting to imagine that because of Gidiney's reputation as a mathematician, his fellow congregation had a heightened awareness of and interest in the numerical references in Scripture. Perhaps Gidiney's reputation for his mathematics influenced the topic of the sermon?

There are several mentions of Gidiney in records for the early 1890s, but after this the references grow much sparser. The federal census data for 1890 was largely destroyed, and Gidiney does not appear in the few extant records. However, there is a Chas. T. Giciney listed in the 1890 Troy city directory. (65) The September 13, 1890 issue of the New York Age reports under "Troy Tropics" that "The surprise party tendered Brother Gidney on his 77th birthday last Friday was pleasant affair" (66); the previous Friday no doubt refers to eight days before, on September 5. Unfortunately, his wife Harriet passed away almost immediately after the party, for the New York Age on Saturday, September 27, 1890, records that "the funeral of Mrs. Harriet Gidney took place from the A.M.E. Zion Church Thursday afternoon, September 11. The service was conducted by the Rev. Decker, assisted by the Rev. Geo. E. Smith, pastor." (67) According to the Troy Times mortuary notice, Harriet Gidiney's death was sudden. (68) The following year a social notice related to the A.M.E. Zion Church appeared in the New York Age, stating that Charles Gidiney had been invited to dinner at Mr. and Mrs. Joseph Bingham's house, 1632 Sixth Avenue. (69)

After his wite's death, Charles thdiney continued to reside at 2168 Sixth Ave. In 1893, the city directory listing includes an important change: Chas T. Gidiney is no longer listed as a whitewasher. Instead, he is listed as "Sexton, A.M.E. Zion's Church. (70) He also appears in the 1895 Troy City Directory as the sexton of the Church. After 1895, however, Gidiney is no longer listed as sexton of the church, and he is not included in the city directories.

By 1900 Charles Gidiney's fortunes had changed for the worse. The 1900 Federal Census includes a "Charles F. Gidiney," age 86, born September 1813 in New York, as a widowed inmate in a poor house (probably the County Poor House) in Milton, Saratoga. A census of inmates in almshouses and poorhouses also lists Gidiney as in inmate in 1900. (71) According to this document, Gidiney is said to be "colored" and a widower. His admittance date is given as January 9, 1900. Under "education" is recorded he can "read and write," and his occupation is listed as "laborer," as is the occupation of his father. His "habits," as well as the "habits" of his mother and father, are listed as "temperate." Under the question, how many children living, the response reads "none." If this is indeed the mathematician Charles Gidiney, his children had all died by this point. "Old Age" is given as the reason for dependence, and "not any" is the kind of labor he is able to pursue. This is the last record related to Gidiney that I have been able to discover. It suggests he died penniless and unknown, his mathematical achievements virtually forgotten.

A quarter of a century after the Troy Times first announced Gidiney's discovery, amateur mathematicians were still attempting to test their wits against pi. For example, the December 8, 1902 Evening News of San Jose, California, reported that a wood-dealer (and former French lawyer) named Benjamin Mercadier had spent nearly half a century in the quest to square the circle and was ready to report his successful results.72 Two days later, the paper printed that his claim was under attack by University of California Berkeley mathematicians who labeled the quest to square the circle "absurd." As the mathematicians explained, squaring the circle had been proved impossible in 1882 by Ferdinand von Lindemann when he demonstrated that pi was a transcendental or non-algebraic number. The "humble" Mercadier responded thus to the criticism: "I think I have the solution. The very simplicity of it inclines me the more to believe it. Of course I may be wrong. The mathematicians can look into my theory when I publish it. If I am wrong, I err in very good company." (73) Five years later, Mercadier died alone in his apartment, his life's work on pi apparently forgotten as well. (74)

It is quite possible that Charles Gidiney's proof never made it fully into print; no doubt he encountered opposition from professional mathematicians who crushed his theory, just as they had crushed Mercadier's. Despite the faulty nature of Gidiney's proof, however, it raises a number of intriguing questions. Firstly, there is the mention of the 1,350 algebraic steps in the proof: What did these steps look like? What kind of math was Gidiney engaged with? What could his proof tell us about his methods of inquiry and argument? Secondly, the proof raises many questions about Gidiney's education, namely, Where did he learn his mathematics? Who taught him, or if he was an autodidact, where did he find the resources to teach himself? While working as a laborer and a white-washer, when did he find time the necessary time to work on his mathematics? Did he work on paper or chalkboard, or entirely in his head? Thirdly, the proof raises questions about how Gidiney practiced his mathematics in his community. What kind of reputation did he have in his community for mathematics? Was he looked to as a mathematical authority by others? If so, how might he have served as a public mathematician or as mentor of numeracy to others? In addition, what were the connections, if any, between Gidiney and the mathematicians of Troy and the surrounding communities? These are questions that still need to be answered.

Even with these many questions left unanswered, we can still draw some significant conclusions from Gidiney's example. The first is an understanding of Gidiney's exceptional intellect in the context and challenges of his time. Charles T. Gidiney is an overlooked person who deserves to be recognized and celebrated, not so much for the accuracy or inaccuracy of his proof, as for his sheer effort and engagement with a problem that had obsessed and defeated many highly educated people before him. He was obviously a very tenacious, intelligent, rhetorically savvy man, one who no doubt played an important role in his church and social community and had earned a reputation for mathematical genius (indeed, as the newspapers indicate, he could answer almost any difficult problem). It is quite probable that Gidiney worked on his pi calculations for a long period of time as other pi enthusiasts did; this suggests that as the Civil War was being fought (and even as the draft riots were occurring in Troy), this man was wrestling with a frustratingly complex mathematical problem. Did Gidiney use his calculations as a way to balance what must have been the enormous stresses and concerns of his everyday life? Were his mathematical calculations a way to transcend the temporal to allow him to focus on the mathematical eternal, of showing his equal intellectual footing with educated white elites who were also occupied with the problem? As Gidiney bravely exposed himself to the media and allowed his work to be submitted to the scrutiny of "competent mathematicians" (i.e. white academics), he was making a strong political statement that African Americans could and should participate in longstanding academic debates.

Secondly, Gidiney's story reminds us that paying more attention to local examples of African American men and women involved with science, technology, and invention in past centuries is important because their lives can offer us alternative ways of thinking about how education and knowledge are acquired. 1 keep thinking about that library of three hundred books owned by the A.M.E. Zion Church of Troy, as well as the kinds of literate and numerate practices promoted by church sermons, benevolent societies, and meetings. Perhaps our list of famous African American mathematicians, such as the list with which I began this paper, could be expanded to include more brilliant practitioners of "vernacular mathematics" who we might uncover in small communities throughout the United States.

(1.) See, for example, "Mathematicians," in The Encyclopedia of African-American Culture and History, ed. Colin A. Palmer, 5 vols. 2nd ed. (Macmillan and University of Michigan, 2006), 4, 1406-7.

(2.) Patricia Clark Kenschaft, Change Is Possible: Stories of Women and Minorities in Mathematics (Providence, R.I.: American Mathematical Society, 2005), 77, quoted from "Thomas Fuller: A Precocious African," The Columbian Centinial, December 29, 1790, No. 707, p. 123, col. 32 (Boston, MA), accessed December 6, 2013, http://www.math.buffalo.edu/mad/snecial/fullerthomas1710-1790.html.

(3.) Kenschaft, Change is Possible, 78-81.

(4.) "Charles L. Reason," accessed December 6, 2013, http://www.math.buffalo.edu/mad/special/reasoncharles1.html.

(5.) "Bouchet, Edward Alexander," in African American Lives, ed. Henry Louis Gates, Jr., and Evelyn Brooks Higginbotham (Oxford: Oxford University Press, 2004), 91.

(6.) "Kelly Miller," accessed December 6, 2013, http://www.math.buffalo.cdu/mad/snecial/millerkellev.html: see also "Hopkins History: In 1887, Kelly Miller, Son of a Slave, Became a JHU First," in The Johns Hopkins University Gazette, January 16, 2001, accessed December 6, 2013, http://www.jhu.edu/gazette/2001/jan1601/, and -Miller, Kelly," in African American Lives, ed. Gates and Higginbotham, 594.

(7.) "Elbert Frank Cox," in African Americans in Science, Math, and Invention, ed. Ray Spangenburg and Kit Moser (New York: Facts on File, 2003) 49-50.

(8.) Charles Gidincy's name is spelled "Gidney," "Gidiney," and even "Gedney" in contemporary documents. In the one extant document that we have in his own hand, he spells his name "Gidiney," a practice I follow in this paper.

(9.) "The True Ratio Between a Diameter and Circumference of a Circle," Troy Daily Times, October 20, 1977, pg. 3; reprinted as "A Negro Mathematician's Claim," New York Times, October 22, 1877, accessed December 6, 2013, Pro Quest Historical Newspapers: The New York Times (1851-2008).

(10.) "A Negro Mathematician," Indianapolis Sentinel (Indianapolis, IN), vol. xxvi, no. 297, October 24, 1877, pg. 1, accessed December 6, 2013, http://www.genealogybank.com/gbnIdnewspvers/doe./.

(11.) "A Negro Mathematician's Claim," Weekly Louisianian (New Orle--s, LA), November 3, 1877, pg. 2 accessed December 6, 2013. http://www.genealogybank.com/gbnk/newspapersidoc/.

(12.) "Minor Topics," Jersey Journal (Jersey City, NJ), October 29, 1877, pg. 2, accessed December 6, 2013, http://www.gencalogybank.com/gbnk/newspapers/doc/.

(13.) "Fact and Fancy," St. Albans Daily Messenger (St. Albans, VT), March 1, 1879, pg. 4, accessed December 6, 2013, http://www.genealogybank.com/gbnk/newsnapers/doc/.

(14.) "A Colored Mathematician," State Journal (Harrisburg, PA), July 26, 1884, pg. 2.

From the Gate City Press (Kansas), accessed December 6, 2013, http://www.genealogvbank.com/gbnIdnewspapers/doc/.

(15.) For the early history of the Evening Standard, see Arthur James Weise, Troy's One Hundred Years, 1789-1889 (Troy, NY: William H. Young, 1891) 373.

(16.) Sylvester C. Gould, Bibliography on the Polemic Problem: What is the Value of Pi? (Manchester, NH: no publisher, 1888) 13.

(17.) See this Library of Congress site for a list of libraries that have early issues of the Evening Standard; unfortunately, none of the libraries have October 2, 1878: Chronicling America: Historic American Newspapers at httri://chronicl ingamerica. loc. gov/I ccn/sn8403 13 0fholdi ngs/.

(18.) S.C. Gould and L.M. Gould, The Bizarre Notes and Queries in History, Folk-Lore, Mathematics, Mysticism, Art Science, Etc., (Manchester, NH: no publisher, 1888) 113. Gidney's name and calculation also appear in a table of calculations of p1 on page 125.

(19.) Underwood Dudley, "Ilt: 1832-1879," Mathematics Magazine 35 (1962): 153-54. Reprinted in Harmony of the World: 75 Years of Mathematics Magazine, ed. Gerald L. Alexanderson (Washington, D.C.: Mathematical Association of American, 2007), 133-34.

(20.) I would like to thank Dr. Richard Cutler and Dr. Brynja Kohler for their help on the definition ofpi.

(21.) For the early publications of Rutherford and Shank, see S. Gould, Bibliography on The Polemic Problem, 20. See also Alfred S. Posamentier and Ingmar Lehmann, Pi: A Biography of the World's Most Mysterious Number (Amherst, NY: Prometheus, 2004) 70.

(22.) S. Gould, Bibliography on The Polemic Problem.

(23.) For Van der Hyde's obituary, see Electric Power, British Electrical and Allied Manufacturers' Association, Vol. 7 (January-June, 1895), 394. 23S. Gould, Bibliography on The Polemic Problem, 6-7.

(24.) Ibid., 21.

(25.) Underwood Dudley, lit: 1832-1879," 133-34.

(26.) For a discussion of the Indiana Pi Bill, see Peter Beckmann, A History of Pi (New York: St. Martin's Press, 1971), 174-77. See also Will E. Edington, -House Bill No. 246, Indiana State Legislature, 1897," 231-39, in Pi: A Source Book, 3rd ed., ed. Lennart Berggren, Jonathan Borwein, and Peter Borwein (New York: Springer, 2004).

(27.) For more on Edwin Goodwin, sec New York Times, January 26, 1890: -Squaring the Circle: A Mathematician Who Meets With Scoffers Only," accessed December 6, 2013, ProQuest Historical Newspapers. For recent enthusiasm for Pi, see Posamentier and Lehmann, Pi: A Biography of the World's Most Mysterious Number, 117-36.

(28.) For the history of Troy University, see Franklin B. Hough, Historical and Statistical Record of the University of the State of New York During the Century from 1784 to 1884 (Albany, NY: Weed, Parsons & Company, 1885), 272-74.

(29.) 1840 United States Federal Census, accessed December 6, 2013, http://search.ancestry.corn/search/db.aspx?dbid=8057 (Provo, UT, USA: Ancestry.com Operations, Inc., 2010).

(30.) Milton C. Semen, North Star Country: Upstate New York and the Crusade for African American Freedom (Syracuse: Syracuse University Press, 2002), 281.

(31.) For a discussion of segregated schools in New York state, see Benjamin Justice, The War that Wasn't: Religious Conflict and Compromise in the Common Schools of New York State, 1865-1900 (Albany: New York Press, 2005), 150 ff.

(32.) 1850 United States Federal Census, accessed December 6, 2013, http://search.ancestry.corn/search/DB.aspx?dbid=8054.

(33.) Semen, North Star Country, 282.

(34.) For Troy and the underground Railroad, see Tom Calarco, The Underground Railroad in the Adirondack Region pp. 194-98. For African-American newspapers, see 1. Garland Penn, The Afro-American Press and its Editors (New York: Arno Press, 1969). See also Deborah Nazon, Brownfields Redevelopment and Competitive Advantage Theory: Urban Revitalization and Stakeholder Engagement in South Troy, NY. Unpublished Dissertation (Rensselaer Polytechnic Institute, Proquest, 2007).

(35.) Don Ritter, Troy: Then and Now (Charleston, S.C.: Acadia, 2007) 4; James Henry Gooding, On the Altar of Freedom: A Black Soldier's Civil War Letters from the Front, ed. Virginia M. Adams (Boston: University of Massachusetts Press, 1991), xxxiii.

(36.) For a history of labor in Troy, see Carole Turbin, Working Women of the Collar City: Gender, Class, and Community in Troy, New York 1864-86 (University of Illinois Press, 1992) and Daniel Walkowitz, Worker City, Company Town: Iron and Cotton-Worker Protest in Troy and Cohoes, New York, 1855-1884 (University of Illinois Press, 1972).

(37.) New York State Census, 1855, accessed December 5, 2013, Farnilysearch.org.

(38.) 1860 United States Federal Census, accessed December 6, 2013, http://search.ancestry.com/search/db.aspx?dbid=7667.

(39.) Sernett, North Star Country, 282.

(40.) Ibid., 191.

(41.) Troy Directory, June, 1861. U.S. City Directories, 1821-1989 (Beta) (Provo, UT, USA: Ancestry.com Operations, Inc.), accessed December 6, 2013, Ancestry.com.

(42.) Troy Directory, June, 1863. US. City Directories. 1821-1989, accessed December 6, 2013, Ancestry.com.

(43.) The Mob in New York," New York Times, July 14, 1863, pg. 1, accessed December 6, 2013, ProQuest Historical Newspapers.

(44.) Weise, Troy's One Hundred Years, 199.

(45.) Ibid., 199.

(46.) My thanks to Stacy Pomeroy Draper, Curator of the Rensselaer County Historical Society, which holds the letter in its research collections, for bringing this letter to my attention and supplying a transcript.

(47.) 1865 New York State Census, Rensselaer County, Troy, 7th Ward, accessed December 6, 2013, http://www.connorsgenealogy.com/troy/1865-7thward.htm.

(48.) Troy Directory, June, 1865; Troy Directory, June, 1866; Troy Directory, June, 1867. US. City Directories, 1821-1989, accessed December 6, 2013, Ancestry.com.

(49.) 1870 United States Federal Census (Provo, UT, USA: Ancestry.com Operations, Inc.), accessed December 6, 2013, http://search.ancestry.com/search/db.aspx?dbid=7163.

(50.) Troy Directory, June, 1872. U.S. City Directories, 1821-1989, accessed December 6, 2013, Ancestry.com.

(51.) Troy Directory, June, 1873; Troy Directory, June, 1874; Troy Directory, June, 1875, and Troy Directory, June, 1878. US. City Directories, 18211989, accessed December 6, 2013, Ancestry.com.

(52.) New York State Census. 1875, accessed December 5, 2013, Familysearch.org.

(53.) Troy Directory, 1882; Troy Directory, 1883. US. City Directories, 18211989, accessed December 6, 2013, Ancestry.com.

(54.) Troy Directory,1886. US. City Directories, 1821-1989, accessed December 6, 2013, Ancestry.com.

(55.) Troy Directory, 1888; Troy Directory, 1889: Troy Directory, 1890, and Troy Directory, 1892. U.S. City Directories, 1821-1989, accessed December 6, 2013, Ancestry.com.

(56.) "Troy Siftings," New York Freeman (New York, NY), October 2, 1886, p. 1. accessed December 6, 2013, http://www.genealogybank.com/gbnk/newspapers/doc.

(57.) Troy Directory, 1884. U.S. City Directories, 1821-1989, accessed December 6, 2013, Ancestry.com.

(58.) Shirley J. Lee, Black Women Abolitionists: A Study in Activism, 18281860 (Knoxville: University of Tennessee, 1992) 78; Melissa Richburg, Black Education in 191hC. Troy, accessed October 21, 2013, http://troyblackedu.weeblv.com/african-female-benevolent-society.html.

(59.) "Troy Gossip," The New York Freeman, March 27, 1886, pg. 1, accessed December 6, 2013, http://www.genealogybank.com/gbnk/newspapers/doc.

(60.) Joseph Hillman, The History of Methodism in Troy, NY (Troy: no publisher, 1888), xix, 278.

(61.) Semen, North Star Country, 66. Arthur James Weise, The City of Troy and Its Vicinity (Troy: E. Green, 1886) 212. See also Hillman, The History of Methodism in Troy, New York and William Jacob Walls, The African Methodist Episcopal Zion Church: Reality of the Black Church (Charlotte, N.C.: A.M.E. Zion Publishing, 1974).

(62.) Hillman, History of Methodism in Troy, New York 216-17. For the photograph, see http://archive.org/stream/historyofmethodi0Ohilliala#page/276/modeaup.

(63.) "Troy Gossip," New York Freeman, January 16, 1886, pg. 4, accessed December 6, 2013, http://www.geneulogybank.com/gbnk/newspapers/doc.

(64.) New York Freeman, December 6, 1890, pg. 4, accessed December 6, 2013, http://www.genealogybank.com/gbnk/newspapers/doc.

(65.) Troy Directory, 1890. U.S. City Directories, 1821-1989, accessed December 6, 2013, at http://search.ancestrylibrary.com/search/db.aspx?dbid=4423.

(66.) New York Age, September 13, 1890, pg. 4, accessed December 6, 2013, httn://www.genealogybank.com/gbnk/newsuaners/doc.

(67.) New York Age, September 27, 1890 pg. 4, accessed December 6, 2013, http://www.genealogybank.com/gbnk/newspapers/doc. See also "Death Records and Obituaries with Troy, NY connections, extracted from a file of Troy, NY newspaper clippings maintained by employees of the Burden Iron Company from March, 1890 - April, 1895": "GIDINEY-In this city, suddenly, Sept. 9, 1890, HARRIET A., wife of Charles T. Gidincy, aged 72 years Funeral Friday at 3 P. M. at Zion church," accessed December 6, 2013, http://www.rootsweb.ancestry.com/-nyties/BurdenDeathsGA-GISurnames.htm.

(68.) Times (Troy, NY), September 18, 1890, Vol. XXXV, issue 8, pg. 2, accessed December 6, 2013, http://www.genealogybank.com/gbnldnewsnaners/doc.

(69.) "Troy Topics," New York Age, May 23, 1891, pg. 4, accessed December 6, 2013, http://www.genealogvbank.com/gbnk/newsnaners/doc.

(70.) Troy Directory, 1893. U.S. City Directories, 1821-1989, accessed December 6, 2013, Ancestry.com.

(71.) Census of Inmates in Almshouses and Poorhouses, 1875-1921, in New York State Archives; Albany, New York, Series: A1978; Reel: A 1978:194; Record Number: 1871. "Name: Charles Gidney; Birth: abt 1813 - New York," in New York, Census of Inmates in Almshouses and Poorhouses, 1830-1920 [database on-line] (Provo, UT, USA: Ancestry.com Operations, inc., 2011), accessed December 6, 2013, http://search.ancestrv.com/search/db.aspx?dbid=1083.

(72.) "Can Square Circle," Evening News (San Jose, CA), December 8, 1902, Vol. XLII, Issue 142, pg. 7, accessed December 6, 2013, http://www.genealogvbank.com/gbnk/newspapers/doc/.

(73.) "Savants Scoff San Jose Man's Claim to Squaring the Circle; Discoverer Maintains Confidence," Evening News (San Jose, CA), December 10, 1902, vol. 42, pg. 3, accessed December 6, 2013, http://www.genealogybank.com/gbnkinewspa.pers/doc/.

(74.) Evening News (San Jose, CA), July 2, 1907, vol. 49, pg. 4, accessed December 6, 2013, http://www.genealogybank.com/gbnk/newspapers/doc/.