These are actual student papers that were not designed to be web pages. They may contain historical, grammatical, mathematical, or formatting errors. These papers were graded using the criterion mentioned in the paper directions, and the writing checklist. The test review sheets and the WebCT tests are good indicators of the mathematics that was discussed in class during and/or after each presentation.
Fuller’s life was affected by both his African heritage and the enforced european culture

Thomas Fuller

 

It is highly possible that social influences led Thomas Fuller to become a mathematician. Africans grew up illiterate but were taught math. Math was taught in games they played such as manacala, weaving patterns and stories. Much of the folklore of the time that was passed down has been said to fall under mathematical patterns that followed the position of the stars. Unfortunately, with slavery and the New World growing hand in hand many Africans became good with math by selling of other Africans.    

 Africans who took part in the profit of slave trade were known to be experts with their accounts. In fact, it was thought that they were better with their finances then Europeans. Thomas Clarkson stated “that African brokers, on exchange of slaves for European goods, were quick to give an accurate, fair price and strike the balance while the Europeans, on the other hand, were busy making their calculations with their pen and paper”(Ref. 1). Thomas Fuller just as the African brokers was able to do long calculations in his head.

Fuller’s mathematical ability was possibly ingrained early in his youth. However, when sold as a slave at the age of fourteen, in Alexandria, Virginia, he was able to perfect his skills on his own.  With his good visualization and ability with numbers, Thomas Fuller was an amazement to all that tried to disprove Africans abilities. 

 It is amazing to think about the barriers Fuller overcame and how his success fully began to change the way people viewed the mental capacity of African slaves.  Had Thomas Fuller had the advantages of an education, there is no telling the limits his abilities would have had.  However, it is interesting to note that Fuller is quoted as saying that “it is best I go not learning; for many learned men be great fools”(Ref 2).

Both his African heritage and the enforced European culture affected Fuller’s life. Forced into slavery at 14, Fuller was unable to control his destiny. It was the thought of most whites, at the time, that blacks were inferior to whites. This idea supported that blacks were best to be thought of as nothing more than servants to whites. Fuller contradicted this idea. Fuller’s calculations threw Europeans off their feet. The idea that a man could calculate large numbers in his mind was unheard of by the pencil and paper orientated Europeans. However, Fuller’s ability was downplayed because of the color of his skin. At the time slavery, racism, and prejudice against blacks were at all time highs. Europeans would never be able to accept the idea that a black man has the same capabilities as them. Many jumped to say that Fuller was a man of many memorized math facts without the ability to figure problems out. Others who did accept his calculations criticized his ability. Rouse Ball wrote, “although more rapid than Buxton, he was a slow worker as compared with some of those whose doings are described as below”(Ref. 2). The works he described belonged to white men. This shows that Fuller was able to great calculations, but ignored because he was black. Others ignored Fuller because whites thought of him as having an “abnormal mentality”(Ref. 2) with no “practical manifestation”(Ref. 2). This means that they thought that Fuller was just one case out of all the blacks who could do this skill and that he was abnormal because of it. Also by saying that it was impractical, they were covering themselves in case it was found that all blacks had the same abilities.

  Much of the racial prejudices that Europeans formed about Africans were based on the fact that Africans could not read or write. Fuller was illiterate until his death, but was able to do math. In Africa literacy wasn’t important but the ability to barter was. In Europe it was important to read and write. Therefore, Fuller and other Africans learned what was needed to survive, just as well Europeans did. Unable to see that education is dependent on social standards Europeans blinded by their own standards set out to dominate people who they thought were weaker then them and or did not have the same social standards as them. This not only seen with Africans but also with Native Americans, Indians and others.

     Calling Fuller a mathematician and not showing his work would preposterous. On the other hand, it is impossible to show his work since he did his calculations in his head. We can only guess at how he obtained his answers. So what we are showing in our math is what we think a model of his thinking pattern may have been. You cannot prove they are right but you can assume that they are since the answers come out the same as his.

 

 

     At the age of 80 Fuller was asked to find the amount of seconds in a man’s life that was 70yrs, 17 days and 12 hours old. Astoundingly he answered with precise accuracy in minutes while even including leap years (a total of 17).  This is how we would attempt this problem on paper.

     First we thought that he would find the amount of leap years.

   

So,

     70yrs/4yrs=17.5

Knowing that every leap year you add a day and that there are 17.5 leap years we know that we have to take into account 17 extra days. We disregard the .5 because that represents that we are still 2 yr. away from the next leap year.

     Next, we will break down the number of days, years, hours and minutes to seconds.

     365 days * 70 yrs =25,550 days

     25,550 days + 17 days + 17 days = 25,584 days

     25,584 days * 24 hrs = 614,016 hrs

     614,016 hrs + 12 hrs = 614,028 hrs

     614,028 hrs * 60 min = 36,841,680 min

     36,841,680 min * 60 sec = 2,210,500,800 sec

   As seen, the numbers are very large and the thought of having to store these numbers in your head while calculating an answer is scary. To Fuller and other Africans who could not read or write this was just common practice. Fuller, was the first to prove that blacks did have the same capabilities as whites. Fuller may have been extraordinarily brilliant or just someone normal who’s education was different from the standards around him. Either way Fuller is proved to be great from his courage that broke through racial stereotypes and started the first steps towards equality for blacks.    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

 

1)1st quote: Smith, Steven. 1983. The Great Mental Calculators. New York: Columbia university press.178-180.

2)2nd, 3rd, 4th, and 5th quote: John Fauvel and Paulus Gerdes. 1990. African Slave and Calculating Prodigy: Bicentnary of the Death of Thomas Fuller. Historia Mathematica 17.141-151.

3) Internet: www.math.bufallo.edu/mad/special/fuller_thomas_1710-1790.html

4) Gerdes, Paulus.1994. On Mathematics in the History of the Sub-Saharan Africa; Historia mathematica 21. 345-376.

 

        

 

 

 

 

 

 

 

 

 

Thoughts on references

1)1st quote: Smith, Steven. 1983. The Great Mental Calculators. New York: Columbia university press.178-180.

This references wasn’t very extensive when it came to talking about Fuller’s life and experiences. Also it didn’t really talk about his cultural heritage. This was a good article to show his ability with math. Its main points were on his ability to calculate in his head. It was good because it was backed up by an interview that went on with Fuller.

2)2nd, 3rd, 4th, and 5th quote: John Fauvel and Paulus Gerdes. 1990. African Slave and Calculating Prodigy: Bicentnary of the Death of Thomas Fuller. Historia Mathematica 17.141-

151.

     History Mathematica 17 is the most reliable and well-rounded source found. It covers African mathematical development, what is known of Fuller in his youth, great examples of his mental ability, and mentions the beginning of the break through of minorities and their mental capacity.

     3) Internet: www.math.bufallo.edu/mad/special/fuller_thomas_1710-1790.html

     This reference was good because it touched on Fuller’s heritage. It gave us an understanding to the education that the Africans followed. It let us know that he wasn’t the only African to do calculations like his. This reference also touched on Fuller’s mathematics lightly.

 

 

4) Gerdes, Paulus.1994. On Mathematics in the History of the Sub-Saharan Africa; Historia Mathematica 21. 345-376.

 This is an excellent source on the development of African mathematics. Though not much information on Fuller, it allows us to make more accurate assumptions in his mathematical ability might have been obtained