Question 3.5
Question 3.6
Dante’s Paradiso reflects a problem that has yet remained unsolved in the mathematical world, that of squaring the circle. Simply put, squaring the circle refers to using only a straight edge and compass to draw a square with an area equal to that of a given circle. In his final stanza, Dante uses a reference to the problem of squaring the circle to depict the problem of an overwhelmed intellect, inspired by his vision of heaven and his inability to grasp it. Dante uses the mathematical explanation to explain his inability to grasp the rationality of the vision he saw, which he does by alluding to the impossible task of squaring a circle. In the Paradiso, Dante perceives a geometric image of the deities, and goes on to allude the paradox to the geometrical sequence. The problem in this stanza is, therefore, to understand the perfect fit of the human figure and the divine subjects. Finally, Dante manages to comprehend the problem but not its solution. From reading, this can be resolved as one paradox, that of explaining two complete entities, the human and the ethereal, in a single entity, which is god. Dante’s attitude, if universally applied, would not much affect mathematical and scientific activity since it is formed of a mathematical impossibility in itself. The problem of squaring the circle was later proved to be impossible due to the transcendental nature of pi, meaning that its square root cannot be accurately determined. Dante’s solution to his problem is not a solution in itself, it is instead an allusion to an impossible mathematical task.
Question 4.2
Two great women mathematicians of all times were Charlotte Angas Scott and Sof’ya Vasil’evna Kryukovskaya, whose careers can be compared since they have many similarities. Both women were born in the 1850’s, though they came from completely different backgrounds. One of the best similarities between these two women is that they got an early boost in their careers due to private tutors who recognized their mathematical ability and agreed to tutor them privately. These professors also followed up on their careers and ensured that they got schools to teach in, and progressed well in their careers. Another major similarity is the hard time that they each had in getting into teaching positions in their careers. Both women had to struggle in order to earn a place equal to their opposite sex. The significant differences in their careers was the beginning of it, Sof’ya had to struggle to get into a place with recognizable mathematics while Charlotte was encouraged by her parents and given a tutor to start off her life in algebra. These differences between the two women can be alluded to a single factor, the continental circles in which they moved. Sof’ya had to move from her country in order to get a good education while Charlotte found her society in her home country and grew her career without trouble. The political atmosphere in Russia and England was different in those times, which is the biggest factor explaining the early careers of Sof’ya and Charlotte respectively.
Question 4.8
Question 4.9
One of the challenges that women faced in admission to universities and their subsequent growth in universities was the opposition that they faced from their peers. For example Loria pointed out that the achievement of the greatest women mathematicians could not be pinpointed since they received collaboration from first-rate mathematicians. This fact is true, that they received help, but only in getting opportunities that helped them advance their careers. Loria is not entirely correct in pointing out that the women excelled since they received collaboration, the true fact is that they got the collaboration in order to be recognized in the mathematical world. In fact male mathematicians like William Young received help from his wife. Loria’s statement that the women were always child prodigies is also not true, since some of them had to seek help from outside their families. Loria’s statement that the women became exhausted at the end of their careers is also wrong, as in the case of Angus, who finished her career and retired. All the other women mathematicians also did as well as their male counterparts. In the honor student fallacy, it cannot be said that gender played an important role, based on the selection of fewer than five women. In fact, the women had a harder time since they were not outright selected or awarded degrees, so they had to fight to be recognized. Since the women were locked out of the best facilities, they did not very well develop their full potential.
