"Mark all mathematical heads which be wholly and only bent on these sciences, how solitary they be themselves, how unfit to live with others, how unapt to serve the world"

In this quote, Roger Ascham is revealing a viewpoint on those who commit themselves completely to the pursuit of mathematical sciences. He suggests that people who are deeply absorbed in mathematics tend to lead singular lives and may fight with social interactions or fulfilling roles within wider society. This point of view highlights a common stereotype, both in Ascham's time and still resonant today, that those who devote themselves to extremely intellectual or abstract fields can become separated or insular, focusing so intently on their work that they distance themselves from more social or communal elements of life.

Ascham's phrasing underscores a concern that intense focus on a specialized area, such as mathematics, can cause an imbalance in an individual's life. The term "singular" suggests an absence of social engagement, possibly indicating that these individuals might pick to live far from societal norms or expectations, either physically or mentally. Moreover, Ascham posits that such people are "unsuited" to live with others and are "unapt to serve the world", which might mean that their abilities and dispositions do not align well with the more useful or interpersonal demands of society.

However, it's important to translate this quote in the context of the 16th century when Ascham lived, a time when mathematical sciences were not as integrated into everyday life as they are now. Therefore, his views may reflect a historic understanding of mathematics as a mystical field, rather than an important part of societal development and innovation. In modern terms, we frequently see mathematics and related fields as vital to technological advancement and problem-solving, and many mathematicians today lead lives that defy these historic stereotypes, actively engaging with diverse communities and contributing significantly to different elements of modern life.

In sum, Ascham's quote reflects a historic care about the possible social mistakes of severe specialization, prompting a balanced technique to intellectual pursuits that also considers social combination and useful contributions to society.