From Here to Infinity: A Guide to Today's Mathematics
By Ian Stewart
"From Here to Infinity" is an enchanting read, which inspires both budding mathematicians, and curious outsiders alike. For mathematicians are mysterious beings to the general population; enshrouded in a cloak of cryptic symbols, they slip into another world, with an aura the ignorant classify as having a residue of chalky smoke, and mundane arithmetic.
Stewart bridges the gap between the uninformed individual and the world of mathematics with friendly, open approach. Several comprehensive chapters discuss intriguing topics, including chaos theory, knots, computer technology, algorithms, fractals, Fermat's last theorem, and how to increase one's odds of winning the lottery.
Never speaking down to the reader, Stewart provides many examples to illustrate a concept, which are punctuated with the occasional joke. For the reader with little exposure, the examples are fascinating, and show another side of thinking all together. However, as the examples develop, the level of math increases steeply. But, the initial feeling of frustration with a challenging idea gives way to a feeling of satisfied accomplishment with the completion of each chapter.
"From Here to Infinity" is probably appropriate for a first or second year university student, or even a tenacious high school student. If the reader feels intimidated by any mathematical symbols or questions, however, an even softer read by Ian Stewart is "Letters to a Young Mathematician." This book describes a girl's progress from an interest in math in high school, to exploring her passion in university, and finally to receiving tenure, explaining how to become a mathematician and the process of entering academia from a mentorship perspective. However, "From Here to Infinity" is more focused to provide a strong introduction to mathematics itself.
After I finished "From Here to Infinity," I felt my brief experience in first year calculus had truly been lacking. If this book had been prescribed reading material, and one chapter had been discussed by the professor every second Friday, for both university terms, the students would have received a much better education. For an introductory course, all we learned was how to differentiate and integrate, without understanding even an inkling of the broader picture of the history of calculus, how it was developed, and a good discussion of the theory. "From Here to Infinity" provides some of this information.
In addition to the above concern, is not an introductory course supposed to provide the basis for a passion for a subject? To teach by route techniques that students simply have to memorize to obtain correct answers, creativity is stifled. All one has to do is plug and chug. The student does not even have the opportunity to ask, "What is mathematics?" And, although the vast majority of students in first year calculus are not going to become mathematicians – but rather are from faculties of physical and life sciences, engineering, and management, to name a few – an appreciation for the discipline is essential for a sound university education.
Consider for a moment, when someone hears another person is a musician. Instantly, the listener is able to connect, if not by understanding the theory, harmony, or chord progression, but by merely attending a performance. Mathematics is not a performance art for the public, but for a select community. However, should it not be easier for the public to gain a faint glimpse into what mathematics as a form of human expression can look like? Especially for those attending an institution of higher education even if they are not enrolled in the mathematics department?
"From Here to Infinity" assigned to a general calculus introductory course would answer the question of why calculus is a worthwhile subject to learn, while showing a fraction of the vast extent of mathematics beyond calculus to a bright, and diverse world, that evolves as the researchers progress.
So be it to expose the uninformed and curious to the nature of mathematics, or to enhance introductory courses, "From Here to Infinity" is not only worthwhile, but also enjoyable from cover to cover.