Visions of Infinity

by: Ian Stewart

Visions of Infinity by Ian Stewart is a book about how the field of mathematics is advanced not just about the field of mathematics. This book was much more about how mathematicians go about discovering their ideas about mathematics then about the proofs themselves. The book gives the reader insight into how mathematicians think and how they approach problems. It also teaches us about the struggle between the field of mathematics as a whole wanting more recognition, and the fact that most mathematicians would rather live without publicity. Mathematicians went a long time without any sort of large accolades being given to the study of mathematics. Unlike other fields which had the Nobel Prize for their scientists to strive for. The book also covers many different theorems and conjectures in mathematics, though it focuses on how the mathematicians focused on the problem. The book also goes over the seven Millennial Problems which are seven problems in mathematics that were so difficult that a $1,000,000 reward was offered for a correct solution. To date only one of these problems the Poincare Conjecture has been solved.

The book starts off with explaining how surprised the BBC was when they presented a TV show about mathematics and people actually watched it with interest. This is because most individuals were, and still are to the most part, that mathematics had stopped growing a long time before. The problem with the program was that it proposed a solution to Fermat’s Theorem which had been proposed 300 years before, so many individuals wrongly assumed that mathematics hadn’t been furthered in 300 years. This could be because while other fields that relied on mathematics received prizes for their works received prestigious prizes, such as the Nobel Prize, and mathematics most prestigious reward was the Fields Medal which is largely unknown about outside of the mathematical community.

Mathematicians are also very cautious about giving out accolades. When Grigori Perelman first proposed his solution to the Poincare conjecture it took eight years for him to be offered the $1,000,000 reward for his solution to the Millennial Problem. He then declined the prize since the recognition and the reward was not important to him after waiting for so long. No mathematician wanted to throw their weight behind Perelman for fear about him being incorrect. This shows how cautious mathematicians can be and how many mathematicians will try and refuse the spotlight if given the chance. Many mathematicians also want their opinions to be accepted on merit and not based upon public opinion, which is problematic because the solution needs to be publicized for other mathematicians to know to look at it. The private nature of most mathematicians prevents the field of mathematics.

The book Visions of Infinity did a very good job about explaining how mathematicians approach problems and why it takes so long for them to receive recognition for their work. It also shows accolades are necessary for public recognition of the advances of mathematics. The book also shows how the nature of mathematicians private lives can contradict what needs to be done in order to achieve greater recognition for the field of mathematics. Overall this book was worth the read for anyone curious about how mathematicians think or about the field of mathematics as a whole.