Dreams of Infinity

Alznauer, Amy. The Boy Who Dreamed of Infinity: A Tale of the Genius Ramanujan. Illus. by Daniel Miyares. Somerville, MA: Candlewick Press, 2020.
Mathematical precocity is one of the most remarkable types of giftedness; yet, it is ironic that so little is written about it. Juvenile biographies of prodigies are scarce and even more so are the early life histories of mathematical geniuses. Rarer still are juvenile biographies of mathematical geniuses from India. Amy Alznauer’s picture book biography of Srinivasa Ramanujan is, therefore, a breakthrough book for gifted children of all ages. It is especially a treasure for mathematically gifted children. In 2015, Ramanujan’s extraordinary life was turned into the movie, “The Man Who Knew Infinity,” based on the book by the same name by Robert Kanigel.
Srinivasa Ramanujan was born with a passion for numbers that never left him. Born in South India in 1887 he grew up in a time when communications with other mathematical geniuses was unimaginable. The few early teachers he did encounter dismissed his enormous gift for numbers, the magnitude of which was completely beyond their comprehension. His first few years were unremarkable until his grandfather taught him to count at the age of three as they jointly traced numbers in bowls of rice. Speech quickly followed with Ramanujan’s forever questions, “What is small?” and “What is big?”
Even as a child, Srinivasa was interested in number theory. He held a single mango in his hand. “It is just one thing,” he reasoned, but he chopped it into two halves and then continued chopping until he would have a great many bits of fruit. Further, the prodigy intuitively understood that if he chopped on and on, endlessly, he might reach infinity. Even so, if he put all the bits and pieces back together he would be left with just one mango. Alznauer portrays the young Ramanujan discovering advanced mathematical content, such as infinite sums, before he even knew what to call them. Young Ramanujan embraced the theory that if he could open just the number one (mango) and discover infinity, what mysteries could he find inside other whole numbers?
Everywhere he turned, there were numbers, even in his dreams. He wrote them in sand, on his slate, on pieces of paper, even on the cool floors of the temple. 
Traditional schooling was a disaster for the prodigy. Teachers were blind to Ramanujan’s conceptualization of how numbers could be understood. He fared little better with his age peers. He was happiest when he worked alone endlessly with numbers on his slate. At the age of ten, Srinivasa Ramanujan entered high school where he finally met up with a school master who recognized his genius. At the age of fifteen, Ramanujan found a college mathematics book. It posed thousands of questions, but provided no answers. The young genius answered every single question and asked even more questions and provided those with answers as well. Not long after, he began to keep his mathematical ideas, formulas, and questions in blank notebooks that he quickly filled. 
As he matured, the math questions Srinvasa posed grew ever more complex. Incredibly, he did not even realize that a discipline known as mathematics existed, so he devised his own formulas, patterns, and questions. In college, he could only focus upon mathematics and quickly flunked out. He had no degree and no job. Shop owners were sometimes impressed with his genius, but they had no jobs for him. “Genius” was not a marketable skill!
Eventually, Ramanujan found work as a clerk in the Port Trust of Madras. Finally convinced of the potential of his genius, British overseers at Port Trust urged him to send his questions and ideas to Cambridge University in England. One of his letters was eventually seen by G. H. Hardy, one of the great mathematicians of his time. Hardy was overwhelmed by the magnificence of Ramanujan’s ideas and immediately invited him to come to England to share his thoughts and questions. This was the defining moment of Ramanujan’s life. It would be the culmination of his lifetime dreams, but could he leave India? He prayed for divine guidance and was visited in a dream by a Goddess who told him to “Speak the thoughts on your tongue.” Thus, in 1914, still a very young man, Ramanujan left India for Cambridge University in England. 
Aboard the steamer, he gazed at the millions of stars nightly and believed that he was, perhaps, seeing a glimpse of infinity. Author Amy Alznauer concludes that this humble young genius could not have imagined that more than a century later scientists would use his ideas to further explore those same stars in the continuing search for the meaning of infinity.
The beginning of Ramanujan’s journey from India to Cambridge University is the end of the narrative story of the great mathematical genius’s life. In two full pages of Author Notes, Alznauer, who is herself a professor of calculus and number theory at Northwestern University, relates the short but significant life Ramanujan experienced at Cambridge. He was acknowledged and honored by mathematical scholars as one of the greatest mathematicians of all time. Tragically, he became fatally ill and died at the age of 32, shortly after his return to India. He left an incredible legacy of hand-written notebooks filled with ideas so far reaching that they are still being deciphered by mathematicians today!
The Boy Who Dreamed of Infinity may best be suited for two distinct audiences. General readers will find Alznauer’s narrative a welcome introduction to the life of a true genius. It is an engrossing and heroic story well told. The author is a theoretical mathematician; without writing down to readers she makes the ideas and questions of her subject accessible to lay readers. A perfect example is revealed in the way she presents Ramanujan’s childhood fascination with a single mango divided to the theoretical point of infinity, yet still capable of being restored to a unit of a single (one) object. 
Alznauer’s Author Notes will find a smaller but essential audience among young readers who are mathematical scholars. She notes how Ramanujan’s ideas influenced areas of science and mathematics not even discovered in his lifetime, such as computers, black holes, and string theory. 
Daniel Miyares’ impressionistic colored ink paintings manage to capture the literal world of South India where Ramanujan grew from infancy to young manhood. The artist also creates swirling images of numbers within the text and on the end pages that further suggest the young hero’s utter preoccupation with integers.  
The Boy Who Dreamed of Infinity is a book of great beauty that introduces children to the life of one of the greatest mathematicians of all time. It is a biography of great riches that deserves a large audience. 
Home Activities
Perhaps on a safe walk or a short family drive, children’s appetite for numbers may be activated. Encourage them to add all the numbers on license plates of parked or moving motor vehicles. Invite children to move beyond simple addition to more complex mathematical operations using still further license plate numbers.
There are a great many Internet resources about the life and works of Srinivasa Ramanujan. Please note that while most public libraries are closed during the COVID-19 pandemic, many encourage the use of their many virtual services including live chats with reference librarians. 
The author of The Boy Who Dreamed of Infinity was only six years old when she accompanied her father, also a mathematician, to Cambridge University where he miraculously discovered what had thought to have been Ramanujan’s Lost Notebook. Can a research librarian help today’s mathematical prodigies unlock the insights and solutions that were found in the Ramanujan’s Lost Notebook? Why are contemporary mathematicians still studying the notebooks of Ramanujan more than a century after they were created?
Ramanujan was a deeply religious man. One of his most famous quotations is, “An equation for me has no meaning unless it expresses a thought of God.” He did not separate his knowledge and love of mathematics from his piety and religious devotion. Ramanujan was a Hindu. Parents can partner with young scholars to use online resources or books at home about world religions to learn about the Hindu faith, one of the oldest of all religions in the world. How is Hinduism similar to, yet also different from, major religions found in the USA today such as Judaism, Christianity, and Islam? 
Many historians who view ancient history through the prism of Western Civilization trace the origins of mathematics to the Ancient Greeks, and in particular to Euclid, Archimedes, and Pythagoras. However, in her Author’s Note, Amy Alznauer writes that centuries before mathematics appeared in Greece, India had a rich mathematical history that included both the concept and the symbol for zero. Even in ancient India, mathematics was not something that stood alone. Mathematics was indivisible from philosophy, art, and religion. 
Can today’s young historians research the evolution and contributions of mathematics as discovered by scholars from India? Ask them to take note of how mathematics and religion were part of the same whole. Perhaps they can create parallel timelines of the history of mathematics in India and in Greece.