# My Search for Ramanujan

Amir Aczel, the author of several popular science books, was the one who had the idea of writing this book. However, he passed away in November 2015 shortly after his book *Finding Zero* about the history of our Hindu-Arabic numeral system and his quest to find and save the stone which has the earliest known engraving of the symbol zero. Ken Ono is a number theorist who tells here the story of Ramanujan and discovers many parallels between Ramanujan's obsession for mathematics and Hardy's efforts that brought Ramanujan to the center of the mathematical community of his time and similar incidents in his own life and the life of his parents.

Ken Ono's father Takashi Ono, was a young Japanese mathematician, in the post WWII period when he was picked up by André Weil, who was then at the IAS in Princeton. Takashi came with his wife to Princeton for what originally was planned to be a short period, but they decided to settle down and stay in the US, despite the initial hostile racist attitude of Americans towards the `Japanese enemy'. Takashi became a respected mathematics professor who spent all his time doing mathematics, while his wife, according to Japanese tradition (the marriage was arranged), was running the household almost invisibly. They had three children of which Ken was the youngest. The three boys were raised as 'tiger children': even performing at the top of their ability was not good enough. To his father, education was like solving a mathematical equation in which there was no place for affection. Ken was mathematically gifted and was therefore predestined to succeed his father. If he did not excel above his schoolmates, he was reproached to make his father to shame. Unable to earn the praise of his father, Ken rebelled, neglected his studies and developed a passion for bicycle racing instead. He eventually dropped out of high school and left his parents to live with his older brother in Canada. He got the consent of his parents because he argued that Ramanujan, much admired by the father, also was a dropout.

At this point, the story is interrupted by a short biography of Ramanujan. How he was obsessed by mathematics. Not professionally educated, he filled notebooks with mathematical identities, inspired by the goddess Namagiri. He is desperately trying to find a job to make a living for him and his much younger wife that was appointed to him by an arranged marriage. He is finally picked up by G.H. Hardy and brought to Cambridge, UK. Together they overcame initial racism, although it drove Ramanujan at some point to an attempted suicide. Hardy could transform Ramanujan's genius into mathematical successes, but Ramanujan's health problems forced him to return to India where he died at the age of 32. Since then many mathematicians had a hard time interpreting and proving the notebooks he left behind.

Ken was accepted for the University of Chicago, but freed from parental supervision neglected his studies and became a very active member of the Psi Upsilon fraternity and was semi-professional cyclist. Although his mathematical skills were not reflected by his results, his professor Paul Sally recognized Ken's mathematical talent and convinced him to start really working for his BA, in which he succeeded, and he recommended Ken to start a master at the UCLA. Ken passed his qualifying exams to start a PhD and since he is now earning some money, he married his girl friend who studied to be a midwife. He is however still very insecure, questioning himself and his work, which is not the best of the best, so that he still hears his father's voice reproaching him that he is an imposter, not good enough or not trying hard enough. He found at UCLA another guardian angel in the form of Basil Gordon, a professor who helped him on the path of mathematical research. However, when he presented his work on modular forms at a conference where also the 'big shots' were present, his lecture turned out to be a disaster and he got so depressed that 'the voices in his head' almost drove him to suicide. Basil Gordon could talk him out of his depression and his next conference talk was well received. This got him back on track to finish his PhD which he defended in 1993. He got a job at the University at Athens (Georgia) where Andrew Granville was interested in his work. His work related to Ramanujan problems placed in the context of work by Deligne and Serre. All of a sudden this research became a hype after Andrew Wiles announced his proof of Fermat's last theorem, and Ken's career boosted, his work being at the center of world wide mathematical attention. He is now a respected professor and he won several prizes for his mathematical contributions. The voices in his head finally became voices of approval. At some point, while he is staying at the IAS he could arrange a reunion of his father and André Weil who was 95 at the time. All's well that ends well and all thanks to Ramanujan who has influenced his life and guided him when in deepest need at crucial moments.

In an epilogue he gives an account of his 2005 visit to India and Ramanujan's home, which is as a pilgrimage to him. In 2011 he is invited to be the mathematics advisor for a Ramanujan documentary *The man who knew infinity* based on Robert Kanigel's biography with the same title that is to be made on the occasion of the 125th anniversary of his birthday. In an afterword we find a number of mathematical problems related to work by Ramanujan and that are easy to explain.

It is clear that the author, giving this account of his life, has great admiration for Ramanujan and feels deeply indebted to him which shows on almost every page of this book. There is a scent of a mathematical canonization of Ramanujan, but the author is wise enough to keep that under control. His book radiates his love for mathematics and the beauty that can be found in it. It is also shown that, even though Hardy once said that he did number theory because it was the least applicable branch of mathematics, but it turns out that prime numbers are most applicable in modern cryptography and research about Ramanujan's work is even related to string theory which is trying to understand the fundamental building blocks of our universe. And most importantly, the message is that no matter how depressed you are, there is always hope that at some point things may turn for the better. All you need is faith in yourself and in what you are capable of, and at some point, when you need it most, some kind soul that still believes in you will come to your rescue. This may hold for your life as a whole, but it certainly holds for mathematical research. At some point, struggling with a hard problem, we all may have experienced a moment of despair with no way out, but as Ken Ono describes in his book, at some moment, when you least expect it, you suddenly see the light, and the whole puzzle falls into place. And that is what brings the whole excitement and joy of doing mathematics.

The book is amply illustrated with grayscale images, which are duplicated in color version in a separate section. All technicalities of the mathematics are avoided so that the book can be read by anyone. A subject and person index is missing and might be helpful to recall some sections, but the story is relatively straightforward so that this is not really a defect. The book is based on a true story but it reads like a script for an American movie with a happy ending.

**Submitted by Adhemar Bultheel |

**21 / Jun / 2016