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Mathematical Treasure: Ramanujan’s “Lost” Notebooks

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

Srinivasa Ramanujan (1887–1920) was an Indian mathematician who lived under British colonial rule. His mathematical talents emerged very early in his life, and he is known as one of the greatest mathematical prodigies in history. In 1914, G.H. Hardy, who recognized his talent, brought him to Cambridge University for university study. Ramanujan was extremely versatile and contributed to many areas of mathematics, including analysis and number theory. Unfortunately, he contracted tuberculosis in England and died at an early age.

Much of his work was done in simple student copybooks. Three of these books were discovered after his death. They became known as “ Ramanujan’s Lost Notebooks” and have since been studied, further revealing the man’s mathematical genius. A few pages from the notebooks are shown below.

Page from Ramanujan's notebooks, dealing with magic squares.

Page from Ramanujan's notebooks, dealing with magic squares.

Page from Ramanujan's notebooks, dealing with magic squares.

Page from Ramanujan's notebooks, showing some of his work on series.

Page from Ramanujan's notebooks, showing some of his work on series.

Page from Ramanujan's notebooks, showing some of his work combining series with magic squares.
                              

These images were provided by K. Srinivasa Rao of The Institute of Mathematical Sciences, Chennai, India, from his website on the life and work of Ramanujan.

References

Rao, K. Srinivasa. 2000. Life and Work of the Mathemagician Srinivasa Ramanujan. arXiv.org.

Rao, K. Srinivasa. 2021. Srinivasa Ramanujan: Life and Work of a Natural Mathematical Genius. Springer. See also the MAA Review.

Srinivasa Ramanujan. Wikipedia.

Wolfram, Stephen. 2016, April 27. Who Was Ramanujan? Writings.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Ramanujan’s “Lost” Notebooks," Convergence (February 2023)