100 years of Punjab School of Mathematics

It is a rare confluence of centenaries: the birth centenary of Prof Ram Prakash Bambah (September 30, 1925 – May 26, 2025) coincides with the 100th year of the Punjab School of Mathematics, whose origin dates back to its mentor Prof Sarvadaman Chowla’s first research paper from Punjab in 1925. The passing of Prof Bambah this year adds a solemn note to the occasion.

As we look back, it is important to recognise how Punjab carved out a lasting place for itself in the national and global landscape of mathematics. The continuity of this tradition was documented by Purabi Mukherjee in her 2020 Springer publication ‘Research Schools on Number Theory in India’. This book placed the Punjab School of Mathematics firmly on the global map — second only in renown to Srinivasa Ramanujan’s South Indian School of Mathematics.

After Ramanujan’s untimely death in 1920, his legacy was carried forward in Madras by Dr Anand Rau, his Cambridge contemporary under GH Hardy. In Punjab, the torchbearer was Sarvadaman Chowla (Servi). His father, Bhai Gopal Singh Chawla, was amongst the first set of Indian teachers of government colleges facilitated to proceed abroad under a scheme introduced after the Indian Universities Act of 1904. Servi was born in England in 1907.

Panjab University, Chandigarh, continues to function under a variant of the same 1904 universities’ legislation.

In 1925, as a BA student at Government College, Lahore, Servi Chowla began solving problems posed by Ramanujan. By the time he completed his MA in 1928, he had 18 papers to his credit, and between 1925 and 1931, he cracked 34 problems in all.

His father, Bhai Gopal Singh, who became a professor at Government College, Lahore, in 1910, accompanied him to Cambridge in 1929, but tragically passed away there due to pneumonia. Servi Chowla completed his PhD in just two years, at the age of 23, under the guidance of JE Littlewood at Trinity College, Cambridge.

At Cambridge, Chowla shared a house with the young Subrahmanyan Chandrasekhar alias Chandra, nephew of Nobel laureate CV Raman, who had been at Lahore. The two remained in lifelong correspondence. Chandra was guided by RH Fowler, who also mentored Homi Bhabha and DS Kothari. The Lahore-born Chandra went on to win the 1983 Nobel Prize in Physics, but only after his two Nobel laureate students: Tsung-Dao Lee and Chen-Ning Yang. Incidentally, CV Raman had included both Servi Chowla and Chandra among the 65 founding members of the Indian Academy of Sciences in 1934.

Chowla’s first teaching job was at St Stephen’s College, Delhi, in 1931, where he married Himani Majumdar, sister of Sucheta Kriplani — later Independent India’s first woman Chief Minister. His career then took him to Banaras Hindu University and Andhra University; the latter’s Vice Chancellor was Sarvepalli Radhakrishnan, the future President of India.

At BHU, Chowla met the budding French mathematician Andre Weil, who had accepted the Chair at Aligarh Muslim University for two years. Andre later became one of the most influential mathematicians of the 20th century, co-founded the legendary Bourbaki group, and reshaped 20th-century mathematics.

Endorsed by his mentor JE Littlewood as the most promising Indian mathematician since Ramanujan, Chowla joined Government College, Lahore, as professor in 1936. He was also inducted into the Indian Education Service (1939). At Waltair, his postgraduate teaching had already lit a spark in the young CR Rao (CRR), later hailed as a “living legend” by the American Statistical Association and a recipient of the Padma Vibhushan.

The teacher (Servi) and student CRR went on to collaborate on several research papers in the 1940s. In 2023, the centurion CRR (1920-2024) was awarded the International Prize in Statistics, an honour often described as the Nobel Prize of Statistics.

At Lahore, Chowla’s first research student was Faqir Chand Auluck, who had topped MA in Mathematics in 1934. Auluck published extensively in number theory with and without Chowla, before moving to astrophysics and statistical physics. In 1942, he joined the Physics Department at Delhi University and soon earned a doctorate in physics.

Servi Chowla’s younger brother, Inder, who also worked with him on number theory at Lahore, had completed his PhD at Cambridge under H Heilbronn in 1942, but his brilliant career was tragically cut short by his untimely death the following year.

Chowla mentored a remarkable galaxy of students and collaborators at Lahore — Hansraj Gupta, Abdul Majid Mian, Daljit Singh, RK Talwar, RP Bambah, JC Luther, Mahendra Raj, FC Kohli, and Abdus Salam, among others. Hansraj, who studied under Servi’s father as an MA student from 1923-24, used to visit Servi too. Bambah set a record with a perfect 600/600 in the MA in Mathematics examination in 1945. Abdus Salam won the Nobel Prize in Physics in 1979.

FC Kohli and RP Bambah were later awarded the Padma Bhushan; the latter served as Vice Chancellor of Panjab University from 1985 to 1991 and remained a trustee of The Tribune Trust. Kohli went on to become co-founder and the first CEO of Tata Consultancy Services (TCS). Raj Kumar Talwar served as chairman of the State Bank of India. Jagdish Luther became Deputy Governor of the Reserve Bank of India.

Mahendra Raj emerged as one of India’s most celebrated structural engineers, collaborating with Le Corbusier on the planning of Chandigarh and designing iconic buildings such as Mumbai’s Usha Kiran, the Hall of Nations at Pragati Maidan in Delhi, and the Salar Jung Museum in Hyderabad.

At Lahore, Chowla disproved one of Ramanujan’s conjectures using Hansraj Gupta’s partition tables. As a schoolboy, Hansraj had devised a 100-year calendar that won a medal at the British Empire Exhibition. He earned the first PhD ever awarded by Panjab University (then in Lahore) in 1935. Gupta had immaculate, typewriter-like handwriting, which won him the rare permission to submit his thesis handwritten.

After World War II, Chowla helped Bambah secure a temporary post at Government College, Hoshiarpur, where Hansraj was the head. With no place to stay, Bambah was taken in by Hansraj, who shared his home for three months. Bambah was called to Delhi by DS Kothari to fill the position vacated by FC Auluck. He received unstinted support from both Kothari and Auluck, and on their recommendation, applied for the 1851 Exhibition Scholarship, under which he earned his PhD from the University of Cambridge in 1950. In 1951, he joined the University of Delhi as a Research Fellow, and was later appointed as a Reader at Panjab University, Hoshiarpur, in 1952.

With stints at the Institute for Advanced Study, Princeton (1952-1954), and the University of Notre Dame (1957-1958), Bambah returned to help establish a dynamic Department of Mathematics at Panjab University, Chandigarh, working closely with Hansraj Gupta. Their friendship laid the foundation of the continuation of the Punjab School of Mathematics in Independent India.

Bambah’s partnership with Hansraj was extraordinary in an academic world often fraught with ego. Along with TP Srinivasan and Luther, they elevated the Department of Mathematics and helped it earn the UGC Centre of Advanced Study (CAS) status. In 1983, the Government of India established the National Board for Higher Mathematics (NBHM), and this Centre for Advanced Study was chosen as its first regional centre.

Meanwhile, in July 1947, Chowla left Lahore with his family, aided by his wife’s sister. Armed with glowing recommendations from Hardy, Davenport, Mordell, and Littlewood — who had hailed him as “the most promising Indian mathematician Cambridge has had since the war” — he applied for posts in India. Yet, despite such praise, Independent India had no place for the Lahore professor.

After Independence, faculty positions were scarce — often a single professor doubling as head. Delhi University had no mathematics department and many talented academicians slipped away. India lost not only the would-be Nobel laureate Har Gobind Khorana, but also Sarvadaman Chowla, who had completed less than half his academic journey by then. Had he joined Panjab University alongside Bambah in the 1950s, the region’s scholarly history might have unfolded very differently.

In 1948, Chowla left for Princeton’s Institute for Advanced Study. Regulations in the US for foreigners left the family in financial strain. They had arrived in the US in the middle of a harsh winter — Selberg remembered his wife Himani braving the snow in thin sandals, surviving on the kindness of strangers. Through it all, Chowla’s mathematics gave them strength and purpose.

In the US, Chowla was rubbing shoulders with giants like Siegel, Selberg, Erdos, and Turan. He built a dazzling career — 350 papers with 60 collaborators, 25 PhD students (including his daughter Promita), and theorems that carry his name: the Chowla-Selberg formula, the Bruck-Ryser-Chowla theorem, the Mian-Chowla sequence. His collected works, published in 2000 by the University of Montreal, trace a journey that began in Lahore’s classrooms and ended on the world’s mathematical stage.

To celebrate the legacy of Prof Chowla, Panjab University instituted the Annual Sarvadaman Chowla Memorial Lecture. The first lecture, delivered 10 years ago by Fields Medallist Prof Manjul Bhargava on the occasion of the 90th birth anniversary of Prof RP Bambah, continues to inspire budding scholars.

The Punjab School of Mathematics shaped leaders across disciplines — Abdus Salam, FC Kohli, Raj Kumar Talwar, Mahendra Raj — and within mathematics, PU faculty like SK Trehan, IBS Passi, SK Malik, and TN Shorey earned the Shanti Swarup Bhatnagar Prize. Five PU mathematicians served as presidents of the Indian Mathematical Society. The School thus influenced science, technology, banking, and engineering as much as pure mathematics.

The centenary of the Punjab School is not merely a celebration of formulas or theorems, but of the human spirit that animates them — a century of mentorship, perseverance, collaboration, and curiosity passed from one generation to the next. A hundred years of intellect, inspiration, and enduring legacy.

— Kainth is chairperson of the Department of Mathematics, Panjab University, Chandigarh. Grover served as the PU Vice Chancellor