Birtwistle came up to Pembroke in 1896. He was awarded a minor scholarship for Mathematics and Natural Sciences and later a Grindall Scholarship, and a Beatson Scholarship. He received his BA in 1899 (Senior Wrangler) and went on to become a Fellow in 1900. He was also Assistant Tutor and Director of Mathematical Studies. Between 1901 until his death he also was a Lecturer in Mathematics at the University, and was particularly valued for his lectures on quantum theory which was developing during this time. He produced two books of these lectures in 1928, before his sudden death in 1929.