In 1959, an Indian mathematician went to settle his hotel bill in New York. The cashier recognised him. "Is it your picture in the New York Times?" "Yes, it is my picture." "You must have done something. The front page of the New York Times cannot be bought for a million dollars." The guest was Raj Chandra Bose. With Sharadchandra Shrikhande and Ernest Parker, he had proved Euler wrong. Let us hear that story.... Euler's puzzle involved 36 officers: 6 regiments, 6 ranks. Could you arrange them in a 6 x 6 square without repeating a regiment / rank in any row / column? You cannot. Euler was right about that. But he also conjectured that the same arrangement was impossible for squares of side 10, 14, 18, 22, and so on. That larger claim stood for 177 years. Bose, Shrikhande and Parker overturned it. Apart from sizes 2 and 6, the supposedly impossible squares could be constructed. The unexpected ingredient was mathematics developed for designing agricultural experiments. Tools used to arrange field trials helped solve a problem Euler had left behind. Bose and Shrikhande's partnership had begun at the Indian Statistical Institute in Calcutta. By 1959, both were working at Chapel Hill. Parker worked at Remington Rand Univac and pursued this mathematics recreationally. On 26 April 1959, the three appeared on the Sunday New York Times front page with a 10 x 10 square. They became known as "Euler's spoilers". Bose's own recollection preserves the hotel cashier's reaction. A man came down to pay his bill and found someone who had read the mathematics news. Sources: "Shrikhande, 'Euler's Spoiler'", Asia Pacific Mathematics Newsletter 8(1), 2018, quoting Bose's and Shrikhande's recollections; New York Times, 26 April 1959. Photo 1: R.C. Bose. Photo 2: The actual New York Times clipping, 26 April 1959. The newspaper's caption identifies them, left to right: E.T. Parker, S.S. Shrikhande and R.C. Bose. Photo 3: Shrikhande, left, and Bose at the blackboard. The Shrikhande Family, via Asia Pacific Mathematics Newsletter 8(1), December 2018.

In late 1951, a man reached K.E.M. Hospital, Bombay, after a railway accident. He needed blood. Routine grouping said he was O. The blood bank cross-matched him against 115 units. Not one was compatible. Then, within a month, another patient arrived with a stab wound. Same problem. But the 2 patients' blood matched each other. Y.M. Bhende, C.K. Deshpande and H.M. Bhatia of Seth G.S. Medical College investigated. A separate search through 160 donors found exactly 1 compatible donor, a man donating for the 1st time in Bombay. Why would someone who tested as O be unable to receive ordinary O red cells? The missing piece was H, an antigen on the surface of red blood cells. It forms the base on which the A and B antigens are built. Ordinary O cells do not have A / B, but they still have H. These patients lacked H too. The 1st patient's serum contained an antibody against it, which explained why even ordinary O cells clumped when tested against his serum. He was given plasma rather than red cells. Samples from the 3 men went to London. Robert Race and Ruth Sanger's blood group unit helped establish the new blood group character. Walter Morgan and Winifred Watkins investigated the missing H substance. On 3 May 1952, The Lancet published their joint report: "A 'new' blood-group character related to the ABO system." It became known as the Bombay blood group, written Oh. The distinction matters in a blood bank: someone with this phenotype can appear to be O on basic grouping, yet ordinary O red cells are incompatible. They need a Bombay compatible red cell donor. The 115 units were unsuccessful laboratory cross-matches, not failed transfusions. And the 160 donor search was a separate step. Two injured patients and one donor had exposed something the usual ABO grouping could not distinguish. Sources: Bhende, Deshpande, Bhatia, Sanger, Race, Morgan & Watkins, The Lancet, 3 May 1952, pp. 903-904; S.R. Joshi, "Discovery of blood groups in India - an update," Asian Journal of Transfusion Science 15(Suppl 1), 2021, pp. S2-S4; D.P. Kasbekar, "History and Development of Genetics Research in India: Three Case Studies," Indian Journal of History of Science 51(2.2), 2016. Photo 1: The historical account of the two patients: railway accident, stab wound, apparent group O, incompatible red cells and plasma transfusions. Relevant passage highlighted. Photo 2: The separate search through 160 donors, which found donor Z. Highlighted on p. 427 of the same paper. Image Source: D.P. Kasbekar, Indian Journal of History of Science (2016).