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While browsing through funny math vides, I came across a YouTube short film comedy, Alternative Math, produced by Ideaman Studios (see [1], [2]). It is a hilarious exaggeration of a teacher who is dragged through the mud for teachng that \(2+2 = 4\) and not 22 as Dany, a young student insisted. In a recent election campaign in India, Prime Minister Narendra Modi declared, 'will make 1+1=11', perhaps by way of hinting the prospects of a tremendous growth in economy if only the State and the Centre act in unison. Let us forget politics and ask for some 'genuine' group laws in which we have both \(1+1=11\) and \(2+2=22\). Indeed there are several such algebras. In this talk we characterize all fields \(k \)having a polynmially defined group law \(+\) satisfying both \(1+1=11\) and \(2+2 = 22\).

References:

1. 2+2=22, video
2. Alternative Math video.
3. The New Indian Express June 4, 2017 and Times of India December 12, 2017.
4. Coleman, R. F. and McGuiness, F. O., Rational Formal Group Laws, Pacific J. Math. 147 (1991), no. 1, 25–27.
5. Padmanabhan, R., Group laws satisfying \(1+1=11\) and \(2+2=22\), Resonance vol 24, Indian Academy of Sciences, Springer 2019