Bolyai was a fellow-student, and Gauss’s only real friend — they corresponded for life. Humboldt inspired Gauss’s researches into magnetism, and sought his help towards a global grid of magnetic observatories. His collaboration with Weber led to the first electric telegraph. Jacobi’s youthful work impressed him, and Dedekind, Cantor and Riemann were among his students, though he disliked teaching. Dirichlet carried his ‘Disquisitiones Arithmeticae’ with him all his life. Germain (under a male pseudonym) conducted a substantial mathematical correspondence with him: other correspondents included Bessel and Olbers.