Fourier believed that the main aim of mathematics should be the understanding of nature and that the purpose of understanding nature should be the benefit of mankind. Yet, interesting though Fourier's own work was, he could point to no direct practical benefit from it. The credit for showing how powerful were the tools that Fourier had forged belongs, above all, to William Thomson, Lord Kelvin.

The life of William Thomson was linked with the University of Glasgow from 1832, when his father became professor there. Thomson was not a late developer. At the age often he and his 12-year-old brother enrolled in the University of Glasgow. Prizes in Greek, logic (what we would now call philosophy), mathematics, astronomy and physics marked his progress. ‘A boy’, he said later, ‘should have learnt by the age of twelve to write his own language with accuracy and some elegance; he should have a reading knowledge of French, should be able to translate Latin and easy Greek authors and should have some acquaintance with German.’

Towards the end of his time as a student in Glasgow he fell under the influence of an inspiring physics teacher called Nichol.

…after I had attended in 1839 Nichol's… Class, I had become filled with the utmost admiration for the splendour and poetry of Fourier. Nichol was not a mathematician and did not profess to have really read Fourier, but he was capable of perceiving his greatness and of understanding what he was driving at, and of making us appreciate it.