Introduction:
The 18th and 19th centuries saw the pioneering work of the brilliant French mathematician and physicist Joseph Fourier, whose scientific contributions will never be forgotten. I am very fortunate to be able to discuss Joseph Fourier’s (1768-1830) series at UCL. As with all techniques and ideas in Mathematics, one fully appreciates a “Giants” work only when one considers its proof, and the Fourier series is no exception. When I first saw the proof as a young undergraduate studying partial differential equations, I thought, “Wow, I understood that “, but my burning question was “, How did he know to commence like this?”
Zeta Function:
It immediately reminds me of a famous quote (which I read years ago but cannot recall the author) that I often use when I am lecturing which is:
“It is easy to follow the steps of genius if that genius shows us how to walk.”
This quote applies to Joseph’s work but also when I introduce some of Euler’s work, e.g. His derivation of the Zeta function or when I use the Cauchy integral formula or his residue theorems.
The Mathematical Theory of Heat:
Returning to Fourier, he is, of course, one of the 72 Great French men/women of Science on the Eifel tower, but Joseph was once part of an elite group of Mathematicians in France at the famed L’Ecole Polytechnique making it the epicentre of Mathematics in the world. Fourier introduced his theory on heat by extending the work of I. Forensic scientists frequently utilise Newton (1643–1727) and his law of cooling to pinpoint the exact moment of a homicide. Joseph created Dimensional Analysis, a technique to develop equations for physical phenomena. Of course, when the number of independent variables is more than three, one must use Buckingham’s Pi theorem and include a considerable amount of linear algebra to appreciate its potency. Still, it is certainly a topic I enjoy discussing at UCL.
Polytechnique:
Simultaneously, Others at the Polytechnique included J. Lagrange (1736-1813) and G. Monge (1746-1818). Even though the French had adopted Lagrange, he was, in fact, Italian (with the name Giuseppe Ludovico De la Grange, it would be difficult not to be Italian). Fourier introduced his theory on heat by extending the work of I.
Fourier Coefficient:
Joseph Fourier introduced the Fourier transform, expanding on his work with the Fourier series. This mathematical method generalises the Fourier series, which is popular in signal processing, image analysis, and other domains. A useful tool for comprehending the frequency content of signals is the Fourier transform, which breaks down a function into its component frequencies.
Conclusion:
Throughout history, many great mathematicians and scientists have been pawns of the military. Fourier and others helped improve weapons accuracy for Napoleon’s campaign in Egypt and during the Manhattan Project. Fermi (1901-1954), R. Feynman (1918-1988), breaking Enigma (A. Turing (1912-1954) ), Germany’s nuclear research W. Heisenberg (1901-1976) is one of my old friends.
