Mathematics Prince
It is a great honour to write about arguably the greatest Mathematician of all time, known today as the Prince of Mathematics, Johann Carl Friedrich Gauss (1777-1855). He is also known for Gauss’ law in Physics, But in the world of mathematics, Gauss is often referred to as the “Prince of the Mathematics.” History considers him more a mathematician than a physicist, and for me, Gauss has the most beautiful description of mathematics which I have been fortunate to write down for many of my students at the LSE, Oxford and UCL, and it is the passage of text that I have engraved in my mind:
Arithmetic (number theory) is the queen of Mathematics, and Mathematics is the Queen of the Sciences; she often condescends to render service to astronomy and other natural sciences but under all circumstances, the first place is her due. – J.C.F Gauss.
Mathematics and Natural Sciences
Notice that Gauss here mentions astronomy and other natural sciences and not the social sciences since it was these two disciplines that influenced the development of Mathematics, in particular astronomy due to man’s need for the correct measurement of time, and seasons (weather prediction for harvesting) and not the social sciences including finance and economics.
Gauss had in his possession the theory of matrices (recall Gaussian elimination), and iterative techniques such as the Gauss-Jacobi, and Gauss-Seidel methods, He developed quadrature techniques, the so-called Cauchy-Riemann equations of complex variable theory were known to him as were quaternions attributed to W.R.Hamilton (1805-1865). We also have Gauss’ creation of differential geometry, and then we have Gauss’ development of the normal distribution the pivotal probability distribution found in any naturally occurring phenomenon, furthermore, we have his development of the method of ordinary least squares (OLS) and multiple ordinary least squares (MOLS) that I am fortunate to discuss on my modules at UCL. As is no doubt known Gauss used the method of OLS to predict the position of planets from astronomical data and not for econometrically modelling house prices in world cities as is so often done by applied Economists.
The Fascination of Primes
Gauss’ first Mathematical love was for the primes, the atoms of the integers proven so beautifully to be infinite in number by a reduction ad absurdum proof of Euclid (300BC). Around the time of Gauss, Mathematicians were trying to find generating functions that could produce primes indefinitely (without success see for example, M. Mersenne (1588-1648)), but what Gauss decided to do was to give an expression on how many primes there were less than an integer n, now known as the Prime number theorem. This is also now intricately related to the work of one of his greatest students Bernhard Riemann (1826-1866), who in his own right was also a “Giant” of Mathematics and in fact, it was Riemannian geometry that Einstein used to frame his General theory of Relativity, but that post is for another day.
Once again, I have overstepped my word limit, so I will have to stop here until next time: “old friends”.
