Aniceto Sarmiento

Quick proof of the Divergence of the Harmonic Series: 1+1/2+1/3+... Assuming it converges: S = 1+1/2+1/3+... then S/2=1/2+1/4+1/6+... But 1+1/3+1/5+...>S/2 Hence S>S/2+S/2=S ■

George Green is the Ramanujan of physics. Born to a miller in Nottingham, Green himself took up the trade and was largely self-educated. At 35, he rented out his mill and penned "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism." In this work, he introduced what are now known as Green's formula, the Green function, and potential, laying the groundwork for potential theory. He self-published this essay as a small booklet, with the financial support of friends. Only after this accomplishment did he attend Cambridge to obtain a formal education. There, he authored a few more papers on mathematical physics, though his initial work remains his most renowned. Tragically, he passed away at 48. Later historians delved into the resources available to Green during his self-education in Nottingham. Among their findings was an intriguing entry in the local gentlemen's club library: Laplace's "Traité de mécanique céleste." If this was the cornerstone of his learning, it remains a mystery how he mastered French, given that he had never attended school prior to writing his seminal work.

G.H. Hardy on proofs by contradiction

⨋ is used to express a sum over all discrete states and an integral over all continuum states

"You keep on learning and learning, and pretty soon you learn something no one has learned before" - Richard Feynman

Googol = 10¹⁰⁰ A Googol is a 1 followed by 100 zeroes. Other names for googol: - ten duotrigintillion on the short scale - ten thousand sexdecillion on the long scale - ten sexdecilliard on the Peletier long scale