## Creator of ‘Grand Unified Theory of Mathematics’ Wins Prestigious Math Prize

Professor Langlands is very famous in the field of Number Theory. Congratulations to Prof. Langlands for winning the very prestigious Abel Prize.

Source: LiveScience

A mathematician who developed what some consider the “grand unified theory of mathematics” has won one of the most prestigious prizes in mathematics.

Robert Langlands, an emeritus professor at the Institute for Advanced Study at Princeton University, has won the Abel Prize, a prestigious mathematics prize that honors a lifetime of groundbreaking work, organizers of the prize announced yesterday (March 20).

Langlands, 81, won the prize for work in which he found deep connections between two seemingly disparate areas of mathematics: number theory and harmonic analysis, according to a statement from the organizers of the prize.

## Summation by parts / Abel’s Lemma

This is an amazing identity by Abel.

Let $\{f_k\}$ and $\{g_k\}$ be two sequences. Then,
$\displaystyle \sum_{k=m}^n f_k(g_{k+1}-g_k)=[f_{n+1}g_{n+1}-f_mg_m]-\sum_{k=m}^n g_{k+1}(f_{k+1}-f_k).$