# Herman te Riele

Hermanus Johannes Joseph te Riele (born January 5, 1947 in The Hague ) is a Dutch mathematician who deals with cryptography , algorithmic number theory and numerical mathematics .

## Life

Te Riele obtained a degree in mathematics engineering from the TU Delft ( A generalization of the Bernstein operator in approximation theory ) in 1970 and received her PhD in mathematics from the University of Amsterdam under Adriaan van Wijngaarden in 1976 ( A Theoretical and Computational Study of Generalized Aliquot Sequences ). Since 1970 he has been employed as a scientist at the " Centrum Wiskunde & Informatica " (CWI) in Amsterdam . There he heads the group Algorithmic Number Theory . From 1973 to 1987 he headed the Numerical Mathematics department . In 1995 he was visiting professor at the Technical University of Sydney and in 2001 visiting scholar at the Mathematical Sciences Research Institute in Berkeley, California.

Te Riele dealt with numerical topics related to the Riemann Hypothesis . With Andrew Odlyzko in 1985 he refuted the Mertens conjecture (from which the Riemann conjecture could have been derived). In 1987 he found a new upper limit for the Skewes number . He dealt with the factorization of large numbers, friendly numbers , discrete computer tomography as well as with the numerical solution of integral equations , numerical analysis, parallel algorithms and computer simulations, for example in plasma physics .

In 1997, together with G. Effinger, Jean-Marc Deshouillers and D. Zinoviev, he solved the ternary Goldbach conjecture (every odd number greater than 5 can be represented as the sum of three prime numbers), assuming the generalized Riemann conjecture .

He was secretary in the organizing committee of the 5th European Congress of Mathematicians (ECM) in Amsterdam in 2008.

Herman te Riele is married and has three children.

3. ^ Te Riele: On the sign difference of - Li (x)${\ displaystyle \ pi (x)}$ , Mathematics of Computation, Vol. 48, 1987, pp. 323-328