#### Introduction

The Norwegian Academy of Science and Letters has announced it coveted 2018 Abel Prize, which is named after 19th century mathematician Niels Henrik Abel. This year’s award is Robert P. Langlands of the Institute for Advanced Study, Princeton, USA, for his “visionary program connecting representation theory to number theory.”

Separately, the Association for Computing Machinery announced today that its Turing Award will be given to John L. Hennessy (until recently the President of Stanford University) and David A. Patterson (University of California, Berkeley) for their work in designing “a systematic and quantitative approach to designing faster, lower power, and reduced instruction set computer (RISC) microprocessors.”

These indeed are very prestigious awards. The Abel Prize is widely considered to be the equivalent of the Nobel Prize in mathematics, and, similarly, the Turing Prize is widely considered as the most prestigious award in the field of computer science.

#### Langlands wins the Abel Prize

Langlands was awarded the Abel Prize for work dating back to 1967, when he penned a letter to the French mathematician Andre Weil, outlining what is now known as the “Langlands program.” His idea was to explore links between number theory and harmonic analysis. As the Abel Prize committee describes it,

In Langland’s letter to Weil, he suggested that prime numbers which arise in higher-degree generalizations of Gauss’ reciprocity law might have a corresponding reciprocity relationship in harmonic analysis. On the face of it, this seems unlikely because number theory (in particular the mathematics of prime numbers) seem completely foreign to the world of harmonic analysis (in particular the study of Fourier spectra as in mathematical physics), which arises from calculus and real analysis. But they do.Langlands’ insights were so radical and so rich that the mechanisms he suggested to bridge these mathematical fields led to a project named the Langlands program. The program has enlisted hundreds of the worldâ€™s best mathematicians over the last fifty years. No other project in modern mathematics has as wide a scope, has produced so many deep results, and has so many people working on it. Its depth and breadth have grown and the Langlands program is now frequently described as a grand unified theory of mathematics.

Work on the Langlands program has definitely been fruitful. One big result was Andrew Wiles’ 1995 proof of Fermat’s Last Theorem, which depended on a connection between number theory and analysis that Langlands had suggested decades earlier.

For additional details, see a Quanta report and the Abel Prize site.

#### Hennessy and Patterson win the Turing Award

Just as the Abel Prize is the premier prize for mathematicians, the Turing Award, named after 20th century computing pioneer Alan Turing, is the premier award in the field of computer science.

Hennessy and Patterson’s work arose in the 1980s, when researchers began to sense limits of conventional computer processor designs. Their idea was to pare down computer processor architectures to a very simple core, observing that it was faster, in many cases, to perform a given operation as a sequence of very small atomic operations that to implement a higher-level operation. What’s more, such pared-down processors use less energy overall, which is a major consideration in modern computing, not just for energy conservation but also for heat dissipation on a circuit board.

The two computer scientists outlined their vision in a 1989 book Computer Architecture: A Quantitative Approach. It quickly became the “bible” of processor design and the standard textbook of many university courses in the field. As ACM describes it,

In Computer Architecture, Hennessy and Patterson encouraged architects to carefully optimize their systems to allow for the differing costs of memory and computation. Their work also enabled a shift from seeking raw performance to designing architectures that take into account issues such as energy usage, heat dissipation, and off-chip communication. The book was groundbreaking in that it was the first text of its kind to provide an analytical and scientific framework, as well as methodologies and evaluation tools for engineers and designers to evaluate the net value of microprocessor design.

The Hennessy-Patterson approach has been widely adopted in real-world microprocessors. Very likely the processor of the computer or tablet you are reading this on was designed with principles from their book and the associated theory.

For additional details, see a New York Times report and the ACM Turing Award site.