#### The Abel Prize

On 21 March 2017 the Norwegian Academy of Science and Letters announced that the 2017 Abel Prize for mathematics, thought by many to be on a par with the Nobel Prize, has been awarded to Yves Meyer for his groundbreaking work on wavelets.

Many of the leading awards made in the field of mathematics are for highly abstract theoretical work. But wavelet theory is certainly in the area of applied mathematics, as it is now used in many different real-world arenas. Applications include data compression, acoustic noise reduction, biomedical imaging, digital movie projection, economics, image correction of Hubble space telescope images, and the recent detection, by the LIGO team, of gravitational waves created in the wake of the collision of two black holes.

The Abel Prize includes a cache award of six million Norwegian kroner, or approximately 675,000 Euros or 715,000 USD.

#### Wavelets

Scientists have for many years used Fourier analysis, which was first developed in the 19th century by Joseph Fourier, to analyze signals and other periodic phenomenon. Beginning in the 1950s, with the development of the fast Fourier transform (FFT), the discrete Fourier transform has been employed very extensively in science and engineering. Mobile phones employ the FFT in encoding and decoding signals sent to/from cell towers.

The FFT is also heavily used in scientific computation, because it permits one to economically perform a convolution operation. As a single example, for sufficiently high numeric precision the most efficient algorithm for multiplying two very high-precision numbers is to treat the multiplication as a linear convolution, which can be evaluated very rapidly using an FFT.

However, discrete Fourier transforms, and corresponding FFT algorithms, have their limitations. Fourier analysis is fine for analyzing periodic behavior of an entire dataset, but in the real world periodic behavior is often a feature of only a small part of a dataset, such as in a sparse dataset.

For many applications of this type, wavelets are superior. Wavelets are wave-like oscillations with amplitudes that start at zero, then increase, then decrease back to zero. Practical applications are facilitated by the development of fast computational algorithms, analogous to the FFT, that are suitable for large-scale computation as well as mobile applications, such as speech recognition and image analysis.

#### For further reading

There is an extensive literature on wavelets. A rather good introduction to the topic is available in the Wikipedia page on wavelets. A good source for a more detailed treatments is a Ten Lectures on Wavelets by Ingrid Daubechies. Additional information on Meyers’ career and research on wavelets is available in a Scientific American article and also in a Quanta Magazine article.