Jørgen Pedersen Gram
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Jørgen Pedersen Gram (27 June 1850 – 29 April 1916) was a Danish actuary and
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
who was born in Nustrup, Duchy of Schleswig,
Denmark ) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of Denmark , establishe ...
and died in
Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...
, Denmark. Important papers of his include ''On series expansions determined by the methods of least squares'', and ''Investigations of the number of primes less than a given number''. The mathematical method that bears his name, the Gram–Schmidt process, was first published in the former paper, in 1883. For number theorists his main fame is the series for the Riemann zeta function (the leading function in Riemann's exact prime-counting function). Instead of using a series of logarithmic integrals, Gram's function uses logarithm powers and the zeta function of positive integers. It has recently been supplanted by a formula of Ramanujan that uses the Bernoulli numbers directly instead of the zeta function. In control theory, the Gramian or Gram matrix is an important contribution named after him. The Controllability Gramian and Observability Gramian are both important in the analysis of the stability of control systems. The Gram matrix is also important in deep learning, where it is used to represent the distribution of features in style transfer. Gram was the first mathematician to provide a systematic theory of the development of skew frequency curves, showing that the normal symmetric Gaussian
error curve In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real constants , and non-zero . It is n ...
was but one special case of a more general class of frequency curves. Gram's theorem, the Gram–Charlier series, and Gram points are also named after him. He died on his way to a meeting of the Royal Danish Academy after being struck by a bicycle.


References

Notes Bibliography * 19th-century Danish mathematicians 20th-century Danish mathematicians 1850 births 1916 deaths Cycling road incident deaths Linear algebraists Pedestrian road incident deaths Road incident deaths in Denmark {{denmark-scientist-stub