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
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, song_type = National and royal anthem
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, 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
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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
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