Of the many areas of pure and applied mathematical research to which Kolmogorov contributed, probability theory is unquestionably the most important, in terms of both the depth and breadth of his contributions.
Writers and journalists paid tribute to Johns on social media, many stressing the breadth of his contribution in numerous disciplines.
"The women of the WVS made great sacrifices for this country, but the breadth of their contribution has been hidden from view until now," she said.
A sufficient contribution from each person towards the upkeep of an institution does not mean enough to counterbalance that particular individual's benefit from, or use of, that institution, but means enough that across the entire breadth of everyone's contributions, the institution can be adequately maintained and provide the services that are both wanted and needed.
The photographs show the breadth of Seeger's contribution to American music and society, as a civil-rights activist, entertainer, husband, and father.
Sadly, much of how we do science these days seems in opposition to this approach; often, professors are hired for their narrow field of expertise rather than for the breadth of their intellectual contribution.
But the breadth of the field's contributions can be glimpsed just by examining this year's nominees.
The impact statement was designed to provide "evidence of the breadth of the unit's contributions to society or the economy" [ 37].
On the other hand, from a technocratic perspective [ 32] which focuses on the value that public expertise (e.g. their knowledge and experience) can add to research, the breadth of public representation and their contribution can be legitimately narrower – as the focus is on the expertise they can supply.
His exaggerated verbal infelicities conceal his heavyweight contributions across the breadth of his vast domain which encompasses environment, transport and the regions.
