If ever there was a knot theorist, it was Vaughan Jones. This New Zealand-American mathematician, a 1990 Fields Medalist, is now renowned worldwide for his contributions to knot theory. French mathematician Alain Connes (born in 1947 and himself a Fields Medalist) described his discoveries as "work of pure genius".
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The mathematician Vaughan Jones, who died on September 6, 2020, profoundly influenced several areas of mathematics, including topology and functional analysis, as well as physics, particularly quantum theory. His name remains associated with powerful invariants in knot theory.
Knots can be combined to form new ones—or, conversely, simplified. We can borrow the vocabulary of number theory and classify them rather like the chemical elements. What varied and unexpected facets knot theory has!
A spherical ball is the set of points whose distance from a center is less than a constant. Mathematicians, always seeking to generalize, accept this definition of a ball… in any space equipped with any kind of "distance."
The metric properties of modelling-clay objects change when they are deformed. Other properties, known as topological properties, remain unchanged. Surprisingly, algebra enters the picture. This naturally leads us to consider knots and the constituent molecules of DNA.
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