People at a coffee shop
As strange as it may seem, Zhenyi is not interested in the way you tie your shoelaces.
Slip knots, square knots, Windsors and all manner of Boy Scout knots are not knots at all
To mathematicians like Zhenyi, a ‘knot’ is a very specific phenomenon. It’s a continuous circle, a continuous ring with no openings. Rubber bands, wedding rings and fan belts qualify as a knot. So do the tangles found in your DNA molecules.
Give a ring a half twist and you have a figure eight. Wrap it around your fingers in certain ways and you create a cat’s cradle which can changed into any number of playful knots.
Since the beginnings of Knot Theory in the 1800s, mathematicians have tried to classify and tabulate all possible knots. More than six billion different variations have been identified to date. In fact all prime knots up to 16 crossings have just recently been tabulated.
Theorists don’t “discover” knot variations so much as they classify and tabulate them. Zhenyi’s PhD efforts center around identifying a new, unique knot.
Different looking knots may actually be the same one. Proving or disproving ‘equivalence’ is part of what gets Zhenyi out of bed in the morning.
His work is not aimed at practical applications – it’s ‘pure’ mathematics. Newton’s pure speculations, he explains, were used to great effect by Einstein.
Along with the elegance of the math, Zhenyi is fascinated by the labyrinthine calligraphy and knot motifs that have graced manuscripts and mosques for millennia.
The knot shown on his computer screen, the Legendrian, is central to his dissertation.
This is a time of stress for Zhenyi. He’ll soon submit his findings to pre-publication review and then beyond that to formal peer review journals.
The man who works standing upright in the windows of our coffee shop will be standing there for at least some part of next year. 
