Who is the greatest mathematician of the 21st century?

I would go for this man here

his name is Terence Tao.

Some facts about his early life and career:

He started to learn calculus when he was 7, at which age he began high school.
By 9 he was already very good at university-level calculus.
By 11, he was thriving in international mathematics competitions.
By 20 he earned his Ph.D. from Princeton University, and he joined UCLA’s faculty that year. UCLA promoted him to full professor at age 24.
His paper “The primes contain arbitrarily long arithmetic progressions” has been awarded as one of the 100 most important discoveries in all of science for 2004.
In 2006, at the ge of 31, he was awarded of the Fields Medal for “his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory”
Some thought about him from other colleagues:

“Someone like Terry comes along once every few decades”
[Tony Chan, dean of the Division of Physical Sciences and professor of mathematics at UCLA University]
“Terry wrote 56 papers in two years, and they’re all high-quality. In a good year, I write three papers.”
[John Garnett, professor and former chair of mathematics at UCLA]
Tao's mathematical knowledge has an extraordinary combination of breadth and depth: he can write confidently and authoritatively on topics as diverse as partial differential equations, analytic number theory, the geometry of 3-manifolds, nonstandard analysis, group theory, model theory, quantum mechanics, probability, ergodic theory, combinatorics, harmonic analysis, image processing, functional analysis, and many others. Some of these are areas to which he has made fundamental contributions. Others are areas that he appears to understand at the deep intuitive level of an expert despite officially not working in those areas. How he does all this, as well as writing papers and books at a prodigious rate, is a complete mystery. It has been said that Hilbert was the last person to know all of mathematics, but it is not easy to find gaps in Tao's knowledge, and if you do then you may well find that the gaps have been filled a year later.
[Timothy Gowers, mathematician at Statistical Department in Cambridge]
"If you're stuck on a problem, then one way out is to interest Terence Tao"
[Charles Fefferman professor of mathematics at Princeton University]

By Luca Manniti, Msc in Mathematics & Applied Mathematics, Sapenza University of Rome (Graduated 2013)