I just came across an article in New York Times about the famous mathematician Terry Tao, who, a onetime math prodigy turned Fields medalist, is a prolific researcher working in diverse areas of mathematics. The title of the article is “The Singular Mind of Terry Tao”. Here is the article.
With Terry Tao being a one of the greatest minds in 21st century mathematics, I know this would be an interesting read. Indeed, it gives a vivid picture of the world of Terry Tao – a prolific mathematician producing important work, a former child prodigy, a husband, father and so on.
It turns out that it is also a gentle introduction of various math concepts. For example, the article has a great short introduction of prime numbers that gives readers a sense that prime numbers are a simple construct that arises out of a concept of numbers and the four arithmetic operations (addition, subtraction, multiplication, and division). Knowing these basic number concepts is all you need to spot the prime numbers. Thus prime numbers are elemental objects in mathematics. It goes on to say that any alien species in other parts of the universe is probably very different from us but “we can be almost certain that their mathematicians have discovered the primes and puzzled over them”. It also points out that “scientists have uncovered deep connections between primes and quantum mechanics that remain unexplained”.
The short intro to prime numbers is to lead the readers to the discussion of the GreenTao Theorem, which led to the award of the Fields medal for Terry Tao.
Another interesting thing about the article is that it gives the readers a sense of what it means to do mathematics. It is not a static pursuit of solving algebra problems from stale old math books. In fact, “The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians”. Mathematical research is a fundamentally creative act. It is a very difficult pursuit. It is akin to a struggle with the devil (as the article playfully suggests). Mathematics research is a long game. Doing math research requires courage; it may take weeks, months and years if success comes at all.
Another interesting tidbit of information is the letter of recommendation written by Paul Erdos, the revered Hungarian mathematician, in supporting Terry Tao’s application to Princeton.

“I am sure he will develop into a firstrate mathematician and perhaps into a really great one,’’ read Erdos’ brief, typewritten note. ‘‘I recommend him in the highest possible terms.”
Based on what we know of Tao, Erdos’ prediction is spot on. The full article is here.