20th Century: More Discovery and More Questions

By in expert-voice, Our experts, Sunil's sandbox

The 20th century was not even a year old when it had one of its most important events in mathematics–The International Congress of Mathematicians in the summer of 1900 in Paris.


The opening address was given by David Hilbert, who while a great mathematician, became rightly known for what he said and proposed at this event. The now famous 23 Hilbert Problems. These were specific math problems that had not been resolved at that time. Hilbert, completely understanding the stubborn time lines of discovery, gave the audience, and the world, the rest of the century to solve them. 

“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.”

– David Hilbert

While many of the problems have been solved, one of the unsolved ones has now become the most famous math problem in the world. This is the Riemann Hypothesis. While the mathematics to fully understand the problem—never mind has the insight to try and solve the problem—requires very deep university-level courses, it basically involves the distribution of prime numbers. While all know what a prime number is, their quirky and random nature, is not well understood by mathematicians today. In fact, the great Hungarian mathematician Paul Erdos issued a staggering omen about when we will come to understand them.


It will be another million years, at least, before we understand the primes.

– Paul Erdős

While I personally don’t think it will take that long, I doubt I or my own kids will live long enough to see this long-awaited breakthrough. I used to tell my students that when The Riemann Hypothesis will be solved, it will make the front page of every newspaper in the world. And, the person who solves it, will automatically become one of the greatest mathematicians in history. 


In fact, the critically acclaimed show, NUMB3RS (2005-2010), had an episode called Prime Suspect, in which a mathematician supposedly had the solution, and criminals, wanting the solution to break encryption codes, kidnapped his daughter. When he realizes he does not have the solution, the FBI has to scramble to create a superficial solution and give access to a fake website with secret financial information. It was a very tense episode! And it has been over 150 years of mathematical tension with the continued irresolution of this massive problem, that goes to the heart of numbers.

While The Riemann Hypothesis is an important unsolved problem in mathematics, it is only one of over 300 that remain unanswered. It seems that the past century, while filled with important milestones and discoveries, has given the world even more problems to think about. 


And even Hollywood has taken notice of just some of these brilliant minds. Of course, there was the Oscar-nominated Hidden Figures (2017), which looked at the great contributions of black female mathematicians in NASA’s early days. But there have been other movies as well. The Man Who Knew Infinity (Ramanujan), The Imitation Game (Turing), and A Brilliant Mind (Nash).


When David Hilbert gave the world the problems that needed solving over the course of the century, he made an emphatic statement that lives inside the heart of every mathematician. In fact, so powerful are the words that it was inscribed onto his tomb.        

Translated in English, it means “We must know. We will know.”


The future of mathematics will continue to raise more questions than answers. But, as long as the spirit of David Hilbert lives in all of us, we will continue to be wildly curious and yes, want to know all the mysteries of mathematics.