Many of us in the present Hi-tech world feel that today we can understand and do anything with all the technologies available (which we think is advanced). If the truth be told we may have advanced in many fields but we still have nature’s deepest mysteries to solve.
In fact in 1900s itself people thought they will be able to complete the circle of mathematics by completely understanding it. When David Hilbert, a German mathematician, published 23 problems in 1900 for 20th century people to solve (some of which are still unresolved in 21st century) he was optimistic about solutions and famously said “we must know, we will know” (however the British already had the words “answerless” and “proofless” in their dictionary!).
Well the 1st question he asked was to prove or disprove continuum hypothesis and it was proved that “it cannot be proved or disproved” while to his second problem solution was “Incompleteness theory” which tells us that there will be things which are true and cannot be proved (so now we can climb that viva questions are indeed answerless questions!)
Why these two results are so ground breaking? That is because very important questions in other fields which are beyond human understanding are affected by this. To quote one “existence of god” can be argued to be true but cannot be proved. But this is the beauty of mathematics and science, isn’t it? Always trying to find out the secrets of nature and logically reasoning and understanding our universe.