Get ready to be astounded
In early 2014, a YouTube video about mathematics went viral and soon had over 1 million views.
Using simple mathematics, it claimed to prove that if you add up all the natural numbers, 1+2+3+4+…, all the way to infinity, the answer is -1/12.
It seemed like an ‘astounding’ result because you are adding all positive whole numbers, getting bigger and bigger, and the result is:
- Not big
- Not positive
- Not a whole number
The video attracted much criticism from mathematicians. The two Physicists in the video were denounced for using non rigorous methods, and they were accused of using the words ‘sum’ and ‘equals’ far too loosely. However, several more rigorous methods were known to produce the same result, and so the true meaning of this -1/12 result remained a mystery… until now.
The true meaning of this -1/12 result is explained in layman’s terms in this response video:
The truly astonishing thing revealed in this response video is that this -1/12 result is simply one huge blunder.
The mistake is one of taking a function that applies to just positive whole numbers, manipulating it in ways that bring fractions and negative numbers into play, and then interpreting the result as though it still relates to positive whole numbers.