Most math feels logical. Sometimes it might be hard to get the right answers, but at least it usually follows a logical pattern. At Mathnasium of Cherry Hills we accomplish our motto, “we make math make sense,” by helping students find the pattern and logic in the math system.
That’s why when we learned of this math idea which defies logic we had to explore it further. The idea is so weird you will want to argue with the famous mathematician, Ramanujan, who created it.
So what is this ridiculous idea?
Are you sure you are ready?
Okay, here it goes.
The sum of all the natural numbers (1, 2, 3, 4, 5, 6, 7 … and so on) into infinity is …
Wait… before we tell you the answer, take a guess.
If you are like most people you will guess that the answer is unknowable because infinity is never ending. How can you even consider the sum of an infinite set of numbers?
Ask a few math teachers and see how they respond. If they studied infinite sets they may launch into an explanation of divergent series and the Riemann Zeta Function. That math is so complex most kids in high school don’t ever learn about it.
However, if you ask physicists to solve 1+2+3 …∞, they may say the answer is -1/12!
How on earth can that be? It defies logic that adding whole, positive numbers could end up as a negative fraction. You can watch this Numberphile video https://www.youtube.com/watch?v=w-I6XTVZXww for Brady Haran’s explanation on this logic-defying math idea. The video stirred up a lot of bewilderment amongst math lovers. The New York Times even wrote an article about it.
ExtremeFinitism.com released a response video to the Numberphile video. https://www.youtube.com/watch?v=BpfY8m2VLtc In the response video the narrator “Karma Peny” explains in detail how Brady Haran’s methodology was misleading and simplistic.
So who is to believe?
Does 1+2+3 …∞= -1/12?
Yes … and No.
David Berman and Marianne Freiberger explain in this blog, https://plus.maths.org/content/infinity-or-just-112, that using pure mathematics does not give such a simple answer. However it is true enough that physicists studying string theory or calculating energy in Quantum physics find the equation useful for their purposes.
Approximately 99.99 percent of our students at Mathnasium of Cherry Hills will never need to use the Reimann Zeta function or the sum of all natural numbers through infinity. It still is fascinating, however, to think about the complexities of math. We hope that this weird math idea sparks an interest and curiosity in math beyond what you have learned so far. Math is so much more than just solving equations from a math book. If you love math as much as we do, give us a call at 720-474-1878.
You may also enjoy these other articles about fun aspects of math.
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