The daily Danish primetime television program "Aftenshowet" on DR1 featured 7 August 2019 Professor Jørgen Ellegaard Andersen as an expert in mathematics.

2019.08.08 |

A simple arithmetic problem had gone viral and "Aftenshowet" contacted Jørgen Ellegaard Andersen to give an expert opinion on the expression

8:2(2+2)=?

Some people get the result 1 and others get the result 16, since they apply two different conventions in regards to the order of division and multiplication in such expressions. Both conventions exist in the literature and they result in the following two unambiguous expressions:

(8:2)(2+2) = 4x4 = 16 and 8:(2(2+2)) = 8:8 = 1

which yields two different results. From a mathematical point of view this is absolutely uninteresting. We note that this is an opinion we share with our international senior mathematician colleagues: https://www.nytimes.com/2019/08/06/science/math-equation-pemdas.html

On the show Jørgen was then asked to provide a problem, which demonstrates the nature of problems interesting for researchers within mathematics, and which at the same time should be understandable for the general public. After a number of attempts "Aftenshowet" accepted the following rather trivial problem:

Problem: Drawing 6 lines, such any two of them intersect and no three or more of them intersect in one point. How many triangles are there in the figure?

Solution: There is a one to one correspondence between the triangles in the figure and subsets of three lines of the six lines. The same is of course the case with n lines satisfying the same conditions and the result is in general n choose 3, which in the case of n=6 is 20.

More advanced such "counting"-problems relates closely to the mathematical version of some parts of quantum field theory and different versions of string theory, which is closely related to the core research area of the center led by Professor Jørgen Ellegaard Andersen at Aarhus University, Center for Quantum Geometry of Moduli Spaces, a Danish National Research Foundation Center of Excellence and further relates also to the ERC-Synergy project, "ReNewQuantum", which the European Research Counsil is funding with 10 million Euro with Professor Jørgen Ellegaard Andersen as lead Principal Investigator.

The mathematics problem given by Jørgen Ellegaard Andersen was posted on "Aftenshowet´s" facebook page and the day after there were approx. 200 comments from the public. See the "Aftenshowet" facebook post: https://www.facebook.com/Aftenshowet/posts/2288461701469035

See the TV program "Aftenshowet" from 7 August 2019 (only in Danish): https://www.dr.dk/tv/se/aftenshowet-9/aftenshowet-11/aftenshowet-2019-08-07