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A game you're almost certain to lose...

What are the challenges of communicating from the frontiers of mathematical research, and why should we be doing it?

Celebrate Pi Day with the stars of our podcast,

*Maths on the move*!Maths meets politics as early career mathematicians present their work at the Houses of Parliament.

Celebrate this year's International Women's Day with some of the articles and podcasts we have produced with women mathematicians over the last year!

While I can appreciate the desire to (and need for) stretching the frontiers of our understanding of all things, numbers included, I do think it's wrong to mess with the meaning and value of symbols like + and =, the foundation of mathematics. And infinity is not a number -- that's why it can only be described as ". . . "

1 + 2 + 3 + . . . doesn't "equal" -1/12. It has no value, other than to say "infinite," which is another way of saying we can't represent it.

Just as one can (and should) draw purple unicorns, or postulate a biology based on something other than carbon, or create any number of interesting non-Euclidean geometries, one can devise all sorts of alternative "maths" where there are different rules (where "infinity" is a number, for example), and these rules will lead to all sorts of fun conclusions, like the sum of all natural numbers equaling -1/12. These endeavors might even turn out to be useful, in some cases . . . complex numbers, for example.

But it's dishonest, unintentionally perhaps, to use familiar symbols in an attempt to present fanciful derivations as mathematical truth. And yes, there is a non-relativistic mathematical truth. And part of that truth is that you can't get a negative fraction by adding a series of positive integers.