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A new machine learning framework provides doctors with a reliable tool to help diagnose Alzheimer's disease early.

What do we know about monkeypox, what do we not know, and what efforts are going into modelling it?

The COVID-19 emergency resulted in some amazing mathematical collaborations.

Here's a simple game at which a human can out-fox even the cleverest algorithm.

The INI is celebrating its 30th birthday. What is it and what is it do for maths and mathematicians?

Extreme care is needed when dealing with infinite sums. From what I can tell, it seems that confusion arises when people assume they are allowed to manipulate infinite sums in the same way as they are used to doing with the finite sums they are accustomed to dealing with. Assuming infinite sums behave anything like finite sums will lead to problems. Reordering a non-convergent infinite sum will often produce different answers - in many cases you can get any result you desire, but it's clearly incorrect. Proceeding term-by-term to calculate the partial sums. What does it even mean to sum an infinite number of terms when the sum is non-convergent? It's unsafe to assume that what works for finite sums must apply to infinite sums as well.

Regarding -1 + -1 ... (Grandi's Series), although it doesn't have a limit, it is Cesaro summable and as a cesaro sum of 1/2. This can be easily proved in lots of ways. This is what Numberphile were talking about no doubt.