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Yesterday, National Academy of Sciences President Marcia McNutt delivered her last annual State of the Sciences Address. Overall the talk basically calls us to adapt to the new reality that industrial and foundation support for research has taken a far larger role in academic research....


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 Odd Scenarios about Research Claims

I blogged about OpenAI's achievement of having AI solve a math problem here.
My post had a few comments about authorship of such results.

Lance had a post about co-...


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The technical paper for the Erdős Unit Distance Problem lists only "OpenAI" as an author. When Bill


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In a 1946 paper in the American Mathematical Monthly, Paul Erdős posed the Erdős Distinct Distance Problem and the Erdős Unit Distance Problem.

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THE ERDŐS DISTINCT DISTANCE PROBLEM

A nice high school math competition problem, if it were not fairly well known, is:

Show that for a...


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Let \(f\) be a function mapping binary strings of length \(m\) to strings of length \(n\) with \(n>m\). Since there are more strings of length \(n\) than \(m\), \(f\) is not onto. Can you find a string not in the range? This is known as the range avoidance problems, or AVOID for short 

Let's do an example. Consider \(f\) that outputs an undirected graph on \(n\)...


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