As per Cauchy's Integral Formula
If f(z) is analytic inside and on a closed path C, and Zo is any point inside C, then the value of the function at Zo is completely determined by its values on the boundary C
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When the JWST pointed its powerful instruments toward the early Universe, scientists were surprised by what it found.
At high-redshift (z) values, corresponding to less than one billion years after the Big Bang, astronomers witnessed an abundance of galaxies that hosted what appeared to be the "seeds" of supermassive black holes SMBH.
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Co- Founder & President of OpenAI, Greg Brockman says that OpenAI has made some significant progress on the second Millennium problem.
This will be the second Millennium problem OpenAI has made some progress on after the Navier Stokes Equations
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As per the Stoke's Theorem
If F is any continuously differentiable vector point function and S is a surface bounded by a curve c, then
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I hope its a sarcams😭😭
WIRED reported today that I began to cry while talking about AI and mathematics. But the article didn’t explain what moved me.
The truth is, I’m not entirely sure myself. I’d like to try to explain. 🧵
wired.com/story/mathematicia…
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AI can't develop a whole new field to solve a particular problem.
Mathematicians can!!!
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10y old Terence Tao with 72y old Paul Erdős in 1985 in Adelaide, Australia.
During Paul's visit to Adelaide, he discussed mathematical problems with Tao, recognizing his immense potential and encouraging him to pursue mathematics.
In the 1930s, Paul Erdős posed the problem - if every infinite sequence of +1s and -1s must contain subsequences whose sums are arbitrarily large.
80 years later, in 2015, Terence Tao solved the Erdős discrepancy problem, he proved that Erdős's conjecture was wrong and such a sequence cannot be constructed, as the sums will inevitably grow to be arbitrarily large.
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