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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The existence of such massive black holes so early in the Universe challenged existing models of black hole formation, in which stars collapse at the end of their lives to form black holes that gradually come together to create SMBHs.
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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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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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25 Field medalists including Terence Tao have published a warning about the Impacts of AI on mathematics.
This keeps getting better given that not a single AI company cares about such statements, infact they will accelerate their research to solve all remaining problems.
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Terence Tao, born in 1975 in Adelaide, is widely regarded as one of the most brilliant mathematicians alive today and arguably the smartest person in the world, with a reported IQ of 230.
At age 2, he was teaching 5-year-old children spelling and addition and by age of 21, Tao received his Ph.D. from Princeton University. He soon joined UCLA and became a full professor at age 24.
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