RT Nick Szabo (@NickSzabo4)@Dr_Gingerballs "Imaginary" numbers make math beautiful. For example, you can't make the Pythagorean theorem a group -- unless you include "imaginary" numbers. ...

Despite their daunting complexity, we have done the maths https://t.co/0mtWS9PWoi ...

RT Google DeepMind (@GoogleDeepMind)Together with @Googleorg, we’re introducing the AI for Math initiative, bringing together five prestigious research institutions pioneering the use of AI in mathematics. ⤵️ ...

Despite their daunting complexity, we have done the maths https://t.co/NjMCAxcE0w ...

RT ilmoi | tensor + vector (@ilmoi)I used to think that all you need to do well in life is study math and csnow I think you should also study historysurprisingly (or not) everything happening has already happened beforeif you see the fractals you see the future ...

AI Innovation - AI领域取得重要进展，开发出一种全新的人工智能驱动方法 [1] - 该方法发现流体动力学中几个复杂方程的全新解族 [1] Collaboration - 该研究由AI专家与来自布朗大学、纽约大学和斯坦福大学的数学家合作完成 [1]

General Overview - The industry has done the maths despite the daunting complexity [1]

Despite their daunting complexity, we have done the maths https://t.co/5R7xDxsAuo ...

Core Mathematical Concepts - Explores the concept of cardinality to compare the sizes of infinite sets, demonstrating that the number of squares and whole numbers have the same cardinality [4][5][6][7] - Introduces Cantor's diagonal proof to illustrate that the cardinality of real numbers is greater than that of whole numbers [8][9] - Discusses the concept of limits, explaining how an output converges on a single value as the input approaches infinity [18][19] Paradoxes and Applications of Infinity - Mentions Zeno's dichotomy paradox to highlight historical challenges in accepting the concept of infinity [10][11] - Explains the Grand Hotel paradox to illustrate the counterintuitive properties of infinity [11][12][13][14] - Showcases the presence of infinity in art through fractals like the Mandelbrot set [15] - Explores the concept of recursivity in language, suggesting the possibility of infinitely long grammatically correct sentences [16][17] Illustrative Examples - Uses the example of summing a half, a quarter, an eighth, and so on, to demonstrate that the series converges to a value of one [20][21][22]

AI Impact on Professionals - The emergence of AI capable of solving IMO (International Mathematical Olympiad) problems is perceived as a significant advancement, potentially impacting mathematicians' sense of identity and professional value [1][2] - The rapid progress of AI in problem-solving, as indicated by the METR agent task length, suggests that AI is quickly approaching human capabilities in various fields [2] - The potential displacement of mathematicians, coders, knowledge workers, and artists due to AI advancements raises concerns about widespread professional disruption [2] Societal Implications - The accessibility of advanced AI technology, exemplified by a hypothetical "universal dog translator" being sold at a low price, highlights the potential for widespread disruption and devaluation of specialized skills [2] - The collective grief and anxiety related to professional relevance and life purpose may become more prevalent and accelerated due to the rapid advancement of AI [2][3] - The industry questions society's readiness to cope with the potential societal and psychological impacts of widespread AI adoption [3]