I think this is the most important concept to understand right now: LLMs can’t jump.
OpenAI says an internal version of Astra, its next major model, has solved ten major open problems in mathematics and theoretical computer science.
This is extraordinary.
And I don’t use this word lightly.
During my PhD in mathematics, I worked on a problem closely related to Gromov’s conjecture. For decades, constructing a non-sofic group—an infinite group whose finite pieces cannot be approximated by finite groups—was a dream shared by many of us.
Now Astra appears to have done it.
This is not a toy result. This is serious mathematics.
But it is not “the most significant day in the history of mathematics”, as some have claimed.
This claim confuses scale with kind.
Astra has solved difficult problems inside existing conceptual worlds.
Calculus, topology, and scheme theory created new conceptual worlds.
They did not merely answer questions. They changed which questions mathematics could ask.
Induction finds patterns. LLMs are extraordinary at it.
Deduction follows implications. Using symbolic AI tools, LLMs are becoming formidable at traversing chains of logic that humans missed, abandoned, or could never afford to search.
But abduction is different.
Abduction invents the right concept, the right representation, the right question.
That is the jump.
Current LLMs can fill the gaps of knowledge left by humans.
But they can’t jump beyond the external boundary of existing knowledge.
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Full paper in the first reply
Detritus of Partition: How Meo Muslims came back back from Pakistan and are creating a mini Pakistan in Mewat
1. In 1999 I was travelling from Delhi to Jaipur by road with my brother in law (a Jat). An hour out of Delhi, we entered Haryana’s Mewat - a 75 percent Muslim majority district. It’s a rough, scary and even dystopian place. The people look noticeably unfriendly and the youth stare grimly at the vehicular traffic as if the passing cars and buses are intruders. Mewat is the stronghold/ghetto of the Meo Muslims, an increasingly radical group that in 1927 gave the world the Tablighi Jamaat (the fundamentalist group that notoriously spat on doctors, nurses and police during Covid-19 lockdown).
Born #OnThisDay in 1887 was Indian mathematician Srinivasa Ramanujan. Though he had very little formal training, his work was substantial, often using methods that were completely novel. In 1918 he became one of the youngest Fellows of the Royal Society. https://t.co/XqvU8okbMK
What happened in China yesterday is massive. I haven’t seen anything as big in my lifetime. Basically Biden said to American engineers working in China in the semiconductor to either resign or be ready to lose their American citizenship. Everyone resigned. Industry collapsed 🤯
लगातार जनसम्पर्क
साथियों नमस्कार 🙏🏻
आज दिनांक 4 मार्च 2022 को * प्रेम नगर * E * ब्लॉक * में डोर टू डोर परचार किया 1
आने वाले निगम चुनाव में बटन दबेगा झाड़ू पर 1
श्रीमती मीना यादव
वार्ड 43 S नजफगढ़
इस वर्ष ‘महिला दिवस’ का बहुत ही उत्साह एवम धूमधाम के साथ आयोजित किया जा रहा है l समस्त नारी शक्ति से आह्वान है कि इस कार्यक्रम मे उत्साहजनक भागीदारी सुनिश्चित करें क्योंकि यह आयोजन महिलाओं के द्वारा-महिलाओं के लिये ही है l इस अवसर पर आप सभी सादर आमत्रित हैं l
अन्य राज्यों में एक आम नागरिक के लिए "शून्य बिजली बिल" के बारे में सोचना भी कल्पना से परे है, लेकिन दिल्ली सरकार की नीतियों से लाखों दिल्लीवासी लाभान्वित हो रहे हैं। @ArvindKejriwal@AamAadmiParty#EkMaukaKejriwalKo