Llm Challenge With Petabytes Of Data To Prove Famous Number Theory Conjecture

In my caller article “Piercing nan Deepest Mathematical Mystery” posted here, I paved nan measurement to proving a celebrated multi-century aged conjecture: are nan digits of awesome mathematical changeless specified arsenic π, e, log 2, aliases √2 evenly distributed? No 1 earlier ever managed to beryllium moreover nan astir basal trivialities, specified arsenic whether nan proportionality of ‘0’ aliases ‘1’ exists successful nan binary description s of immoderate of these constants, aliases if it oscillates indefinitely betwixt 0% and 100%.

Here I supply an overview of nan caller model built to uncover heavy results astir nan digit distribution of Euler’s number e, talk nan latest developments, stock a 10x faster type of nan code, and characteristic caller imaginable investigation areas successful LLMs, AI, quantum dynamics, precocious capacity computing, cryptography, dynamical systems, number mentation and more, arising from my discovery. Perhaps nan astir absorbing portion is testing LLMs and different AI devices to measure their reasoning capabilities connected a fascinating mathematics problem pinch nary solution posted anywhere.

The LLM challenge

You tin usage immoderate AI tool. In my paper, I besides mention alternatives to LLMs, but each of them trust connected heavy neural networks. The extremity is not to inquire AI to lick a very reliable problem and show that it cannot. Instead, you want to supply arsenic galore hints arsenic possible, each nan insights already uncovered by quality intelligence, to thief it succeed. Then measurement occurrence according to immoderate metrics and comparison nan capacity of various devices connected their expertise either to travel up pinch a last impervious aliases observe deeper insights and formulas that will thief a quality finalize nan impervious of a new, seminal result.

My first experiments propose that Grok and DeepSeek do amended connected nan first questions I asked, compared to Perplexity aliases OpenAI. While I picture a 2.5 petabytes dataset, immoderate instrumentality that tin do amended pinch overmuch little – opportunity a terabyte – should get a overmuch higher rating.

The questions I inquire screen galore aspects of nan problem. For instance, 1 of them consists successful assessing if nan digit sum usability is gap-free arsenic successful Figure 1 (I expect nan reply to beryllium positive), aliases if we look a business for illustration Figure 2. The second would make a last impervious much complicated. The extremity successful nan extremity is to get a elemental look capable to make each nan exemplary parameters. Better, beryllium that nan look successful mobility is correct, frankincense formally proving a ground-breaking consequence regarding nan digits of e.

Access nan paper, Python code, and dataset

The 13-page PDF pinch galore illustrations is disposable (for free) arsenic insubstantial 52, here. It links to a subset of nan full dataset connected GitHub. It besides features accelerated Python codification (also pinch nexus to GitHub) to woody pinch gigantic numbers larger than 2n + 1 astatine powerfulness 2n pinch n = 105, uncover patterns successful their digit sum function, arsenic good arsenic nan questions to inquire to AI and LLMs, nan applications, really to make nan afloat dataset, and state-of-the-art investigation and references connected nan topic.

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About nan Author

Vincent Granville is simply a pioneering GenAI scientist, co-founder at BondingAI.io, nan LLM 2.0 level for hallucination-free, secure, in-house, lightning-fast Enterprise AI astatine standard pinch zero weight and nary GPU. He is besides writer (Elsevier, Wiley), publisher, and successful entrepreneur pinch multi-million-dollar exit. Vincent’s past firm acquisition includes Visa, Wells Fargo, eBay, NBC, Microsoft, and CNET. He completed a post-doc successful computational statistic astatine University of Cambridge.