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Linear Algebra. Chemistry. Physics. Graphing. Upgrade. Calculators. Examples. About. Help. Sign In. Sign Up. Mathematical capabilities were previously believed to emerge in common language models only at a very large scale or require extensive math-related pre-training. This paper shows that the LLaMA-2 7B model with common pre-training already exhibits strong mathematical abilities, as evidenced by its impressive accuracy of 97.7% and 72.0% on the GSM8K and MATH benchmarks, respectively, when ... Take a natural number. If it is odd, multiply it by 3 and add 1; if it is even, divide it by 2. Proceed in the same way with the result x: if x is odd, you calculate 3 x + 1; otherwise calculate x ... The Key to Better Math Education? Explaining Money. March 4, 2024, 3:00 p.m. ET. Illustration by Akshita Chandra/The New York Times; Images by Ilbusca and Sofya Ivanova/Getty Images. +. By Peter ... For many years, I have been collecting math jokes and posting them on my website. 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