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May 29

Prove or disprove

Prove or disprove: All even numbers >=4 can be written as $2^{m}+3^{n}+p$ with m>=0, n>=0, and p prime. 61.224.134.44 (talk) 11:20, 29 May 2023 (UTC)[reply]

OEIS:A303702 gives the number of solutions for each even number and conjectures there are always solutions. It states a low search limit of 3×10⁹. PrimeHunter (talk) 12:59, 29 May 2023 (UTC)[reply]

Prove or disprove:

All odd numbers >3 can be written as sum of “twice a triangular number” (>0) and a prime.
All odd numbers >3 can be written as sum of “twice a square number” (not necessary >0, the square number 0 is allowed, or 17 cannot be written as this form) and a prime.
All odd numbers >3 can be written as sum of “twice a generalized pentagonal number” (>0) and a prime.

2001:B042:4005:47FA:78CF:2178:A4F1:85F0 (talk) 13:39, 29 May 2023 (UTC)[reply]

For question 1, see OEIS A144590. No numbers are known that cannot be written as such. GalacticShoe (talk) 15:03, 29 May 2023 (UTC)[reply]

For question 2, see OEIS A046923. In particular, note that 5777 and 5993 cannot be written as two times a square plus a prime. Testing up to 1,000,000 reveals no other numbers that cannot be written as such. GalacticShoe (talk) 14:56, 29 May 2023 (UTC)[reply]

The theory behind AI

What is the mathematical theory behind AI? Graph theory or statistics? 2A02:908:424:9D60:2463:DEAC:9F20:EBA9 (talk) 16:55, 29 May 2023 (UTC)[reply]

Um. Big subject. Have you tried reading Artificial intelligence for starters to get a basic grounding? NadVolum (talk) 17:07, 29 May 2023 (UTC)[reply]

If one must select a single area of mathematics (not theory), mathematical optimization is IMO the best (most relevant) choice. There is no unified theory underlying AI. --Lambiam 17:38, 29 May 2023 (UTC)[reply]

This video series, by 3blue1brown, is an excellent overview of the mathematics of artificial neural networks, which form one of the most common ways that machine learning and artificial intelligence works. It provides a surface-level overview of the mathematics, but in a way that gives you plenty of opportunities for further study. --Jayron 32 17:51, 30 May 2023 (UTC)[reply]