The Role of Mathematics in Artificial Intelligence and Its Applications

Krisn Pratap Meena

doi:10.31149/ijot.v5i10.4842

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Krisn Pratap Meena Associate Professor, Department of Mathematics, S.R.R.M. Govt. College, Nawalgarh, Rajasthan, India

Vol. 5 No. 10 (2023): International Journal on Orange Technologies (IJOT)

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May 31, 2025

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Artificial intelligence (AI) is revolutionizing industries and our lives at an unprecedented rate, and mathematics plays a fundamental role in this progress. In this article, we explore the vital role of mathematics in AI, including the innovative contributions of mathematicians, the challenges they face, and the opportunities for applied mathematicians in this dynamic field.

1. Google (2016).
2. Copeland, J (Ed.) (2004). The Essential Turing: the ideas that gave birth to the computer age. Oxford: Clarendon Press. ISBN 0-19-825079-7.
3. Dartmouth workshop:
 Russell & Norvig (2021, p. 18)
 McCorduck (2004, pp. 111–136)
 NRC (1999, pp. 200–201)
The proposal:
 McCarthy et al. (1955)
4. Successful programs the 60s:
 McCorduck (2004, pp. 243–252)
 Crevier (1993, pp. 52–107)
 Moravec (1988, p. 9)
 Russell & Norvig (2021, pp. 19–21)
5. Funding initiatives in the early 80s: Fifth Generation Project (Japan), Alvey (UK), Microelectronics and Computer Technology Corporation (US), Strategic Computing Initiative (US):
 McCorduck (2004, pp. 426–441)
 Crevier (1993, pp. 161–162, 197–203, 211, 240)
 Russell & Norvig (2021, p. 23)
 NRC (1999, pp. 210–211)
 Newquist (1994, pp. 235–248)
6. First AI Winter, Lighthill report, Mansfield Amendment
 Crevier (1993, pp. 115–117)
 Russell & Norvig (2021, pp. 21–22)
 NRC (1999, pp. 212–213)
 Howe (1994)
 Newquist (1994, pp. 189–201)
7. Second AI Winter:
 Russell & Norvig (2021, p. 24)
 McCorduck (2004, pp. 430–435)
 Crevier (1993, pp. 209–210)
 NRC (1999, pp. 214–216)
 Newquist (1994, pp. 301–318)
8. Deep learning revolution, AlexNet:
 Goldman (2022)
 Russell & Norvig (2021, p. 26)
 McKinsey (2018)
9. Toews (2022).
10. Frank (2022).
11. Artificial general intelligence:
 Russell & Norvig (2021, pp. 32–33, 1020–1021)
Proposal for the modern version:
 Pennachin & Goertzel (2007)
Warnings of overspecialization in AI from leading researchers:
 Nilsson (1995)
 McCarthy (2007)
 Beal & Winston (2009)
12. Russell & Norvig (2021, §1.2)
13. Problem solving, puzzle solving, game playing and deduction:
 Russell & Norvig (2021, chpt. 3–5)
 Russell & Norvig (2021, chpt. 6) (constraint satisfaction)
 Poole, Mackworth & Goebel (1998, chpt. 2,3,7,9)
 Luger & Stubblefield (2004, chpt. 3,4,6,8)
 Nilsson (1998, chpt. 7–12)
14. Uncertain reasoning:
 Russell & Norvig (2021, chpt. 12–18)
 Poole, Mackworth & Goebel (1998, pp. 345–395)
 Luger & Stubblefield (2004, pp. 333–381)
 Nilsson (1998, chpt. 7–12)
15. Intractability and efficiency and the combinatorial explosion:
 Russell & Norvig (2021, pp. 21)
16. Psychological evidence of the prevalence sub-symbolic reasoning and knowledge:
 Kahneman (2011)
 Dreyfus & Dreyfus (1986)
 Wason & Shapiro (1966)
 Kahneman, Slovic & Tversky (1982)
17. Knowledge representation and knowledge engineering:
 Russell & Norvig (2021, chpt. 10)
 Poole, Mackworth & Goebel (1998, pp. 23–46, 69–81, 169–233, 235–277, 281–298, 319–345)
 Luger & Stubblefield (2004, pp. 227–243),
 Nilsson (1998, chpt. 17.1–17.4, 18)
18. Smoliar & Zhang (1994).
19. Neumann & Möller (2008).
20. Kuperman, Reichley & Bailey (2006).
21. McGarry (2005).
22. Bertini, Del Bimbo & Torniai (2006).
23. Russell & Norvig (2021), pp. 272.
24. Representing categories and relations: Semantic networks, description logics, inheritance (including frames and scripts):
 Russell & Norvig (2021, §10.2 & 10.5),
 Poole, Mackworth & Goebel (1998, pp. 174–177),
 Luger & Stubblefield (2004, pp. 248–258),
 Nilsson (1998, chpt. 18.3)