Thanks, it's interesting and gives some suggestive information about the motivations concerning navigation and calendrical reform.
It has some severe weaknesses when trying to make the case for influence on mathematics, though.
The authors mention Pell's equation x^2+Ny^2=1, and the method given by Bhaskara II to find solutions x,y for arbitrary N (though others note the method was given earlier by Jayadeva).[0] Bhaskara gives the example of N=61. Fermat, in a letter to his friendly rival Frenicle, also gives the example N=61 as a challenge. Now, if 61 were arbitrary in this context, then this would be something like a smoking gun showing almost certain influence. However, 61 is very special here, because the smallest solutions x and y that satisfy the equation are suddenly much larger for 61 than for any smaller N (they're of order 10^10). The authors of the paper don't mention this crucial detail. Fermat also challenges his pal with N=109, which has similarly huge minimal solutions (order 10^15), and which Bhaskara does not give. Fermat writes that he's chosen smallish values of N, "pour ne vous donner pas trop de peine," so he's obviously chosen these values precisely because they're fiendishly difficult, and that's no doubt why Bhaskara also chose 61 as an example, and that's adequate explanation for why the same value shows up in the two places. Fermat had been working on number theory for some decades prior to this point, and his correspondence shows him working through simpler versions of this and related problems, making many original contributions along the way.[0]
The example the authors give about influence on calculus has similar weaknesses. The example they give involves using the sum of the kth powers to integrate x^k. They write that "the formula had no natural epistemological basis in European mathematics," which almost made me spit out my tea because it suggests the authors haven't heard of Archimedes, who used exacly this method with k=2 to give his quadrature of the parabola, and this was well known in Europe at the time (although his works had only really been rediscovered in Europe in the 1500s). The Arab mathematician Al-Haytham had extended the method with k=1,2,3, and 4 in the 10-11th cenury, Cavalieri in 1635 had calculated up to k=9 and conjectured the integral was (1/(k+1))x^(k+1), before Fermat, Pascal, and Roberval gave their proofs of this general relation.[1][2] This last point especially means I don't understand what the authors of the paper mean when they say "the European mathematicians were unable to prove the formula or provide a rigorous rationale for it within their epistemology." ... They did give proofs, and what they were doing was completely intelligible within the historical development leading up to that time.
These are the points I know about, and they don't fill me with confidence about the authors' other judgements.
[0] Andre Weil 1984 Number Theory: An approach through history (ch.1 section 9 mentions Jayadeva and see ch.2 on Fermat, esp. sections 12 and 13)
[1] Edwards 1979 The Historical Development of the Calculus (p.109ff.)
[2] Stillwell 2010 Mathematics and its History (section 9.1)
It has some severe weaknesses when trying to make the case for influence on mathematics, though.
The authors mention Pell's equation x^2+Ny^2=1, and the method given by Bhaskara II to find solutions x,y for arbitrary N (though others note the method was given earlier by Jayadeva).[0] Bhaskara gives the example of N=61. Fermat, in a letter to his friendly rival Frenicle, also gives the example N=61 as a challenge. Now, if 61 were arbitrary in this context, then this would be something like a smoking gun showing almost certain influence. However, 61 is very special here, because the smallest solutions x and y that satisfy the equation are suddenly much larger for 61 than for any smaller N (they're of order 10^10). The authors of the paper don't mention this crucial detail. Fermat also challenges his pal with N=109, which has similarly huge minimal solutions (order 10^15), and which Bhaskara does not give. Fermat writes that he's chosen smallish values of N, "pour ne vous donner pas trop de peine," so he's obviously chosen these values precisely because they're fiendishly difficult, and that's no doubt why Bhaskara also chose 61 as an example, and that's adequate explanation for why the same value shows up in the two places. Fermat had been working on number theory for some decades prior to this point, and his correspondence shows him working through simpler versions of this and related problems, making many original contributions along the way.[0]
The example the authors give about influence on calculus has similar weaknesses. The example they give involves using the sum of the kth powers to integrate x^k. They write that "the formula had no natural epistemological basis in European mathematics," which almost made me spit out my tea because it suggests the authors haven't heard of Archimedes, who used exacly this method with k=2 to give his quadrature of the parabola, and this was well known in Europe at the time (although his works had only really been rediscovered in Europe in the 1500s). The Arab mathematician Al-Haytham had extended the method with k=1,2,3, and 4 in the 10-11th cenury, Cavalieri in 1635 had calculated up to k=9 and conjectured the integral was (1/(k+1))x^(k+1), before Fermat, Pascal, and Roberval gave their proofs of this general relation.[1][2] This last point especially means I don't understand what the authors of the paper mean when they say "the European mathematicians were unable to prove the formula or provide a rigorous rationale for it within their epistemology." ... They did give proofs, and what they were doing was completely intelligible within the historical development leading up to that time.
These are the points I know about, and they don't fill me with confidence about the authors' other judgements.
[0] Andre Weil 1984 Number Theory: An approach through history (ch.1 section 9 mentions Jayadeva and see ch.2 on Fermat, esp. sections 12 and 13)
[1] Edwards 1979 The Historical Development of the Calculus (p.109ff.)
[2] Stillwell 2010 Mathematics and its History (section 9.1)