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    Scientists / Open questions

    Alan Baker

    Number theory; transcendental numbers

    1970 Fields Medal

    10 questions

    1. Open directions of Baker's effective program for two-variable Diophantine equations: effective resolution beyond the Thue equation, optimal effective bounds, and effective irrationality exponents

    2. The missing normative bridge in the practice-based anti-nominalist argument: from mathematical acceptability to philosophers' epistemic entitlement

    3. Stronger mathematics for fewer concrete commitments: the extent, case standing, nominalist replicability, and normative weight of the parsimony trade-off in mathematical explanations in science (Baker 2016)

    4. Rational Justification of Quantitative Parsimony in Non-Additive Cases and the Scope of Its Applicability

    5. Closing the open avenues of SPIR-V formal cross-checking and CFG fleshing: the memory model, barrier-aware strategies, and general-purpose compilers

    6. Cellular basis and optimization of impaired hepatitis B vaccine responses in chronic kidney disease

    7. Sharpening effective upper bounds for integer solutions of the Mordell equation y2=x3+ky^2 = x^3 + k

    8. The Multiple-Foundations Challenge to the Indispensability Argument: Can the Indispensable Role of Mathematics in Science Determine Which Mathematical Objects Exist?

    9. Maturing the bonded repair coupon (BRC) torsion proof test to TRL 6 prototype application for through-life bond-integrity assurance of adhesively bonded aircraft repairs

    10. Coupling plant growth dynamics with nickel uptake in hyperaccumulator phytoextraction: mechanistic model development, experimental test of the growth-phase uptake hypothesis, and translation to field conditions

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