Clergyman's

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“Just as Weil's conjectures were about counting solutions to equations in a situation where the number of solutions is known to be finite, the BSD conjecture concerns the simplest class of polynomial equations—elliptic curves—for which there is no simple way to decide whether the number of solutions is finite or infinite.”

— Michael Harris (mathematician)

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“Just as Weil's conjectures were about counting solutions to equations in a situation where the number of solutions is known to be finite, the BSD conjecture concerns the simplest class of polynomial equations—elliptic curves—for which there is no simple way to decide whether the number of solutions is finite or infinite.”
— Michael Harris (mathematician)

“Langlands' life has been by no means as extravagant as Grothendieck's, but his romanticism is evident to anyone who reads his prose; the audacity of his program, one of the most elaborate syntheses of conjectures and theorems ever undertaken, has few equivalents in any field of scholarship.”

— Michael Harris (mathematician)

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“Langlands' life has been by no means as extravagant as Grothendieck's, but his romanticism is evident to anyone who reads his prose; the audacity of his program, one of the most elaborate syntheses of conjectures and theorems ever undertaken, has few equivalents in any field of scholarship.”
— Michael Harris (mathematician)

“Langlands and Grothendieck are both Giants by any measure, and both were consciously successors of Galois.”

— Michael Harris (mathematician)

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“Langlands and Grothendieck are both Giants by any measure, and both were consciously successors of Galois.”
— Michael Harris (mathematician)

“Within mathematics itself, Voevodsky's proposal, if adopted, will create a new paradigm. In his “fairy tale” and some of his other papers, Langlands made deft use of categories and even 2-categories, but number theory is only superficially categorical, and so is the Langlands program. In the event that Univalent Foundations could shed light on a guiding problem in number theory — the Riemann hypothesis or the Birch Swinnerton-Dyer conjecture, which is not so far removed from Voevodsky's motives — then we could easily see Grothendieck's program absorbing the Langlands program within Voevodsky's new paradigm.”

— Michael Harris (mathematician)

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“Within mathematics itself, Voevodsky's proposal, if adopted, will create a new paradigm. In his “fairy tale” and some of his other papers, Langlands made deft use of categories and even 2-categories, but number theory is only superficially categorical, and so is the Langlands program. In the event that Univalent Foundations could shed light on a guiding problem in number theory — the Riemann hypothesis or the Birch Swinnerton-Dyer conjecture, which is not so far removed from Voevodsky's motives — then we could easily see Grothendieck's program absorbing the Langlands program within Voevodsky's new paradigm.”
— Michael Harris (mathematician)

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