| 11. | The first rigorous proof for the discrete case is due to Amiel Feinstein in 1954.
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| 12. | However, mathematicians generally prefer rigorous proofs that do not require an appeal to physical intuition.
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| 13. | Rigorous proofs require proper and more careful treatment of the divergent terms of the harmonic series.
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| 14. | :Here is your rigorous proof.
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| 15. | However, the first mathematically rigorous proof of this fact was obtained only in the 19th century.
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| 16. | A rigorous proof has been given by Bertini and Giacomin in the case of the SOS model.
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| 17. | Basic complex variables ( perhaps not including very rigorous proofs, at least not to begin with ).
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| 18. | According to Knuth a rigorous proof of Faulhaber's formula was first published by Carl Jacobi in 1834.
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| 19. | A rigorous proof of the Parisi solution has been provided in the work of Francesco Guerra and Michel Talagrand.
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| 20. | Nevertheless, the mechanical method was what he used to discover the relations for which he later gave rigorous proofs.
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