March 13, 2022

Yevamot 5

Much of yesterday, today’s (Yevamot 5), as well as the upcoming dapim are dedicated to the topic of proof, and specifically, proof for the halacha that a positive mitzvah (otherwise known as a מצות עשה) can override a negative mitzvah (otherwise known as a מצות לא תעשה).
And why is this the focus of our discussion? Because there is a biblical prohibition of a man marrying his brother’s wife, which is then overridden in the case of Yibbum where a man ‘marries’ his brother’s wife.
In terms of today’s daf, a proof is found for the overall principle from the juxtaposition of the mitzvah of tzitzit with the prohibition of sha’atnez (see Devarim 22:11-12) from where we learn that the positive mitzvah of tzitzit overrides the negative mitzvah of sha’atnez. However, the question to which the Gemara then turns is how do we know that this same calculus applies when dealing with a more severe negative mitzvah such as the relationship between a Yavam and a Yevama?
The pursuit of this proof spans over numerous dapim. However, I would like to make mention to one line of enquiry in our daf where it is suggested that while no singular biblical source may exist to provide the necessary proof, תיתי מתרתי – ‘perhaps it can be deduced from two?’, meaning that perhaps evidence can be drawn from two different sources which, together, may be sufficient to prove this conclusion. And when I read this, I thought back to a very different pursuit of a very different proof.
You may or may not know the story of Andrew Wiles’ proof of Fermat’s Last Theorem, or how his drive to pursue a proof led him to work in isolation for six years to try and solve this incredibly difficult problem. Yet it was when he shared him proof in 1993 to great acclaim that it was soon discovered that the proof contained a flaw in one area which, notwithstanding the incredible creativity demonstrated in all the work he had done, meant that his proof was incomplete.
Wiles tirelessly tried and failed for over 14 months to repair his proof, and then, just over a year after first sharing his proof, and just before he was about to give up, he had a revelation: “Suddenly, totally unexpectedly, I had this incredible revelation. I realised that, although the Kolyvagin-Flach method wasn’t working completely, it was all I needed to make my original Iwasawa theory work.” As Simon Singh explains in his book on the topic, ‘Iwasawa theory on its own had been inadequate. The Kolyvagin-Flach method on its own was also inadequate. Together they complemented each other perfectly. It was a moment of inspiration that Wiles will never forget. As he recounted these moments, the memory was so powerful that he was moved to tears: “It was so indescribably beautiful; it was so simple and so elegant. I couldn’t understand how I’d missed it.”’
At times we often look for simple and singular solutions to our problems, and when we do so, we often look towards one source with the hope that it can provide us with all that we need. But as Wiles’ story demonstrates, sometimes it takes more than one source to help us reach the conclusion and find the ‘proof’ that we are looking for, which means that there can be times when we miss a solution that is staring right at us.
From here we should learn that תיתי מתרתי – ‘perhaps it can be deduced from two?’ isn’t only a suggestion that can be applied to Talmudic proofs or mathematical proofs, but also to other aspects of life as well – and sometimes the right solution that we need requires the fusing of forces, inspiration and wisdom from more than one singular source.
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