Yevamos 61b: A man may not stop trying to have children unless he has children already. Beis Shamai says two boys, and Beis Hillel says a boy and a girl, as the Torah says, “Male and female He created them.”

יבמות סא ע”ב: לא יבטל אדם מפריה ורביה אלא א״כ יש לו בנים. ב״ש אומרים: שני זכרים, וב״ה אומרים: זכר ונקבה, שנאמר: (בראשית ה׳) זכר ונקבה בראם.

A man came to Rabbi Yisroel Reisman and asked the following question. He and his wife were going through the process of IVF and preimplantation genetic testing to select for embryos that were free of genetic disease and were most likely to survive. They already had a boy; so should he tell the doctors to select a girl so that he could fulfill the mitzvah of “be fruitful and multiply”?  

“There are actually two questions here,” said Rabbi Reisman. “Let’s start by asking if you can fulfill the mitzvah of having children through IVF at all.”

The Chelkas Mechokek (Even Hoezer 1:8) says: “When a woman gets pregnant from going to the bath after a man, I am not certain whether that man fulfills the mitzvah of having children.”

The Beis Shmuel 1:10 says there is proof from the Rabbeinu Peretz quoted by the Bach (and later quoted by the Taz in Yoreh Deah 195:7). Rabbeinu Peretz was asked: why is a Jewish woman particular not to sleep on another man’s sheets, out of fear that she might get pregnant from that man’s seed, but she has no problem sleeping on her husband’s sheets when she is a niddah? If she gets pregnant from her husband’s seed, wouldn’t the child have the spiritual disadvantage of being a “ben niddah”? Rabbeinu Peretz replied that since the child was not born from a forbidden sexual act, he is not a “ben niddah,” and even if he were born from another man’s seed, he would not be a mamzer. The real reason to avoid another man’s sheets is so that the child knows who his father is, so that he doesn’t end up marrying his sister.  We see from Rabbeinu Peretz that a child born through IVF is halachically the son of the sperm donor. If so, that sperm donor (in our case, the husband) fulfills the mitzvah to have children.

However, the commentary on Even Hoezer 1 attributed to the Taz (actually written by the Chacham Tzvi) rejects this proof. Perhaps Rabbeinu Peretz said this only as a stringency (that such a child marrying his sister from the sperm donor’s side might be a sin) but he was not certain enough about it to be lenient and say that this is called fulfilling “be fruitful and multiply.” Furthermore, if the woman got pregnant from the bathwater, the man took no action toward having a child and so he would not get the mitzvah. (This last argument would not apply to IVF or artificial insemination, where the man takes deliberate action to make it happen.)

The Minchas Chinuch (Mitzvah 1, Section 26 in the Machon Yerushalayim edition) quotes the Beis Shmuel position that one does fulfill the mitzvah through a bath, and comments that this makes sense based on the concept he developed earlier that the mitzvah of having children is not action-based; it’s result-based. The action (of having marital relations) is only a preparation for the mitzvah. This explains why, if one had children and they later died, he did not do the mitzvah (Yevamos 62a, opinion of Rabbi Yochanan, brought as halacha in EH 1:6). Why not? Didn’t he do the mitzvah already? The answer is that it is result-based. Similarly, if a non-Jew had children with his non-Jewish wife and then he and the children later converted, he fulfills the mitzvah (ibid. 1:7). Although the usual rule is that doing a mitzvah at a time when you are exempt from it is not called fulfilling the mitzvah, here we look at the result, and the result is that he has children.

Reb Moshe (EH 2:18) adds that even if the mitzvah of having children is an action-based mitzvah like all other mitzvos, we can explain that having a boy and a girl is not the goal of the mitzvah; it’s an exemption from the mitzvah. That’s why the Mishnah in Yevamos doesn’t say, “How many children is a man obligated to have?” It says, “A man may not stop trying to have children unless he has children already.” Therefore, the convert fulfills the mitzvah with his children born before the conversion, because having a son and daughter, no matter how they were born, exempts you from the mitzvah. Similarly, if one had children but they later died, his exemption from the mitzvah ends and he must have more children. Accordingly, children born through IVF would also be an exemption.

“Your second question,” continued Rabbi Reisman, “is, assuming that you do fulfill the mitzvah this way, should you select for a girl?

“Let me tell you a story. When my wife had given birth to seven boys and no girls yet, I asked Rav Pam if I should make a change in the Tefillas Haramban and leave out the request for a boy, or perhaps I should even pray for a girl. Rav Pam said, ‘No. Say the tefillah the normal way, and let Hashem run the world.’

“I said: ‘If my tefillah doesn’t change anything, and Hashem runs the world the way He wants, then why say it at all? So obviously, we pray because Hashem sometimes answers tefillos. If so, why shouldn’t I pray for a girl?’ Rav Pam replied, ‘Our hishtadlus for a mitzvah should only be by doing things the natural way, not praying.’ I felt uncomfortable pushing the issue because Rav Pam himself only had sons.

Rabbi Reisman concluded, “I tell you the same thing Rav Pam said: don’t do anything unnatural in order to get the mitzvah. Tell the doctors to implant the most viable embryos, whether they’re male or female.”

Source: Rabbi Reisman, shiur on YD 195

[How could Rav Pam say that there is no praying for mitzvos? Don’t some people daven on Tu Bishvat to get a good esrog? And the chazzan says the “Hineni” asking for Hashem’s help in leading the tzibur in prayer.

Perhaps Rav Pam meant to say something along the lines of the Igros Moshe quoted above. Having a son and daughter is not the mitzvah; it’s just the ptur from the mitzvah. You’re not obligated to try to become potur. Your job is to make an effort to do the mitzvah naturally. Hashem runs the world, and He will decide if you will be exempt or not.

We could ask, however, from the Gemara which says (Berachos 54a): If a man prays, “May it be Your will that my wife give birth to a boy,” when she is already pregnant, then his prayer is in vain. The implication is that he should say this prayer earlier, when she is not yet pregnant. Why is he allowed to pray for a boy? Let Hashem run the world! The answer is that he is not praying for a boy in order to fulfill the mitzvah. The Gemara isn’t talking about someone who already has a girl and therefore wants a boy. It’s talking about someone who wants a boy for personal reasons – in order to do the mitzvos of bris milah and pidyon haben, or in order to have someone to teach Torah to, or to say kaddish for him. The Tefillas Haramban is also written for people who want a boy for personal reasons. It has nothing to do with the mitzvah of having children.]  

Yevamos 45b: The final halacha is: if a non-Jew or a slave fathered a child with a Jewish woman, the child is kosher, whether the woman was single or married.

יבמות מה ע”ב והלכתא: עובד כוכבים ועבד הבא על בת ישראל ־ הולד כשר, בין בפנויה בין באשת איש.

Cindy was a student at Boston University who became closer to her Jewish roots under the influence of the Bostoner Rebbe and Rebbetzin. She frequently attended the Chassidic Center, often came to help the Rebbetzin with household chores, and did chesed for mothers in the community. With time, Cindy became engaged to a boy named David she had met at the Chassidic center, and all agreed that theirs was a perfect match. Both were newly religious and thoroughly committed to their Judaism and to each other.

One evening, she called the Rebbe and sobbed, “Rebbe, I’m in trouble. I’m supposed to get married at the end of the month, and I just learned that I’m… that I’m a mamzer!”

“Cindy,” the Rebbe said gently, “I don’t know why you suspect that you might not be a legitimate Bas Yisroel, but mamzerus is a somewhat esoteric and very technical halachic term and is often misinterpreted. Why don’t you come over and we’ll talk about it.”

The Rebbetzin escorted Cindy into the study and placed a box of Kleenex at her side. Cindy made quick work of the tissues even before she commenced her tale of woe. Her sobbing plunged them all into a state of deep despair. The saga was but four hours old, yet its ramifications would affect and conceivably ruin a lifetime.

Earlier that afternoon at her university, a noted Torah scholar had lectured on the sanctity of marriage. In the course of his talk, he had explained that the term mamzer does not necessarily apply to a child born out of wedlock, a common misconception, but to one born of a woman who has remarried without receiving a get from her previous husband. “Even before the lecture was over,” Cindy related, “I rushed out to call home. I confronted my mother and insisted that she tell me if her first husband had given her a get. As you know, Rebbe, my mother is not at all religious, and I doubt that she’d ever bothered with a get. She wouldn’t answer my question and when I pressed her, she became very flustered. ‘Why do you want to know?’ she asked. ‘Because it affects me in the most serious way,’ I said. I begged her to be honest with me because my future depended upon her answer. But she reacted with a tirade against religious observance. “You chose this absurd way of life, this cult of yours. Now your belief will bury you!”

Although the Rebbe had had to deal with terrible devastating situations like this in the past, experience didn’t make it any easier. The plight of this sweet young girl, a neshamala who had practically grown up in his home, was like a knife in his heart. The Rebbetzin was dabbing at her eyes, and the Rebbe too was on the verge of tears. He entreated the Ribono Shel Olam to spare Cindy from the tragic fate of being a mamzer. He prayed for an eitzah, anything that might confirm her legitimacy.

After questioning Cindy for several minutes, the Rebbe thought it might be more productive if he were to speak to Cindy’s father, Mr. George Fried, instead. “Are you still in contact with your father?” he asked. “No, Rebbe, no one knows where he is. He has simply vanished. Last year I wanted to send him a birthday card, so I called my grandparents, but even they –“  

“Grandparents?” the Rebbe cried excitedly. “Your paternal grandparents, they’re alive? Where do they live?” “In Dallas,” Cindy replied, startled by the Rebbe’s keen interest in this detail. The Rebbe dialed the number and an elderly Mr. Fried answered.

The Rebbe identified himself, explaining that he was calling about a very important matter. Cindy’s grandfather responded to all of the Rebbe’s questions but made no significant contribution. Then the Rebbe asked, “Did your son have a bar mitzvah?” Instead of replying right away with a simple yes or no, Mr. Fried covered the mouthpiece and a muffled conversation between him and presumably his wife took place. Finally, the grandmother got on the line and told the Rebbe that George had been confirmed at the local temple when he was thirteen. She passed the phone back to her husband.

Something indefinable prompted the Rebbe to ask the next question. “Was that the same temple where he had his bris, that is, his circumcision?” Silence followed and then some awkward hemming and hawing. The Rebbe asked Cindy if she would please step out of the study so that he might continue the conversation in private. He explained to the Frieds that while under normal circumstances he would never pry into someone’s personal life, these were not normal circumstances. “Cindy’s future is at stake,” the Rebbe declared, and paused for the words to sink in. Only when he was certain that they grasped the gravity of the situation did he proceed to detail his relationship with their granddaughter. “I am a rabbi, he said, a Chassidic rebbe, in fact, if that means anything to you. Will you accept my word that what you tell me I will never reveal to a living soul?”

“Yes, Rabbi,” they said apprehensively. In a somber voice, the Rebbe asked them if, in fact, their son was adopted. They hesitated for a while and the Rebbe implored them to be frank with him. After what seemed an eternity, Mrs. Fried confessed that they had adopted their son at the age of fifteen months. No one, she said, including George himself, was aware of this. She told the Rebbe that although they had wanted to adopt a Jewish baby, they had been unable to get one and had to accept a child whose natural mother was gentile. (The Rebbe later received independent confirmation of this.) The Frieds had never formally converted him to Judaism.

“Boruch Hashem,” the Rebbe sighed and resumed breathing. He could not remember ever being so happy to learn that a Jew was not a Jew. Since George Fried was not Jewish, Cindy was not a mamzer. Mamzeirus applies only to the offspring of a forbidden union between Jews. Cindy could marry David.

Source: The Bostoner, by Hanoch Teller, p. 150