How did Imam al-Bukhaari collect 600,000 hadiths in 16 years?

Firstly:

This calculation and estimation that you mention is not correct, and is not in accordance with the real life of Imam al-Bukhaari. That is for several reasons, as follows:

-1-

 Sixteen years is the period that he spent in compiling his book as-Saheeh, not the length of time he spent in seeking and memorizing hadith.

Al-Khateeb al-Baghdadi said in Taareekh Baghdad (2/333), with his isnaad from ‘Abd ar-Rahmaan ibn Rasaayin al-Bukhaari: I heard Muhammad ibn Ismaa‘eel al-Bukhaari say: I compiled my book as-Sihaah in sixteen years; I selected the sound hadiths from among six hundred thousand hadiths.

So this number of six hundred thousand hadiths is the total of what he collected and acquired from the time when he first began to seek and study hadiths until he began to write his book as-Saheeh, from which he chose hadiths after that. During the sixteen-year period mentioned, he spent time choosing what to include in as-Saheeh.

His seeking and studying of hadith began in childhood.

Al-Khateeb al-Baghdadi narrated in Taareekh Baghdaad (2/324-325) with his isnaad from Abu Ja‘far Muhammad ibn Abi Haatim al-Warraaq an-Nahwi that he said: I said to Abu ‘Abdillah Muhammad ibn Ismaa‘eel al-Bukhaari: How did you start to seek hadith? He said: I was inspired to memorise hadith when I was still in the kuttaab (school).

He said: How old were you at that time?

He said: Ten years old or less. Then I finished from the kuttaab after the age of ten, and I started to go and learn from ad-Daakhili and others.

When I reached the age of sixteen, I memorized the books of Ibn al-Mubaarak and Wakee‘, and I learned the words of other scholars…

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Al-Bukhaari was blessed with a strong memory, as he was able to memorise things quickly. Hence he collected knowledge to an extent that no one else did. This is according to the consensus of the scholars of his own era, as they gave him precedence over many of the scholars of his time, to the extent that some of them even gave him precedence over Imam Ahmad ibn Hanbal.

Ibn Katheer (may Allah have mercy on him) said:

They stated that he would read a book once and memorise its contents with a single glance. The reports to that effect are many.

The scholars of his time, including his shaykhs and peers, praised him. Imam Ahmad said: Khurasan never produced a scholar like him. ‘Ali ibn al-Madeeni said: al-Bukhaari never saw anyone else like himself.

Mahmood ibn an-Nadr Abu Sahl ash-Shaafa‘i said: I went to Basrah, Syria, the Hijaz and Kufah, and I saw how, every time mention was made of Muhammad ibn Ismaa‘eel al-Bukhaari, their scholars admitted that he was superior to them in knowledge.

Al-Fallaas said: Any hadith that al-Bukhaari does not know is not a hadith…

Some of them gave him precedence in the fields of fiqh and hadith over Imam Ahmad ibn Hanbal and Ishaaq ibn Raahawayh…

Abu Muhammad ‘Abdullah ibn ‘Abd ar-Rahmaan ad-Daarimi said: Muhammad ibn Ismaa‘eel al-Bukhaari is the most intelligent of us, the most knowledgeable, the most well-versed and the one who strove the hardest in seeking knowledge.

Someone else said: I saw Muhammad ibn Yahya adh-Dhuhali asking al-Bukhaari about names, kunyahs and deficiencies [in narration], and he answered readily, as if he was reciting Qul huwa Allahu ahad [Soorat al-Ikhlaas].

Ibn Khuzaymah said: I never saw anyone under the canopy of heaven who was more knowledgeable of the hadith of the Messenger of Allah (blessings and of Allah be upon him) and had memorized more hadiths than Muhammad ibn Ismaa‘eel al-Bukhaari.

If we wanted to list all the accolades that the leading scholars gave to his memory, precision, deep knowledge, understanding, piety and asceticism, it would take us a very long time." (Al-Bidaayah wa’n-Nihaayah  14/529-531).

In addition to his speed in memorizing, strong memory and complete devotion to the science of hadith, he was not distracted from his study by trade, work or buying and selling, because Allah, may He be exalted, granted him provision. Taking all of that into account, it is not far-fetched to suggest that he was able to memorise this huge number of hadiths.

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This number includes many repeated hadiths. One hadith may be counted as ten hadiths because of its having many isnaads.

Secondly:

The fact that his original manuscripts did not survive, in which he collected these hadiths during his pursuit of knowledge, should not cause any confusion, because the knowledge of the scholars that usually survives is what he teaches to his students or includes in his books, which he then teaches to his students, and they transmit it to those who come after them, and thus the scholars learn it and transmit it generation after generation.

Hence his books – such as as-Saheeh, al-Adab al-Mufrad, at-Taareekh and others – have reached us because he taught them to the people and to his students, and the scholars are still narrating them, teaching them, studying them and transmitting them among themselves, since the time when al-Bukhaari wrote his Saheeh and up until the present day. Look at as-Saheeh and study what it contains, and ignore this nonsense and specious arguments.

And Allah knows best.