Just like the Qur`an, even the Ahadeeth used to be memorized and transmitted further
For examples :
It was narrated that Samurah bin Jundab said: “There are two pauses in which I memorized from the Messenger of Allah ….[Sunan ibn Majah]
Narrated Abu Huraira: I have memorized two kinds of knowledge from Allah’s Messenger ..[Saheeh al-Bukhaari]
So much so that this was the norm among people, they would first and foremost ask what have you memorized than what have you written?
It was narrated that Abu Al-Hawra’ As-Sa’di said:
“I said to Al-Hasan bin ‘Ali, may Allah be pleased with him: ‘What did you memorize from the Messenger of Allah [sallalahu `alayhi wa sallam]?’ He said: I memorized from him: ‘Leave that which makes you doubt for that which does not make you doubt.'”
[Ref: Sunan an-Nasa’i 5711]
Narrated `Abdullaah bin `Amr: I said: O Messenger of Allaah صلىاللهعليهوسلم Should I write all that I hear from you? He said: “Yes.” I said: Irrespective of whether you are pleased or angry? He said: “Yes! For in either state, I am not allowed to say except the truth.”
[Musnad Ahmad (11/139) and authenticated by Shaikh Ahmad Shaakir]
On the authority of Yahya bin Ayoob from Abu Qubail who narrated from `Abdullaah bin `Amr that he said: We used to be with the Prophetصلى الله عليه وسلم and write whatever he said.
[al-Dhahabee graded it as “Hasan Ghareeb” and it was reported by Sa`eed bin `Ufair (i.e. the chain is good but Sa`eed is the only one reporting it.)]
On the authority of Abu Al-Naḍhar Haamish bin al-Qaasim said, Is-ḥaaq bin Yahyaa narrated on the authority of Mujaahid that he said:
I came to `Abdullaah bin `Amr, and he pushed his scrolls under his head, and prevented me from touching it. I said: You are preventing me from reading from your book? He said: This is the truthful scrolls which I heard directly from the Prophet صلى الله عليه وسلم and there was no one between me and him. So, if I only have the Book of Allaah and these scrolls and al-Wahṫ, then I don’t care of what I miss of this world.[Al-Wahṫ was a huge garden in al- Ṫaaif which belonged to `Abdullaah bin `Amr and it was 3 miles long
[see al-Saheehah al-Albaanee (1/11)].
al-Dhahabee said: `Abdullaah bin `Amr inherited from his father heaped-up treasures of Egyptian gold. He was one of the kings amongst the Sahaabah.[`Amr bin al-`Aas the father of `Abdullaah was the one who had conquered Egypt]
Abdullah ibn Amr reported: I would write down everything I heard from the Messenger of Allah, peace and blessings be upon him, wanting to memorize it, but the Quraish told me not to do it and they said, “Do you write down everything you hear from him? The Messenger of Allah is a human being; he speaks when he is angry and content.” So I stopped writing things down. I mentioned it to the Messenger of Allah and he pointed to his mouth and he said, “Write, for by the one in whose Hand is my soul, nothing comes out of it except the truth.”
[Sunan Abu Dawud, Book of Knowledge, Number 3646, Sahih, Also reported in Tabaqat Ibn Sa’ad , Mustadrak Al Haakim]
Aboo Qaabeel said: We were with ‘Abdullaah ibn ‘Amr ibn al-‘Aas and he was asked which city will be conquered first Constantinople or Rome? So ‘Abdullaah called for a sealed trunk and he said, “Take out the book from it.” Then ‘Abdullaah said, “While we were with the Messenger of Allaah (s.a.w) writing, The Messenger of Allaah (s.a.w) was asked, “Which city will be conquered first, Constantinople or Rome?” So Allaah’s Messenger (s.a.w) said: “The city of Heracilius will be conquered first,” meaning Constantinople
[Saheeh: Musnad Ahmad (2: 176), Sunan ad-Daarimee (1: 126) and Mustadrak al Haakim (3: 422)]
Al-Waleed reported: I said to Abu Amr, “What have you written?” He said, “The sermon which we heard today.”
[Sunan Abu Dawud, Book of Knowledge, Number 3650, Sahih]
Sa’eed Ibn Hilaal narrates that Anas Ibn Maalik (radi-Allaahu ‘anhu) would mention everything he had written by memory; whilst showing us he would say :
I heard this narration from the Messenger of Allaah (sal-Allaahu alayhe wa sallam) myself and I would write it down and repeat it to the Messenger of Allaah (sal-Allaahu ‘alayhe wa sallam) so that he would affirm it.”
[Saaheefa Ibn Humaam (p. 34) from Khateeb al-Baghdaadee and al-Haakim (3/574)]
– 120حَدَّثَنَا أَبُو خَيْثَمَةَ ثنا مُحَمَّدُ بْنُ عَبْدِ اللَّهِ الْأَنْصَارِيُّ، حَدَّثَنِي أَبِي، عَنْ ثُمَامَةَ بْنِ عَبْدِ اللَّهِ، قَالَ: ” كَانَ أَنَسٌ، يَقُولُ: لِبَنِيهِ: يَا بَنِيَّ قَيِّدُوا الْعِلْمَ بِالْكِتَابِ “
Abu Khaithama narrated to us, saying: Muhammad Ibn ‘Abdillaah Al-Ansaaree reported to us, saying: My father  narrated to me from Thumaamah Ibn ‘Abdillaah that he said: “Anas (radyAllaahu ‘anhumaa) used to tell his son: ‘O my son! Secure knowledge by writing.'”
 Shaykh Albanee said : He is `Abdullaah Ibn Al-Muthnaa Ibn ‘Abdillaah Ibn Anas. He was honest yet made many mistakes. This hadeeth has been reported in marfoo’ form as a saying of the Prophet, and it is not authentic. Later, I encountered many paths of narration for the hadeeth reported in marfoo’ form, such that it directs towards the fact that it is saheeh. I have clarified this in Al-Ahaadeeth As-Saheehah (no. 2026).
[Ref: Kitaab al-`Ilm of Abu Khaithama an-Nasa`ee (120)]
Narated By Ash-Sha’bi : Abu Juhaifa said, “I asked Ali, ‘Have you got any book (which has been revealed to the Prophet apart from the Qur’an)?’ ‘Ali replied, ‘No, except Allah’s Book or the power of understanding which has been bestowed (by Allah) upon a Muslim or what is (written) in this sheet of paper (with me).’ Abu Juhaifa said, “I asked, ‘What is (written) in this sheet of paper?’ Ali replied, it deals with The Diyya (compensation (blood money) paid by the killer to the relatives of the victim), the ransom for the releasing of the captives from the hands of the enemies, and the law that no Muslim should be killed in Qisas (equality in punishment) for the killing of (a disbeliever).
[Sahih Bukhaari, Volume 001, Book 003, Hadith Number 111.Also see Volume 004, Book 053, Hadith Number 397, Volume 009, Book 083, Hadith Numbers 040 & 50]
Narated By Warrad : (The clerk of Al-Mughira bin Shu’ba) Muawiya wrote to Al-Mughira: “Write to me a narration you have heard from Allah’s Apostle.” So Al-Mughira wrote to him, “I heard him saying the following after each prayer: ‘La ilaha illal-lahu wahdahu la sharika lahu, lahu-l-mulk wa lahuI-hamd, wa huwa ‘ala kulli Shai-in qadir.’ He also used to forbid idle talk, asking too many questions (in religion), wasting money, preventing what should be given, and asking others for something (except in great need), being undutiful to mothers, and burying one’s little daughters (alive).”
[Sahih Bukhaari, Volume 008, Book 076, Hadith Number 480]
The hadeeth of Abu Shaah was narrated by al-Bukhaari from Abu Hurayrah (may Allaah be pleased with him), who said: ‘When Allaah granted His Prophet (peace and blessings of Allaah be upon him) victory over Makkah, he stood before the people and praised and glorified Allaah, then he said: “Allaah protected Makkah from the elephant and has given authority to His Messenger and the believers over it, so fighting was forbidden for anyone before me, and was made permissible for me for part of a day, and it will not be permissible for anyone after me. Its game should not be chased, its thorny bushes should not be uprooted, and picking up its fallen things is not allowed except for one who makes public announcement for it, and he whose relative is murdered has the option either to accept a compensation for it or to retaliate.” Al-‘Abbas said, “Except Al-Idhkhir (a kind of plant), for we use it in our graves and houses.” The Messenger of Allaah (peace and blessings of Allaah be upon him) said, “Except Al-Idhkhir.” Abu Shaah, a Yemeni, stood up and said, “O Messenger of Allaah! Get it written for me.” The Messenger of Allaah (peace and blessings of Allaah be upon him) said, “Write it for Abu Shaah.”
Narrated Abu Huraira: I said: “O Allah’s Apostle! Who will be the luckiest person, who will gain your intercession on the Day of Resurrection?” Allah’s Apostle said: O Abu Huraira! “I have thought that none will ask me about it before you as I know your longing for the (learning of) Hadiths.The luckiest person who will have my intercession on the Day of Resurrection will be the one who said sincerely from the bottom of his heart “None has the right to be worshipped but Allah.”
قيدوا العلم بالكتاب، قيدوا العلم بالكتاب
As al-Khateeb al-Baghdadi noted in his book Taqyeed al-I’ilm, an as I detailed in paper titled Writing of Hadith, Ali (r.a) used to repeatedly tell the people to write down knowledge. These wordings have also been attributed to `ibn Abbas and Anas ibn Maalik and `Abdullah ibn `Amr and have been authenticated by some and weakened by some. Shaykh Al-Albaanee gives a summary strengthening them combining their routes in Silsilah al-Saheeha 2026 and Saheeh al-Jaami` 4434.
من يشتري مني علما بدرهم
In the same book, Khateeb al-Baghdadi also noted that Ali used to ask the people who would buy knowledge from him for a Dirham . Shaykh Albaanee authenticated this by saying :رجال إسناده ثقات صحيح إن كان علباء
سمعه من علي , In his work : العلم لأبي خيثمة
-149حَدَّثَنَا أَبُو خَيْثَمَةَ ثنا وَكِيعٌ، حَدَّثَنِي الْمُنْذرُ بْنُ ثَعْلَبَةَ، عَنْ عَلْبَاءَ، قَالَ: قَالَ عَلِيٌّ، عَلَيْهِ السَّلَامُ: «مَنْ يَشْتَرِي مِنِّي عِلْمًا بِدِرْهَمٍ؟» قَالَ أَبُو خَيْثَمَةَ يَقُولُ: «يَشْتَرِي صَحِيفَةً بِدِرْهَمٍ يَكْتُبُ فِيهَا الْعِلْمَ»
Abu Khaithama narrated to us, saying: Wakee’ reported to us, saying: Al-Mundhir Ibn Tha’alaba narrated to me from ‘Ilbaa  that he said: ‘Alee (radyAllaahu ‘anhu) said: “Who will buy knowledge from me for a dirham?” Abu Khaithama said: “He means by this: “Buy a piece of paper so that knowledge can be written down on it.”
[Ref: Kitaab al-`Ilm Abu Khaithama an-Nasa`ee (149)  Shaykh Albaanee said : He (‘Ilbaa) is Ibn Ahmar Al-Yushkaree Al-Basree and he was a Taabi’ee of trustworthy and reliable status. Likewise, the rest of the narrators of the chain are all reliable. So it is saheeh, if ‘Ilbaa heard it from ‘Alee, because there is no report mentioned from him on his authority]
A similar narration in al-Mustadrak of al-Haakim says :
أمير المؤمنين ع فقد أخرجه الحاكم رقم 3299/ 3695 وصححهم وصححه الذهبي برقم3736
-3299أخبرني أبو جعفر محمد بن علي الشيباني بالكوفة ، ثنا أحمد بن حازم الغفاري ، ثنا أبو نعيم ، ثنا بسام الصيرفي ، ثنا أبو الطفيل عامر بن واثلة قال : سمعت عليا ، قام فقال سلوني قبل أن تفقدوني ، ولن تسألوا بعدي مثلي ، فقام ابن الكواء فقال : « من الذين بدلوا نعمة الله كفرا وأحلوا قومهم دار البوار ؟ قال : منافقوا قريش قال : فمن الذين ضل سعيهم في الحياة الدنيا وهم يحسبون أنهم يحسنون صنعا ؟ قال : منهم أهل حروراء »
« هذا حديث صحيح عال » « وبسام بن عبد الرحمن الصيرفي من ثقات الكوفيين ممن يجمع حديثهم ولم يخرجاه »
`Ali `alayhis salaam said “ Ask me (oh people about deen) before you loose me
Also reported by Imaam Khateeb al-Baghdadi in Al-Faqeeh
This hadeeth shows how the time of fitan in Koofa emerged to such an extent that `Ali radhiallahu `anhu had to openly proclaim so as to impart the AUTHENTIC knowledge.
يا بني وبني أخي إنكم صغار قوم يوشك أن تكونوا كبارا آخرين، فتعلموا العلم، فمن لم يستطع منكم أن يرويه فليكتبه، وليضعه في بيته
ibn Sa’ad reported in his Tabaqat al-Kubra that Imam Hassan (r.a) gathered his son and nephew and instructed them to write their knowledge if they cannot narrate it:
تذاكروا هذا الحديث وتزاوروا فإنكم إن لم تفعلوا يدرس
Ali (r.a) said in Sunan al-Darimi and Ma’arifat U’ulum al-Hadith by al-Hakim used to advise his followers to study the Hadith and to visit one another to discuss it otherwise it will be gone and lost
)حديث موقوف) أَخْبَرَنَا أَخْبَرَنَا إِسْمَاعِيل بْنُ أَبَانَ ، حَدَّثَنَا يَعْقُوبُ بْنُ عَبْدِ اللَّهِ الْقُمِّيُّ ، حَدَّثَنَا جَعْفَرُ بْنُ أَبِي الْمُغِيرَةِ ، عَنْ سَعِيدِ بْنِ جُبَيْرٍ ، عَنْ ابْنِ عَبَّاسٍ رَضِيَ اللهُ عَنْهُ ، قَالَ : ” تَذَاكَرُوا هَذَا الْحَدِيثَ لَا يَنْفَلِتْ مِنْكُمْ ، فَإِنَّهُ لَيْسَ مِثْلَ الْقُرْآنِ مَجْمُوعٌ مَحْفُوظٌ ، وَإِنَّكُمْ إِنْ لَمْ تَذَاكَرُوا هَذَا الْحَدِيثَ يَنْفَلِتْ مِنْكُمْ ، وَلَا يَقُولَنَّ أَحَدُكُمْ حَدَّثْتُ أَمْسِ فَلَا أُحَدِّثُ الْيَوْمَ ، بَلْ حَدِّثْ أَمْسِ ، وَلْتُحَدِّثْ الْيَوْمَ ، وَلْتُحَدِّثْ غَدًا ” .
`ibn Abbas (r.a) is reported to have said : “Study the Hadith so it does not get forgotten, as it is not like the Quran which is learnt by heart. If you don’t study it, it will slip away from you. Do not say that you have narrated yesterday so you will not narrate today. But say that you have narrated yesterday, you will narrate today and tomorrow as well. ”
[Sunan al-Darimi, Chapter : بَاب مُذَاكَرَةِ الْعِلْمِ See : http://library.islamweb.net/hadith/display_hbook.php?bk_no=137&pid=64071&hid=600]
– 148حَدَّثَنَا أَبُو خَيْثَمَةَ ثنا وَكِيعٌ، عَنْ عِكْرِمَةَ بْنِ عَمَّارٍ، عَنْ يَحْيَى بْنِ أَبِي كَثِيرٍ، عَنِ ابْنِ عَبَّاسٍ، قَالَ: «قَيِّدُوا الْعِلْمَ بِالْكِتَابِ، مَنْ يَشْتَرِي مِنِّي عِلْمًا بِدِرْهَمٍ؟»
Abu Khaithama narrated to us, saying: Wakee’ reported to us, saying: ‘Ikrimah Ibn ‘Amaar reported from Yahyaa Ibn Abee Katheer on the authority of Ibn ‘Abbaas (radyAllaahu ‘anhu) that he said: “Take hold of knowledge by writing and taking notes. Who will buy knowledge from me for a dirham?”
[Ref: Kitaab al-`Ilm Abu Khaithama an-Nasa`ee (148)]
حدثني أبو كثير ، عن أبيه ، قال : أتيت أبا ذر وهو جالس عند الجمرة الوسطى ، وقد اجتمع الناس عليه يستفتونه ، فأتاه رجل ، فوقف عليه ، فقال : ألم ينهك أمير المؤمنين عن الفتيا ؟ فرفع رأسه ، ثم قال : أرقيب أنت علي ، لو وضعتم الصمصامة على هذه -وأشار بيده إلى قفاه- ثم ظننت أني أنفذ كلمة سمعتها من رسول الله -صلى الله عليه وسلم- قبل أن تجيزوا عليّ لأنفذتها .
The above narration is said to show how Abu Dharr (r.a) used to keep narrating and teaching the hadeeth firmly.
أطيلوا كر الحديث لا يدرس
ibn Asakir reported in his Mukhtassar Tarikh Dimashq that Alqama ibn Qays al-Nakha’i (scholar from among the taba’een and pupil of Abd-Allah ibn Mas’ud, died in 62 AH) used to say: Keep narrating the Hadith so it does not get lost.
And ‘Umar bin ‘Abdul ‘Aziz wrote to Abu Bakr bin Hazm,
“Look for the knowledge of Hadith and get it written,as I am afraid that religious knowledge will vanish and the religious learned men will pass away (die). Do not accept anything save the Hadiths of the Prophet. Circulate knowledge and teach the ignorant, for knowledge does not vanish except when it is kept secretly (to oneself).”
(Sahih Bukhari Volume 1:Book #3, Hadith #98)
Alee ibn Muhammad ibn ‘Abdullaah informed us…on the authority of Hammaan ibn Munabbih that he heard Abu Hurayrah saying:
لم يكن أحد من أصحاب النبي ، صلى الله عليه ، أكثر حديثا مني إلا عبد الله بن عمرو فإنه كتب ولم أكتب
“There were none from the companions of the Messenger – صلى الله عليه و سلم – who had more Hadeeth than me except ‘Abdullah ibn ‘Amr ibn al ‘Aass. For indeed he used to write and I never used to write.
[Ref: Khateeb al-Baghdaadi, Taqyeed al ‘Ilm P. 74 -82]
Ahmad ibn Muhammad ibn Ghaalib narrated to us…on the authority of Wahb in Munabbih that his brother said: I heard Abu Hurayrah saying:
سمعت أبا هريرة ، يقول : ما من أصحاب رسول الله ، صلى الله عليه ، أكثر حديثا عنه مني إلا ما كان من عبد الله بن عمرو فإنه كان يكتب وكنت لا أكتب لفظ ابن صالح ، وقال ابن أبي عمر ، حدثنا عمرو
“There are none from amongst the companions of the Messenger – صلى الله عليه و سلم – who have more Hadeeth on his authority than me, except ‘Abdullah ibn ‘Amr ibn al ‘Aass, for indeed he used to write while I never used to write.”
[Ref: Khateeb al-Baghdaadi, Taqyeed al ‘Ilm P. 74 -82]
On the authority of Abu al Qaasim al Hasan ibn al Husayn ibn ‘Alee ibn al Mundhir al Qaadee…on the authority of al Mugheerah ibn Hakeem who heard Abu Hurayrah saying:
ما كان أحد أعلم بحديث رسول الله ، صلى الله عليه ، مني إلا عبد الله بن عمرو فإنه كان يكتب بيده فاستأذن رسول الله ، صلى الله عليه ، في أن يكتب ما سمع منه فأذن له ، فكان يكتب بيده ويعي بقلبه ، وإنما كنت أعي بقلبي
“There was nobody more knowledgeable about the Hadeeth of the Messenger of Allah – صلى الله عليه و سلم – than me, except ‘Abdullah ibn ‘Amr ibn al ‘Aass. He took permission from the Messenger of Allah – صلى الله عليه و سلم – to write what he heard from him, and he gave him permission. So he used to write with his hand and memorize with his heart, while I only used to memorize with my heart.”
[Ref: Khateeb al-Baghdaadi, Taqyeed al ‘Ilm P. 74 -82]
we find in Sunan Abi Dawud:
حدثنا موسى بن إسمعيل حدثنا حماد حدثنا عاصم الأحول عن أبي عثمان النهدي قال كتب عمر إلى عتبة بن فرقد أن النبي صلى الله عليه وسلم نهى عن الحرير إلا ما كان هكذا وهكذا أصبعين وثلاثة وأربعة
Rough translation: …that `Umar ibn al Khattab (r.a) wrote to Utba bin Farqad that the Prophet (pbuh) prohibited the wearing of silk except for this much (the size of a finger, two or three). [This chain is authentic.]
`Umar ibn al-Khattab radhiallahu `anhu is also reported to have said:
قَيِّدُوا الْعِلْمَ بِالْكِتَابِ
Bind knowledge with writing
[Ref: Sunan Darimi (514); Shaykh Hussain salim asad said : إسناده ضعيف فيه عنعنة ابن جريج]
We find in Sunan Al-Tirmithi that:
حدثنا بندار حدثنا أبو أحمد الزبيري حدثنا سفيان عن عبد الرحمن بن الحارث عن حكيم بن حكيم بن عباد بن حنيف عن أبي أمامة بن سهل بن حنيف قال كتب عمر بن الخطاب إلى أبي عبيدة أن رسول الله صلى الله عليه وسلم قال الله ورسوله مولى من لا مولى له والخال وارث من لا وارث له
`Umar ibn al-Khattab (r.a) wrote to Abu Ubaida that the Prophet (pbuh) said that Allah and the Prophet (pbuh) are the mawla of those that do have a mawla, and that the uncle (from the mother’s side) is the heir if there is no heir.[Al-Tirmithi authenticated the narration.]
حَدَّثَنَا أَبُو خَيْثَمَةَ ثنا وَكِيعٌ، عَنْ أَبِي كِيرَانَ، قَالَ: ” سَمِعْتُ الشَّعْبِيَّ، قَالَ: «إِذَا سَمِعْتَ شَيْئًا فَاكْتُبْهُ وَلَوْ فِي الْحَائِطِ»
Abu Khaithama narrated to us, saying: Wakee’ reported to us from Abu Keeraan  that he said: I heard Ash-Sha’bee say: “If you hear anything, then write it down, even if you have to write it on a wall.”
[Ref: Kitaab al-`Ilm Abu Khaithama an-Nasa`ee (146);  Shaykh Albaanee said : His name is Al-Hasan Ibn ‘Uqbah Al-Muraadee. Ibn Ma’een declared him to be reliable and Abu Haatim said of him: “He was a shaikh, his hadeeth were written down.” The chain of narration linked to Ash-Sha’bee is saheeh]
-147حَدَّثَنَا أَبُو خَيْثَمَةَ ثنا وَكِيعٌ، ثنا أَبِي، عَنْ عَبْدِ اللَّهِ بْنِ حَنَشٍ، قَالَ: «لَقَدْ رَأَيْتُهُمْ يَكْتُبُونَ عَلَى أَكُفِّهِمْ بِالْقَصَبِ عِنْدَ الْبَرَاءِ»
Abu Khaithama narrated to us, saying: Wakee’ reported to us, saying: Ubay reported to us from ‘Abdullaah Ibn Hanash that he said: “I have indeed seen them (people) writing on their palms with stalk reeds in the presence of Al- Baraa’ (radyAllaahu ‘anhu).”
[Ref: Kitaab al-`Ilm Abu Khaithama an-Nasa`ee (147)]
Ibn Abi Mulayka (rahimahullah) said :
“I would see Mujahid with tablets asking ibn `Abbas about the Tafseer of the qur’an. Ibn `Abbas would say to him “write”. This continued until he asked him about the whole Tafseer
[Ref: Tafseer at-tabari 1/85]
There are many more, umpteen books and hundred thousands of pages that talk about this topic, but i believe this should suffice those who raise objections.