Islamic law is easy and does not require complex calculations or science

"We are an unlettered Ummah, we do not use astronomical counting or computation. The month is like this, and this, and this," he did three times, showing it as twenty-nine.  

عَنِ النَّبِيِّ ﷺ قَالَ إِنَّا أُمَّةٌ أُمِّيَّةٌ لاَ نَكْتُبُ وَلاَ نَحْسِبُ الشَّهْرُ هَكَذَا وَهَكَذَا وَهَكَذَا ثَلاَثًا حَتَّى ذَكَرَ تِسْعًا وَعِشْرِينَ  

The Prophet ﷺ said: The month consists of twenty-nine days, but do not fast till you sight it (the moon) and do not break your fast till you sight it. If the weather is cloudy, calculate it thirty days. When the twenty-ninth of Sha'ban came, Ibn Umar would send someone (who tried) to sight the moon for him. If it was sighted, then well and good; in case it was not sighted, and there was no cloud and dust before him (on the horizon), he would not keep fast the next day. If there appeared (on the horizon) before him cloud or dust, he would fast the following day. Ibn Umar would end his fasting alone with the people, and did not follow this calculation.  

قَالَ رَسُولُ اللَّهِ ﷺ إِنَّا أُمَّةٌ أُمِّيَّةٌ لاَ نَكْتُبُ وَلاَ نَحْسُبُ الشَّهْرُ هَكَذَا وَ هَكَذَا وَهَكَذَا وَخَنَسَ سُلَيْمَانُ أُصْبَعَهُ فِي الثَّالِثَةِ يَعْنِي تِسْعًا وَعِشْرِينَ وَثَلاَثِينَ  

[Machine] From the Prophet ﷺ, he said: "Indeed, we are an unlettered nation, we do not write nor calculate. And indeed, the month is like this and this and this, then it decreases one day in every third month."  

عَنِ النَّبِيِّ ﷺ أَنَّهُ قَالَ إِنَّا أُمَّةٌ أُمِّيَّةٌ لَا نَكْتُبُ وَلَا نَحْسُبُ وَإِنَّ الشَّهْرَ هَكَذَا وَهَكَذَا وَهَكَذَا ثُمَّ نَقَصَ وَاحِدَةً فِي الثَّالِثَةِ  

[Machine] From the Prophet ﷺ he said, "Indeed, we are an unlettered nation. We do not write nor calculate the month like this and like that until he mentioned twenty-nine. Ishaq said, and he gestured with his hand three times and held his thumb on the third."  

عَنِ النَّبِيِّ ﷺ قَالَ إِنَّا أُمَّةٌ أُمِّيَّةٌ لَا نَكْتُبُ وَلَا نَحْسُبُ الشَّهْرُ هَكَذَا وَهَكَذَا حَتَّى ذَكَرَ تِسْعًا وَعِشْرِينَ قَالَ إِسْحَاقُ وَطَبَّقَ يَدَيْهِ ثَلَاثَ مَرَّاتٍ وَحَبَسَ إِبْهَامَهُ فِي الثَّالِثَةِ  

he heard Ibn 'Umar narrate that the Prophet said; "We are an unlettered Ummah; we do not use computation. The month is like this, and this, and this," and he held down his thumb the last time. "And the month is like this, and this, and this," completing thirty. (Using translation from Nasāʾī 2141)  

عَنِ النَّبِيِّ ﷺ أَنَّهُ قَالَ إِنَّا أُمَّةٌ أُمِّيَّةٌ لَا نَكْتُبُ وَلَا نَحْسُبُ الشَّهْرُ هَكَذَا وَهَكَذَا وَهَكَذَا وَعَقَدَ الْإِبْهَامَ فِي الثَّالِثَةِ وَالشَّهْرُ هَكَذَا وَهَكَذَا وَهَكَذَا يَعْنِي تَمَامَ ثَلَاثِينَ  

"We are an unlettered Ummah, we do not use astronomical counting or computation. The month is like this, and this, and this," he did three times, showing it as twenty-nine. (Using translation from Nasāʾī 2140)   

عَنِ النَّبِيِّ ﷺ «إِنَّا أُمَّةٌ أُمِّيِّةٌ لَا نَكْتُبُ وَلَا نَحْسُبُ الشَّهْرُ كَذَا وَكَذَا» ثَلَاثًا حَتَّى ذَكَرَ تِسْعًا وَعِشْرِينَ  

"إِنَّا أمَّةٌ أمِّيَّةٌ، لا نَكْتب ولا نَحْسُبُ الشهر هكذا وهكذا وهكذا؛ وعقد الإِبهام في الثالثة والشَّهرُ هكذا وهكذا وهكذا. يعنى مرةً تسعةً وعشرين، ومرةً ثلاثين".