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This is a prime number whose decimal digits are all ones. It has 317 ones. It's not the world record. The number with 1031 ones is also known to be prime!

Even larger guys like this are suspected to be prime. Are there infinitely many? Mathematicians believe so, but they can't prove it. Why do they believe it? The main reason is that we have an estimate of the "probability" that a number with some number of digits is prime, which we can use to guess the answer to this puzzle.

Of course the whole idea of "probability" is a bit weird here. A number is either prime or not: the math gods do not flip coins to decide which numbers are prime!

Nonetheless, treating primes as if they were random turns out to be useful. Mathematicians have made many guesses using this idea, and then proved these guesses are right, using a lot of extra work.

Of course it's subtle. If I wrote down a number with 317 twos in its decimal expansion, you'd instantly know it's not prime - because it would be even. So when we talk about the probability that a number is prime, this must depend on what else we know about that number.

In the European Congress of Mathematics, a number theorist named James Maynard just announced that he's proved something cool. There are infinitely many prime numbers with no sevens in their decimal expansion. And his proof works equally well for any other number: there infinitely many primes without 1 as a digit, or 2 as a digit, or 3, or 4, or 5, and so on.
@infinitymath

Visual explanations of convolution
@infinitymath

Visual explanations of convolution
@infinitymath

The line integral over a scalar field f can be thought of as the area under the curve C along a surface z = f(x,y), described by the field.
@infinitymath

@infinitymath
Saharon Shelah is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey.

👆👆👆👆👆👆Saharon Shelah
According to the list of Shelah's papers, he had published 1044 mathematical papers up to 2014 (including joint papers with over 220 co-authors). His main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory.

In model theory, he developed classification theory, which led him to a solution of Morley's problem. In set theory, he discovered the notion of proper forcing, an important tool in iterated forcing arguments. With PCF theory, he showed that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the continuum hypothesis), there are still highly nontrivial ZFC theorems about cardinal exponentiation. Shelah constructed a Kurosh monster, an uncountable group for which every proper subgroup is countable. He showed that Whitehead's problem is independent of ZFC. He gave the first primitive recursive upper bound to van der Waerden's numbers V(C,N). He extended Arrow's impossibility theorem on voting systems.
@infinitymath

@infinitymath
About Shelah 👆👆👆👆(quote from Anatoly Vorobey):
I took his advanced course in set theory once, a long time ago. It was the closest I've ever come in my life to feeling that I've encountered not just someone much smarter than me, but a truly superior intellect from a whole different level. His atomic inferential step was unbelievably wide - that is, he (genuinely and humbly, without any attempt at showing-off) saw as an immediate consequence something it took a hard effort of several minutes for others to work through, again and again. It was incredible to watch, and I've never seen anything like that with any other mathematician.

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The exponential function e^z can be defined as the limit of (1 + z/N)^N, as N approaches infinity, and thus e^{iπ} is the limit of (1 +iπ/N)^N. In this animation N takes various increasing values from 1 to 100. The computation of (1 + iπ/N)^N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 +iπ/N)^N. It can be seen that as N gets larger (1 +iπ/N)^N approaches a limit of −1.
@infinitymath

Animation of a linear Bézier curve, t in [0,1]
@infinitymath

Animation of a quadratic Bézier curve, t in [0,1]
@infinitymath

Animation of a cubic Bézier curve, t in [0,1]
@infinitymath

Animation of a quartic Bézier curve, t in [0,1]
@infinitymath

🎓 دانشگاه علم و صنعت ایران، میزبان چهلمین مسابقه‌ ریاضی دانشجویی ایران با حضور وزير علوم و شخصيت هاي علمي و سياسي
✅ چهلمین مسابقه ریاضی دانشجویی ایران از تاریخ 3 الی 6 شهریور 1395 با رقابت بین 35 تیم دانشجویی از بین دانشجویان نخبه ریاضی از دانشگاههای سراسر کشور با میزبانی دانشگاه علم و صنعت ایران و همکاری انجمن ریاضی کشور در دانشکده ریاضی برگزار خواهد شد.
✅ این مسابقه در مواد «آنالیز ریاضی و توابع مختلط»، «جبر و جبر خطی» و «ریاضیات عمومی، ریاضیات گسسته و ترکیبیات، نظریه اعداد، احتمال» برگزار می شود. یک نفر از اعضای هیات علمی دانشگاه به عنوان سرپرست و حداکثر پنج نفر از دانشجویان دوره کارشناسی علوم ریاضی هر دانشگاه به عنوان تیم در مسابقات شرکت دارند.
پس از پذیرش تیمهای شرکت کننده، آزمونها در روزهای 3 و 4 شهریورماه از ساعت 9 صبح آغاز خواهد شد و تا ساعت 13 ادامه خواهد داشت. پس از برگزاری هر آزمون، کمیته علمی مسابقه اقدام به تصححیح اوراق خواهد نمود. شایان ذکر است کمیته علمی و داوران این مسابقه از نخبگان ریاضی کشور می باشند.
✅ مراسم اختتامیه روز شنبه ششم شهریورماه، از ساعت 9 صبح در مجتمع امام خمینی (ره) برگزار خواهد شد. از دکتر فرهادی (وزیر علوم، تحقیقات و فناوری)، دکتر ستاری (معاون علمی ریاست جمهوری)، سفیر کشور کره جنوبی، اعضای هیات رئیسه دانشگاه، هیات رئیسه انجمن ریاضی ایران و چندین شخصیت علمی بارز کشور برای شرکت در مراسم اختتامیه و توزیع مدالهای این مسابقه دعوت به عمل آمده است.
✅ گفتنی است این مسابقه از دیدگاه بین المللی دارای اعتبار بسیار زیادی است و نفرات برگزیده آن بسیار مورد توجه محافل علمی و دانشگاههای معتبر داخل و خارج کشور هستند.
@qomat



@INFINITYMATH

30 ثانیه به این تصویر نگاه کنید بعد به کف دستتون نگاه کنید😳😐
@infinitymath

Dear Iranian Mathematicians,

The following Telegram group is founded at the request of Iranian Association for Logic (IAL) administrative board in order to make the circulation of logic-related news in Iran easier and faster. A selection of the shared posts in this group will appear in the IAL News Bulletin periodically. Read more about us here:

http://irlogic.org/

http://alidaghighi.org/blog/an-online-national-forum-for-iranian-logicians/

We sincerely invite all those graduate students and professors whose area of research is related to any branch of mathematical or philosophical logic to join the other Iranian logicians in this academic group.

Please note that our group is a professional academic forum for logicians and those who have some strong interest in logic. Thus all new members need to let us know their full name, academic affiliation and research area in logic, mathematics or philosophy after joining the group. The information will be shared with your other colleagues in the IAL group in order to make it easier for them to know you and your research field.

Please feel free to contact us via @alisadeghdaghighi if you have any questions. Also please let your logician friends and students know about IAL group.

Best Regards
Ali Sadegh Daghighi
Moderator at IAL Group
Editor at IAL News Bulletin
Amirkabir University of Technology

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Invitation link of the main IAL group (for sharing announcements and news):

https://telegram.me/joinchat/CHCYWj-iwl9AjSGUDR9L3w

Invitation link of our associated chatroom (for free discussions and asking questions):

https://telegram.me/joinchat/CHCYWj681dAckOj-rGtcVQ

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فردا آغاز میشود....
بزرگترین گروهمایی ریاضیاتی کشور....
ریاضیدانان، اساتید و دانشجویان ریاضی کشور ....
@infinitymath

راهنملی رسیدن به دانشگاه خوارزمی کرج .....
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برنامه ارائه های مقاله ها و فهرست پوستر های پذیرفته شده ....
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