Highly complex proofs and implications of such proofs.

نویسنده

  • Michael Aschbacher
چکیده

Conventional wisdom says the ideal proof should be short, simple, and elegant. However there are now examples of very long, complicated proofs, and as mathematics continues to mature, more examples are likely to appear. Such proofs raise various issues. For example it is impossible to write out a very long and complicated argument without error, so is such a 'proof' really a proof? What conditions make complex proofs necessary, possible, and of interest? Is the mathematics involved in dealing with information rich problems qualitatively different from more traditional mathematics?

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Quranic way of presenting proofs for God`s existence

Regardless of the view of those philosophers like Plantinga who see no need in any proof for the existence of God, scholars have presented four views on Quranic way of proving the existence of God including demonstration, awakening, implication and clear demonstration. Describing and criticizing the views in detail, the author has viewed differently. God has regarded the level of the addressee`...

متن کامل

On the pointfree counterpart of the local definition of classical continuous maps

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

دوره 363 1835  شماره 

صفحات  -

تاریخ انتشار 2005