yeh spasht hai ki ganit ko siddhant banane wale aur samasya hal karne wale, dono tarah ke ganitagyon ki aavashyakta hoti hai.
It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers.
It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers.
ek ganitiya siddhant (proof) asal mein yeh dikhata hai ki kuch nishkarsh, jaise kisi sankhya ka aparimey (irrational) hona, kuch purv-manyataon (premises) se nikalte hain, jaise ki ganitiya aagaman (induction) ka siddhant. in purv-manyataon ki sarthakta ek bilkul alag vishay hai jise darshnikon par chhor dena hi behtar hai.
What a mathematical proof actually does is show that certain conclusions, such as the irrationality of, follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.
What a mathematical proof actually does is show that certain conclusions, such as the irrationality of, follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.
iske alawa, agar koi kisi samasya ko chunta hai, uspar akele mein kuch saal mehnat karta hai aur aakhirkar use hal kar leta hai, toh is baat ka khatra rehta hai ki, jab tak vah samasya bahut prasiddh na ho, use utna mahatvapurna nahi mana jayega.
Moreover, if one selects a problem, works on it in isolation for a few years and finally solves it, there is a danger, unless the problem is very famous, that it will no longer be regarded as all that significant.
Moreover, if one selects a problem, works on it in isolation for a few years and finally solves it, there is a danger, unless the problem is very famous, that it will no longer be regarded as all that significant.
ek aam ganitagya sakriy roop se upyogi banne ki koshish nahi karta. vyaktigat roop se ganitagya mukhya roop se mahatvakanksha aur bauddhik jigyasa ke kisi barik mel se prerit hote hain, samaj ko laabh pahunchane ki ichha se nahi, fir bhi, ek samuhik roop se ganit samaj ko laabh pahunchata hai.
A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society, nevertheless, mathematics as a whole does benefit society.
A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society, nevertheless, mathematics as a whole does benefit society.
bhale hi abhedya sankhyaen (prime numbers) nishchit niyamron se bani hoti hain, par fir bhi unhe dekhkar aisa lagta mano vah koi prayogik data ho.
Although the prime numbers are rigidly determined, they somehow feel like experimental data.
Although the prime numbers are rigidly determined, they somehow feel like experimental data.
yahan ek aisi cheez hai jo category-theorists ko bahut pasand aati hai: yeh aasan hai, par aisi aasan nahi jo bekaar ho.
Here is something Category-Theorists like: it is trivial, but not trivially trivial.
Here is something Category-Theorists like: it is trivial, but not trivially trivial.
kya hum bina apni kursi se uthe antariksh ya sthan ka vastavik gyan prapta kar sakte hain?
Can we have genuine knowledge of space without ever leaving our armchairs?
Can we have genuine knowledge of space without ever leaving our armchairs?