Archimedes- "Mathematics reveals its secret only to those who approach it with pure love, for its own beauty"
Formula:
In The Quadrature of the Parabola, Archimedes proved that the area enclosed by a parabola and a straight line is 4/3 times the area of a corresponding inscribed triangle as shown in the figure at right. He expressed the solution to the problem as an infinite geometric series with the common ratio 1/4:

${\displaystyle \sum _{n=0}^{\infty }4^{-n}=1+4^{-1}+4^{-2}+4^{-3}+\cdots ={4 \over 3}.\;}$Archimedes of Syracuse (/ˌɑːkɪˈmiːdiːz/; Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.Other mathematical achievements include deriving an accurate approximation of pi, defining and investigating the spiral bearing his name, and creating a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, which Archimedes had requested to be placed on his tomb, representing his mathematical discoveries.

David Hilbert-"Mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street."

Formula: One of Hilbert's formula in Axioms of Numbers>>
 From the primitive variables we derive further kinds of variables by applying logical connectives to the propositions associated with the primitive variables, for example, to Z. The variables thus defined are called variable-sorts, and the propositions defining them are called sort-propositions; for each of these a new particular sign is introduced. Thus the formula

F(f) ≡ ∀(a)(Z(a) - Z(f (a)))

David Hilbert (German: [ˈdaːvɪt ˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.
Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.

Godfrey Harold "G.H. Hardy"-"The mathematicians patterns... Must be beautiful... beauty is the first test:  there is no permanent place for ugly mathematics." 

 

Formula: The allele frequencies at each generation are obtained by pooling together the alleles from each genotype of the same generation according to the expected contribution from the homozygote and heterozygote genotypes, which are 1 and 1/2, respectively:

${\displaystyle f_{t}({\text{A}})=f_{t}({\text{AA}})+{\frac {1}{2}}f_{t}({\text{Aa}})}$

Godfrey Harold "G. H." Hardy FRS(7 February 1877 – 1 December 1947)was an English mathematician, known for his achievements in number theory and mathematical analysis. Hardy is remembered also for his 1940 essay on the aesthetics of mathematics, A Mathematician's Apology, and for mentoring the brilliant.Indian mathematician Srinivasa Ramanujan.G. H. Hardy is usually known by those outside the field of mathematics for his essay from 1940 on the aesthetics of mathematics, A Mathematician's Apology, which is often considered one of the best insights into the mind of a working mathematician written for the layman.Hardy is credited with reforming British mathematics by bringing rigour into it, which was previously a characteristic of French, Swiss and German mathematics. British mathematicians had remained largely in the tradition of applied mathematics, in thrall to the reputation of Isaac Newton (see Cambridge Mathematical Tripos). Hardy was more in tune with the cours d'analyse methods dominant in France, and aggressively promoted his conception of pure mathematics, in particular against the hydrodynamics which was an important part of Cambridge mathematics.Hardy's collected papers have been published in seven volumes by Oxford University Press.