Quantitative Finance: What It Is & How It Works 2026

What Is Quantitative Finance?

Quantitative finance is the application of mathematical models, statistical methods, and computational techniques to financial problems. It covers everything from pricing a complex derivative to building an algorithm that trades thousands of instruments simultaneously - any situation where rigorous, numbers-driven analysis replaces intuition or guesswork.

The field sits at the intersection of mathematics, computer science, and finance. A quantitative analyst (quant) might spend their morning deriving the partial differential equation that governs the price of an exotic option, their afternoon coding a Monte Carlo simulation to verify the result, and their evening calibrating the model to live market data. The unifying thread is precision. Every assumption is stated explicitly, every model is tested against data, and every risk is quantified.

Quantitative finance emerged as a distinct discipline in the early 1970s, when Fischer Black, Myron Scholes, and Robert Merton published their options pricing framework. Before that, derivatives pricing was largely ad hoc. After Black-Scholes, it became a science. The field has expanded enormously since then - absorbing ideas from physics, engineering, machine learning, and information theory - but the core mission hasn't changed: use mathematics to understand financial markets, price financial instruments, measure risk, and make better decisions.

In 2026, quantitative methods dominate modern finance. Systematic trading strategies account for over 60% of equity volume in developed markets. Banks price trillions of pounds' worth of derivatives using quant models daily. Asset managers use factor models and optimisation algorithms to construct portfolios for pension funds and sovereign wealth funds. Insurance companies model catastrophic risk with stochastic simulations. Quantitative finance isn't a niche specialism anymore - it's the operating system of global capital markets.

If you're interested in the people who do this work, our guide to what a quant is breaks down the roles in detail.

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The Main Areas of Quantitative Finance

Quantitative finance is broad. It encompasses several distinct sub-fields, each with its own models, tools, and career paths. Here are the core areas.

Derivatives Pricing

This is where quantitative finance began. Derivatives pricing is the problem of determining the fair value of financial contracts whose payoff depends on an underlying asset - options, swaps, futures, and structured products.

The fundamental approach is risk-neutral pricing: the idea that in a complete, arbitrage-free market, the price of any derivative equals the discounted expected value of its payoff under a special probability measure. In practice, this translates to solving partial differential equations (the Black-Scholes PDE and its extensions), building binomial and trinomial trees, or running Monte Carlo simulations for instruments too complex for closed-form solutions.

Derivatives pricing quants work primarily at investment banks, where they develop and maintain the models used to price and hedge the bank's trading book. They also work at hedge funds that trade options and volatility, and at insurance companies pricing embedded guarantees.

Risk Management

Risk management is about measuring, monitoring, and controlling exposure to financial loss. Quantitative risk managers build models that answer questions like: What's the maximum we could lose in a day with 99% confidence? How would our portfolio perform if interest rates rose 200 basis points? What's our exposure to a credit downgrade of our largest counterparty?

Key tools include Value at Risk (VaR), Expected Shortfall, stress testing, scenario analysis, and sensitivity analysis (the Greeks for derivatives portfolios). Since the 2008 financial crisis, regulators have imposed increasingly detailed quantitative requirements on banks and insurers - Basel III and IV for banks, Solvency II for insurers - making risk quants essential to regulatory compliance.

Algorithmic and Quantitative Trading

This is where quantitative methods are used to generate trading profits directly. Quant traders and researchers build models that identify patterns in market data, generate trading signals, and execute trades systematically.

Strategies span a wide range of time horizons and approaches: high-frequency market making measured in microseconds, statistical arbitrage with holding periods of days, momentum and mean reversion strategies running over weeks, and factor-based approaches operating over months. The common thread is that decisions are driven by data and models rather than human judgement. Our quant trading strategies guide covers the major strategy families in depth.

Portfolio Construction and Optimisation

Portfolio construction is the problem of deciding how to allocate capital across assets to achieve the best risk-adjusted returns. The foundation is Markowitz's mean-variance optimisation, but modern approaches go well beyond it - incorporating transaction costs, constraints on gearing and sector exposure, factor models, and shrinkage estimation techniques that account for uncertainty in expected returns.

Quantitative portfolio managers work at asset managers, pension funds, and hedge funds. The maths involves linear algebra (covariance matrices, eigenvector decomposition), optimisation theory (convex and non-convex programming), and statistics (shrinkage estimators, Bayesian methods).

Financial Engineering

Financial engineering is the design, pricing, and hedging of bespoke financial products - structured notes, credit derivatives, exotic options, insurance-linked securities, and other instruments created to meet specific risk-transfer needs. It sits at the intersection of derivatives pricing and product design.

Financial engineers need deep knowledge of stochastic calculus, numerical methods, and market conventions. They work primarily at investment banks and structured products desks. If you're considering a formal programme in this area, our financial engineering degree guide covers the leading courses.

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The Mathematics of Quantitative Finance

Mathematics is the language of quantitative finance. You can't work in the field without genuine fluency in several branches of maths, though the exact mix depends on your specialisation.

Probability and Statistics

The foundation of everything. Financial markets are inherently random, so virtually every model in quant finance is probabilistic. You need to be comfortable with probability distributions, conditional expectation, the law of large numbers, the central limit theorem, Bayesian inference, hypothesis testing, regression analysis, time series modelling, and maximum likelihood estimation.

In practice, you'll spend as much time thinking about the statistical properties of your data - stationarity, autocorrelation, heteroscedasticity, regime changes - as you will building models. A model is only as good as the data and assumptions that feed it.

Stochastic Calculus

Stochastic calculus is the mathematical framework for modelling random processes that evolve continuously over time. It's essential for derivatives pricing and any work involving continuous-time models.

The key concepts are Brownian motion (the mathematical model for random stock price movements), Ito's lemma (the chain rule for stochastic processes), stochastic differential equations, and the Girsanov theorem (which allows you to change between probability measures). If you work in derivatives, you'll use stochastic calculus daily. If you work in statistical trading, you may rarely touch it directly.

Linear Algebra

Linear algebra underpins portfolio theory, factor models, principal component analysis, and machine learning. You need fluency with matrix operations, eigenvalue decomposition, singular value decomposition, and least-squares regression. When a portfolio manager talks about factor exposures or a risk manager discusses correlation matrices, they're speaking linear algebra.

Optimisation

Almost every decision in quantitative finance can be framed as an optimisation problem: maximise returns subject to risk constraints, minimise tracking error, find the parameters that best fit a model to data. You need to understand convex optimisation, Lagrange multipliers, gradient descent, and linear and quadratic programming. For more complex problems, familiarity with numerical optimisation methods and their convergence properties is important.

Partial Differential Equations

The Black-Scholes equation is a PDE. So are the equations governing many other pricing models. If you work in derivatives, you'll need to understand how to set up, solve (analytically where possible and numerically where not), and interpret PDEs. Finite difference methods are the workhorse numerical technique for solving pricing PDEs.

Numerical Methods

Many problems in quantitative finance don't have closed-form solutions. Monte Carlo simulation, finite difference methods, binomial trees, and numerical integration are the standard toolkit for approximating answers to problems that can't be solved on paper. Understanding convergence rates, variance reduction techniques, and the trade-offs between speed and accuracy is essential.

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Key Models and Theories

Quantitative finance is built on a collection of models and theoretical frameworks that have shaped how markets operate. Here are the most important ones.

The Black-Scholes-Merton Model

Published in 1973, the Black-Scholes model provides a closed-form formula for pricing European options. It assumes that stock prices follow geometric Brownian motion with constant volatility - assumptions that are provably wrong in real markets, but useful enough that the model remains the starting point for all options pricing. Every subsequent options model is, in some sense, a correction to Black-Scholes.

The Capital Asset Pricing Model (CAPM)

CAPM, developed by William Sharpe in the 1960s, states that the expected return of an asset is determined by its beta - its sensitivity to the overall market. Assets that move more with the market should offer higher expected returns as compensation for bearing systematic risk. CAPM is theoretically elegant but empirically limited; it fails to explain many observed patterns in returns, which led to multi-factor models.

The Fama-French Factor Model

Eugene Fama and Kenneth French extended CAPM by adding two factors beyond the market: size (small stocks tend to outperform large stocks) and value (cheap stocks tend to outperform expensive ones). The three-factor model, later expanded to five factors including profitability and investment, explains much more of the cross-section of stock returns than CAPM alone. It forms the intellectual basis for systematic factor investing.

Arbitrage Pricing Theory (APT)

Stephen Ross's APT, introduced in 1976, takes a different approach from CAPM. Rather than specifying what the risk factors are, APT says that expected returns are a linear function of exposure to multiple systematic risk factors - without saying what those factors must be. It's more flexible than CAPM but less prescriptive. In practice, APT provides the theoretical justification for multi-factor models.

GARCH Models

Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models, developed by Tim Bollerslev in 1986, capture a key empirical feature of financial markets: volatility clustering. Periods of high volatility tend to be followed by high volatility, and calm periods by more calm. GARCH models are widely used for volatility forecasting, risk management, and options pricing where constant-volatility assumptions are inadequate.

Value at Risk (VaR)

VaR isn't a single model but a risk measurement framework. It answers the question: What's the maximum loss over a given time period at a given confidence level? A one-day 99% VaR of £5 million means there's a 1% chance of losing more than £5 million in a single day. VaR is the standard risk metric used by banks and regulators, though it has well-known limitations - particularly its failure to describe the size of losses in the tail.

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Quant Finance vs Financial Engineering vs Data Science

These three fields overlap significantly, and the boundaries can be blurry. Here's how they differ in practice.

Quantitative finance is the broadest term. It's the umbrella that covers all applications of quantitative methods to finance. Derivatives pricing, risk management, portfolio construction, and trading all fall under it.

Financial engineering is a subset of quantitative finance focused on product design. A financial engineer creates the structured note or exotic derivative; a quant prices and hedges it. In practice, the skills overlap heavily, and many professionals move between the two.

Data science in finance is newer and reflects the increasing role of machine learning and alternative data in financial decision-making. A data scientist in finance might build an NLP model that reads earnings call transcripts to predict stock movements, or develop a deep learning system that forecasts volatility from order flow data. The maths tends to emphasise statistical learning theory over stochastic calculus.

The boundaries are dissolving. In 2026, a quant researcher at a hedge fund uses machine learning alongside traditional statistical models. A derivatives quant at a bank writes production-quality code. The most effective practitioners draw from all three traditions.

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Who Works in Quantitative Finance?

Quantitative finance professionals work across the financial industry. The nature of the work, the compensation, and the culture vary significantly by employer type.

Investment Banks

Banks are the traditional home of quantitative finance. Quants at banks price derivatives, build risk models, develop execution algorithms, and validate models for regulatory compliance. Goldman Sachs, J.P. Morgan, Morgan Stanley, Barclays, and Deutsche Bank all run large quant teams. Bank quant work tends to be more structured and regulatory-driven than at hedge funds, with clearer hierarchies and more formal processes.

Hedge Funds

Quantitative hedge funds use systematic models to trade financial markets and generate returns for investors. Renaissance Technologies, Two Sigma, D.E. Shaw, Citadel, Man AHL, and Winton Group are among the most prominent. Hedge fund quants focus on alpha generation - finding signals that predict returns - and the work is more research-oriented and entrepreneurial than at banks. Compensation is higher but more variable, tied to fund performance.

Proprietary Trading Firms

Prop firms trade their own capital with no external investors. Jane Street, Optiver, IMC Trading, Jump Trading, and Virtu Financial are major players. These firms specialise in market making and short-horizon strategies, requiring extremely fast systems and strong quantitative reasoning. They tend to offer the highest starting compensation for junior hires.

Asset Managers

Large asset managers like BlackRock, Vanguard, and Dimensional Fund Advisors use quantitative methods for portfolio construction, factor investing, and index tracking. The time horizons are longer, the portfolios are larger, and the focus is on systematic allocation rather than short-term trading.

Insurance Companies

Actuarial science and quantitative finance overlap significantly. Insurance quants model catastrophic risk, price complex insurance-linked securities, and manage the investment portfolios that back insurance liabilities. Solvency II regulations in the UK and Europe require sophisticated quantitative modelling.

Fintech and Technology

A growing number of quants work at fintech companies and technology firms applying quantitative methods to lending, payments, crypto markets, and retail investing platforms. These roles often emphasise machine learning and software engineering alongside financial modelling.

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Career Paths in Quantitative Finance

The field offers several distinct career tracks, each requiring a different mix of skills. Here's what each looks like.

Quantitative Analyst (Pricing/Modelling Quant)

The classic quant role. You develop, implement, and maintain the mathematical models used to price financial instruments and manage risk. Most commonly found at investment banks, working on derivatives desks. The work is mathematically intense, requiring strong stochastic calculus and PDE skills alongside production-quality coding.

Quantitative Researcher

You develop trading strategies by analysing data, building statistical models, and testing hypotheses. This is the core research role at hedge funds and prop firms. The emphasis is on finding signals - patterns in data that predict future returns. Strong statistics, machine learning, and research methodology skills are essential. Our guide to becoming a quant covers the preparation path in detail.

Quantitative Trader

You manage the deployment of quantitative strategies in live markets, making decisions about position sizing, risk limits, and when to override model signals. Some quant traders also do their own research. This role requires deep market knowledge alongside quantitative skills, and strong performance under pressure.

Quantitative Developer (Quant Dev)

You build the software infrastructure that quants depend on - pricing libraries, backtesting frameworks, execution systems, risk engines, and data pipelines. This is a software engineering role with a quantitative twist. Strong C++, Python, and systems design skills are essential. Quant devs don't typically build models themselves, but they need to understand them well enough to implement them correctly.

Risk Quant

You build and maintain models for measuring and managing financial risk - VaR models, stress testing frameworks, counterparty credit risk models, and regulatory capital calculations. Risk quants work primarily at banks and insurers, often in close collaboration with regulators.

Model Validator

You independently assess the models built by other quants. Are the assumptions reasonable? Is the implementation correct? Does the model perform as expected under stress conditions? Model validation is a regulatory requirement for banks, making it a stable and growing career path.

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Education and Qualifications

Undergraduate Degrees

A quantitative undergraduate degree is the baseline requirement for most quant roles. Mathematics, statistics, physics, computer science, and engineering are the most common backgrounds. The specific subject matters less than the depth of mathematical training. A physics graduate who's comfortable with differential equations and programming is well prepared. A business graduate with only introductory statistics will struggle.

Master's Degrees

Many quant roles require or strongly prefer a master's degree. The most relevant programmes include:

• Financial Engineering / Mathematical Finance - programmes at Imperial College, UCL, Oxford, ETH Zurich, and CMU are specifically designed for quant careers
• Statistics / Machine Learning - increasingly valuable as the field incorporates more data science methods
• Applied Mathematics / Computational Science - strong preparation for modelling roles

PhDs

For research-focused roles at top hedge funds and certain bank quant positions, a PhD is the norm. Physics and mathematics PhDs are most common, followed by statistics, computer science, and electrical engineering. The PhD itself is less about the specific topic and more about the research skills it develops - the ability to formulate problems precisely, work independently, and produce original results.

Professional Qualifications

The Certificate in Quantitative Finance (CQF) is the most widely recognised professional qualification specifically for quant finance. It covers derivatives pricing, risk models, numerical methods, and data science, and can be completed part-time alongside work.

The CFA (Chartered Financial Analyst) is valuable for portfolio management and asset management roles but less directly relevant for derivatives or trading quant roles.

Self-Study Paths

It's entirely possible to build strong quant skills through self-study, particularly for the programming and market knowledge components. Start with solid textbooks (see the resources section below), work through problems, and build projects that demonstrate your skills. What you can't easily replicate through self-study is the depth of mathematical training that a strong university programme provides - if your maths foundation is thin, formal education is probably necessary.

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The Evolution of Quantitative Finance

Quantitative finance has gone through several distinct phases, each driven by new ideas and new technology.

1973 - 1990: The Theoretical Foundations

The publication of the Black-Scholes model in 1973 marks the birth of modern quantitative finance. Through the late 1970s and 1980s, academics and practitioners developed the theoretical frameworks that still underpin the field: risk-neutral pricing, term structure models (Vasicek, Cox-Ingersoll-Ross, Heath-Jarrow-Morton), credit risk models, and the mathematical foundations of portfolio theory.

During this period, quants were relatively rare in finance. Most worked at investment banks, building models for the rapidly growing derivatives market. The work was highly mathematical, done on paper and mainframe computers.

1990 - 2007: Expansion and Sophistication

The 1990s saw quantitative methods spread beyond derivatives into risk management, trading, and portfolio management. The adoption of Value at Risk as a standard risk metric, the growth of mortgage-backed securities, and the explosion of credit derivatives all created demand for quants. Hedge funds like D.E. Shaw (founded 1988) and Renaissance Technologies (founded 1982, but achieving fame in the 1990s) demonstrated that systematic, model-driven trading could produce extraordinary returns.

Computing power grew rapidly, enabling more complex models and larger-scale simulations. Monte Carlo methods became practical for pricing exotic derivatives. Statistical arbitrage emerged as a viable strategy as electronic markets provided the data and execution speed it required.

2008 - 2015: Crisis and Recalibration

The 2008 financial crisis exposed significant weaknesses in quantitative models. VaR models had underestimated tail risk. Correlation assumptions in CDO pricing proved catastrophically wrong. Models that assumed liquid, functioning markets broke down when liquidity evaporated.

The response was a major recalibration. Regulators imposed stricter model requirements (Basel III, stressed VaR, CVA/DVA adjustments). The industry moved toward models that better captured tail risk, counterparty credit risk, and liquidity risk. Risk management quants became more prominent. Model validation became a regulatory requirement.

2016 - Present: Machine Learning and Alternative Data

The current era is defined by the integration of machine learning into quantitative finance. Techniques from deep learning, natural language processing, and reinforcement learning are being applied to trading signal generation, risk modelling, and execution optimisation.

Alternative data - satellite imagery, web scraping, credit card transactions, social media sentiment - has become a major source of alpha for systematic funds. The quant researcher of 2026 is as likely to be training a neural network on earnings call transcripts as solving a stochastic differential equation.

At the same time, the traditional mathematical core remains essential. Machine learning models still need to be validated, understood, and embedded within sound risk management frameworks. The best practitioners combine classical quant techniques with modern computational methods.

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Top Employers in Quantitative Finance (2026)

The most sought-after employers span hedge funds, prop firms, and banks.

Quantitative Hedge Funds: Renaissance Technologies, Two Sigma, D.E. Shaw, Citadel, Man AHL, Winton Group, AQR Capital Management, Millennium Management, Point72, Balyasny Asset Management.

Proprietary Trading Firms: Jane Street, Optiver, IMC Trading, Jump Trading, Virtu Financial, Flow Traders, Hudson River Trading, SIG (Susquehanna), DRW, Five Rings Capital.

Investment Banks (Quant Divisions): Goldman Sachs (Strats), J.P. Morgan, Morgan Stanley, Barclays, Deutsche Bank, UBS, BNP Paribas, Citigroup.

Asset Managers: BlackRock, Vanguard, Dimensional Fund Advisors, AQR, Bridgewater Associates.

UK-Specific: London is Europe's largest hub for quantitative finance. Major UK-based or London-headquartered quant employers include Man Group, Winton, GSA Capital, Aspect Capital, Marshall Wace, G-Research, and Qube Research & Technologies (QRT).

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Books and Resources

The best way to build a foundation in quantitative finance is through a combination of textbooks and hands-on practice. Here are the essential reads.

For Beginners:

• Paul Wilmott, Paul Wilmott Introduces Quantitative Finance - the most accessible broad introduction to the field
• John Hull, Options, Futures, and Other Derivatives - the standard reference for derivatives markets and pricing

For Stochastic Calculus and Derivatives Pricing:

• Steven Shreve, Stochastic Calculus for Finance I & II - rigorous but readable treatment of the mathematics
• Mark Joshi, The Concepts and Practice of Mathematical Finance - excellent for bridging theory and practice

For Risk Management:

• John Hull, Risk Management and Financial Institutions - comprehensive coverage of risk models and regulation
• Philippe Jorion, Value at Risk - the standard reference for VaR methodologies

For Trading and Strategies:

• Ernest Chan, Quantitative Trading - practical introduction to building and backtesting systematic strategies
• Marcos Lopez de Prado, Advances in Financial Machine Learning - essential for anyone applying ML to finance

For Interview Preparation:

• Mark Joshi, Quant Job Interview Questions and Answers - the standard interview prep book for quant roles
• Xinfeng Zhou, A Practical Guide to Quantitative Finance Interviews (the "Green Book")

For a more complete list, see our recommended books for quant finance.

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Frequently Asked Questions

Is quantitative finance hard?

Yes - it's one of the most intellectually demanding fields in finance. The mathematical prerequisites are substantial: you need genuine fluency in probability, statistics, calculus, and linear algebra at a minimum, with stochastic calculus required for derivatives-focused roles. The programming demands are high too - you're expected to write production-quality code, not just scripts. And the problems themselves are genuinely difficult. You're modelling systems with millions of interacting participants, incomplete information, and non-stationary dynamics. That said, "hard" doesn't mean "impossible." If you have a strong STEM background and enjoy mathematical problem-solving, the learning curve is steep but manageable.

What salary can you expect in quantitative finance?

Compensation varies significantly by role, employer, and seniority. In London in 2026, graduate quant analysts at investment banks typically earn £60,000 to £90,000 base salary, with total compensation of £80,000 to £130,000 including bonuses. At hedge funds and prop firms, first-year total compensation ranges from £100,000 to £300,000 or more - Jane Street, Citadel, and similar firms pay at the top end. Senior quants with 10+ years of experience can earn £300,000 to over £1 million annually, with portfolio managers and senior researchers at top hedge funds earning well above that. Quant developers command slightly lower compensation than researchers and traders but still well above typical tech industry rates.

Do you need a PhD to work in quantitative finance?

Not always, but it depends on the role. Research positions at top hedge funds (Renaissance, Two Sigma, D.E. Shaw) strongly prefer PhDs, and for many of these roles a doctorate is effectively required. Derivatives pricing and modelling roles at banks often require a master's or PhD. However, quant developer roles, trading roles at prop firms, and some risk quant positions are accessible with a strong master's degree or even a bachelor's from a top university. The trend in 2026 is toward valuing demonstrated skill - through projects, competitions, and work experience - alongside formal credentials.

What's the difference between quantitative finance and quantitative trading?

Quantitative finance is the broader field. It encompasses all applications of mathematical and statistical methods to financial problems - derivatives pricing, risk management, portfolio construction, insurance modelling, and trading. Quantitative trading is a subset that specifically uses these methods to make trading decisions and generate profits from market activity. A quant building risk models at a bank is working in quantitative finance but not in quantitative trading. A researcher developing alpha signals at a hedge fund is working in both. Think of quantitative finance as the discipline and quantitative trading as one of its applications.

Can you transition into quantitative finance from another career?

Yes, though the difficulty depends on your starting point. Career changers from physics, engineering, or computer science have the easiest path - the mathematical and programming skills transfer directly, and you mainly need to learn the financial domain. Transitions from less quantitative fields are harder and usually require formal retraining, such as a master's in financial engineering or the CQF. The most common successful transitions involve people who are already strong in maths and programming and simply need to redirect those skills toward finance. If you lack quantitative training entirely, you'll need to invest one to two years in building that foundation before you're competitive.

What programming languages are used in quantitative finance?

Python is the dominant language across quantitative finance in 2026. It's used for research, data analysis, prototyping, backtesting, and increasingly for production systems. C++ remains essential for performance-critical applications - execution engines, real-time risk systems, and high-frequency trading infrastructure. R still appears in some academic-leaning firms for statistical analysis. SQL is expected everywhere for database queries. MATLAB has declined but persists at some banks and insurance firms. Newer entrants include Rust (as a safer alternative to C++ for systems work) and Julia (for numerical computing). If you're entering the field, start with Python and add C++ when you need it.